# relevant packages
devtools::install_github("tdienlin/td@v0.0.2.6")
required <- c("GGally", "ggplot2", "lavaan", "lme4", "magrittr", 
              "MissMech", # attention: pkg is obsolete, needs to be installed manually
              "papaja", "psych", "pwr", "MVN", "semTools", 
              "sjstats", "tidyverse", "td")

# load required libraries
lapply(required, function(x) library(x, character.only = T))

load("data/workspace.RData") 

In what follows, we report the results of additional analyses that were also calculated. For example, for each measure we also report exploratory factor analyses, first order model solutions, and unconstrained solutions to estimate longitudinal invariance.

1 Measures

1.1 Concerns about online privacy

1.1.1 EFA

# set-up
no <- 0
name <- "pri_con"
d_tmp <- select(d_wide, contains(paste0("t1_", name)), -contains("_m"), -contains("_fs"))
model <- fa.parallel(d_tmp, fa = "fa", fm = "ml")

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA
factan <- fa(d_tmp, fm = "ml", nfactors = model$nfact, rotate = "promax")
print(factan, sort = TRUE, cut = 0.3)
## Factor Analysis using method =  ml
## Call: fa(r = d_tmp, nfactors = model$nfact, rotate = "promax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
##               item   ML2   ML1   ML3   h2   u2 com
## t1_pri_con_03    3  0.84             0.65 0.35 1.1
## t1_pri_con_02    2  0.83             0.62 0.38 1.1
## t1_pri_con_05    5  0.57             0.52 0.48 1.3
## t1_pri_con_04    4  0.53             0.65 0.35 1.5
## t1_pri_con_01    1  0.36             0.45 0.55 2.0
## t1_pri_con_09    9        0.89       0.74 0.26 1.1
## t1_pri_con_08    8        0.86       0.73 0.27 1.1
## t1_pri_con_07    7        0.60  0.37 0.70 0.30 1.7
## t1_pri_con_06    6              0.72 0.73 0.27 1.1
## 
##                        ML2  ML1  ML3
## SS loadings           2.40 2.31 1.08
## Proportion Var        0.27 0.26 0.12
## Cumulative Var        0.27 0.52 0.64
## Proportion Explained  0.41 0.40 0.19
## Cumulative Proportion 0.41 0.81 1.00
## 
##  With factor correlations of 
##      ML2  ML1  ML3
## ML2 1.00 0.69 0.71
## ML1 0.69 1.00 0.71
## ML3 0.71 0.71 1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  36  and the objective function was  5.18 with Chi Square of  7246
## The degrees of freedom for the model are 12  and the objective function was  0.06 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic number of observations is  1392 with the empirical chi square  29.4  with prob <  0.0035 
## The total number of observations was  1403  with Likelihood Chi Square =  89.1  with prob <  7.3e-14 
## 
## Tucker Lewis Index of factoring reliability =  0.968
## RMSEA index =  0.068  and the 90 % confidence intervals are  0.055 0.081
## BIC =  2.16
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    ML2  ML1  ML3
## Correlation of (regression) scores with factors   0.93 0.95 0.90
## Multiple R square of scores with factors          0.87 0.90 0.81
## Minimum correlation of possible factor scores     0.75 0.79 0.61

1.1.2 CFA

1.1.2.1 First-Order Model Unconstrained

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_01 + t1_pri_con_02 + t1_pri_con_03 + t1_pri_con_04 + t1_pri_con_05 + t1_pri_con_06 + t1_pri_con_07 + t1_pri_con_08 + t1_pri_con_09
t2_pri_con_f =~ 1*t2_pri_con_01 + t2_pri_con_02 + t2_pri_con_03 + t2_pri_con_04 + t2_pri_con_05 + t2_pri_con_06 + t2_pri_con_07 + t2_pri_con_08 + t2_pri_con_09
t3_pri_con_f =~ 1*t3_pri_con_01 + t3_pri_con_02 + t3_pri_con_03 + t3_pri_con_04 + t3_pri_con_05 + t3_pri_con_06 + t3_pri_con_07 + t3_pri_con_08 + t3_pri_con_09

# error covariances
t3_pri_con_01 ~~ t2_pri_con_01 + t1_pri_con_01
t3_pri_con_02 ~~ t2_pri_con_02 + t1_pri_con_02
t3_pri_con_03 ~~ t2_pri_con_03 + t1_pri_con_03
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_01 ~~ t1_pri_con_01
t2_pri_con_02 ~~ t1_pri_con_02 
t2_pri_con_03 ~~ t1_pri_con_03
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 101 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        111
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        29
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2726.529
##   Degrees of freedom                               294
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             29137.955
##   Degrees of freedom                               351
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.915
##   Tucker-Lewis Index (TLI)                       0.899
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -45195.456
##   Loglikelihood unrestricted model (H1)     -43832.192
##                                                       
##   Akaike (AIC)                               90612.913
##   Bayesian (BIC)                             91195.260
##   Sample-size adjusted Bayesian (BIC)        90842.654
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077
##   90 Percent confidence interval - lower         0.074
##   90 Percent confidence interval - upper         0.079
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.051
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pri_con_01     1.000                               0.728    0.672
##     t1_pri_con_02     0.927    0.039   23.800    0.000    0.675    0.675
##     t1_pri_con_03     1.103    0.047   23.669    0.000    0.803    0.662
##     t1_pri_con_04     1.198    0.043   27.544    0.000    0.872    0.806
##     t1_pri_con_05     1.176    0.050   23.621    0.000    0.857    0.669
##     t1_pri_con_06     1.226    0.047   25.980    0.000    0.892    0.757
##     t1_pri_con_07     1.343    0.050   26.665    0.000    0.978    0.777
##     t1_pri_con_08     1.243    0.048   26.133    0.000    0.905    0.767
##     t1_pri_con_09     1.115    0.042   26.333    0.000    0.812    0.774
##   t2_pri_con_f =~                                                       
##     t2_pri_con_01     1.000                               0.724    0.683
##     t2_pri_con_02     0.944    0.039   24.509    0.000    0.684    0.677
##     t2_pri_con_03     1.126    0.045   24.972    0.000    0.815    0.682
##     t2_pri_con_04     1.192    0.042   28.303    0.000    0.863    0.810
##     t2_pri_con_05     1.215    0.050   24.474    0.000    0.879    0.680
##     t2_pri_con_06     1.230    0.045   27.083    0.000    0.891    0.770
##     t2_pri_con_07     1.395    0.049   28.252    0.000    1.010    0.807
##     t2_pri_con_08     1.293    0.047   27.719    0.000    0.936    0.793
##     t2_pri_con_09     1.202    0.043   27.945    0.000    0.870    0.801
##   t3_pri_con_f =~                                                       
##     t3_pri_con_01     1.000                               0.779    0.716
##     t3_pri_con_02     0.949    0.035   27.110    0.000    0.740    0.720
##     t3_pri_con_03     1.065    0.040   26.378    0.000    0.830    0.688
##     t3_pri_con_04     1.126    0.037   30.533    0.000    0.878    0.826
##     t3_pri_con_05     1.108    0.044   25.221    0.000    0.863    0.668
##     t3_pri_con_06     1.148    0.040   28.735    0.000    0.895    0.776
##     t3_pri_con_07     1.273    0.043   29.592    0.000    0.992    0.797
##     t3_pri_con_08     1.194    0.040   29.630    0.000    0.931    0.800
##     t3_pri_con_09     1.101    0.038   29.296    0.000    0.858    0.795
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.188    0.018   10.432    0.000    0.188    0.319
##  .t1_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.198    0.019   10.556    0.000    0.198    0.324
##  .t2_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.186    0.016   11.324    0.000    0.186    0.351
##  .t1_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.164    0.016   10.173    0.000    0.164    0.311
##  .t2_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.405    0.025   16.132    0.000    0.405    0.528
##  .t1_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.383    0.026   14.928    0.000    0.383    0.481
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.047    0.012    3.894    0.000    0.047    0.126
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.059    0.013    4.709    0.000    0.059    0.155
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.381    0.029   13.280    0.000    0.381    0.418
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.402    0.029   13.809    0.000    0.402    0.440
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.157    0.017    9.272    0.000    0.157    0.293
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.153    0.018    8.736    0.000    0.153    0.274
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.195    0.018   10.585    0.000    0.195    0.351
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.235    0.020   11.730    0.000    0.235    0.395
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.166    0.017    9.991    0.000    0.166    0.331
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.175    0.017   10.092    0.000    0.175    0.332
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.129    0.014    9.247    0.000    0.129    0.301
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.113    0.014    8.049    0.000    0.113    0.259
##  .t1_pri_con_01 ~~                                                      
##    .t2_pri_con_01     0.215    0.019   11.310    0.000    0.215    0.346
##  .t1_pri_con_02 ~~                                                      
##    .t2_pri_con_02     0.191    0.017   11.391    0.000    0.191    0.348
##  .t1_pri_con_03 ~~                                                      
##    .t2_pri_con_03     0.358    0.025   14.190    0.000    0.358    0.450
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.065    0.013    5.034    0.000    0.065    0.163
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.358    0.028   12.611    0.000    0.358    0.397
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.149    0.018    8.377    0.000    0.149    0.262
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.210    0.019   10.796    0.000    0.210    0.358
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.141    0.017    8.085    0.000    0.141    0.260
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.097    0.014    7.036    0.000    0.097    0.225
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.413    0.027   15.322    0.000    0.783    0.783
##     t3_pri_con_f      0.434    0.028   15.608    0.000    0.764    0.764
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.443    0.028   15.956    0.000    0.785    0.785
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     3.334    0.029  115.127    0.000    3.334    3.078
##    .t1_pri_con_02     3.834    0.027  143.391    0.000    3.834    3.835
##    .t1_pri_con_03     3.623    0.032  111.778    0.000    3.623    2.989
##    .t1_pri_con_04     3.745    0.029  129.436    0.000    3.745    3.460
##    .t1_pri_con_05     3.842    0.034  111.938    0.000    3.842    3.002
##    .t1_pri_con_06     3.314    0.032  105.186    0.000    3.314    2.812
##    .t1_pri_con_07     3.623    0.034  107.747    0.000    3.623    2.880
##    .t1_pri_con_08     3.624    0.032  114.843    0.000    3.624    3.070
##    .t1_pri_con_09     4.095    0.028  146.054    0.000    4.095    3.905
##    .t2_pri_con_01     3.334    0.028  117.727    0.000    3.334    3.146
##    .t2_pri_con_02     3.824    0.027  141.720    0.000    3.824    3.787
##    .t2_pri_con_03     3.577    0.032  112.037    0.000    3.577    2.994
##    .t2_pri_con_04     3.675    0.028  128.972    0.000    3.675    3.448
##    .t2_pri_con_05     3.784    0.035  109.118    0.000    3.784    2.925
##    .t2_pri_con_06     3.258    0.031  105.352    0.000    3.258    2.818
##    .t2_pri_con_07     3.555    0.033  106.315    0.000    3.555    2.842
##    .t2_pri_con_08     3.550    0.032  112.492    0.000    3.550    3.007
##    .t2_pri_con_09     3.994    0.029  137.529    0.000    3.994    3.675
##    .t3_pri_con_01     3.337    0.029  114.707    0.000    3.337    3.068
##    .t3_pri_con_02     3.770    0.027  137.192    0.000    3.770    3.669
##    .t3_pri_con_03     3.557    0.032  110.186    0.000    3.557    2.947
##    .t3_pri_con_04     3.664    0.028  128.933    0.000    3.664    3.448
##    .t3_pri_con_05     3.710    0.035  107.098    0.000    3.710    2.872
##    .t3_pri_con_06     3.255    0.031  105.623    0.000    3.255    2.824
##    .t3_pri_con_07     3.492    0.033  104.929    0.000    3.492    2.806
##    .t3_pri_con_08     3.560    0.031  114.458    0.000    3.560    3.061
##    .t3_pri_con_09     3.960    0.029  137.133    0.000    3.960    3.668
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     0.643    0.026   24.370    0.000    0.643    0.548
##    .t1_pri_con_02     0.544    0.022   24.301    0.000    0.544    0.544
##    .t1_pri_con_03     0.825    0.034   24.259    0.000    0.825    0.561
##    .t1_pri_con_04     0.411    0.019   21.877    0.000    0.411    0.351
##    .t1_pri_con_05     0.904    0.037   24.229    0.000    0.904    0.552
##    .t1_pri_con_06     0.592    0.025   23.324    0.000    0.592    0.426
##    .t1_pri_con_07     0.626    0.028   22.490    0.000    0.626    0.396
##    .t1_pri_con_08     0.574    0.025   22.683    0.000    0.574    0.412
##    .t1_pri_con_09     0.440    0.019   22.680    0.000    0.440    0.400
##    .t2_pri_con_01     0.600    0.024   24.517    0.000    0.600    0.534
##    .t2_pri_con_02     0.552    0.023   24.417    0.000    0.552    0.542
##    .t2_pri_con_03     0.764    0.031   24.251    0.000    0.764    0.535
##    .t2_pri_con_04     0.391    0.018   22.204    0.000    0.391    0.345
##    .t2_pri_con_05     0.901    0.037   24.409    0.000    0.901    0.538
##    .t2_pri_con_06     0.544    0.023   23.388    0.000    0.544    0.407
##    .t2_pri_con_07     0.546    0.024   22.352    0.000    0.546    0.349
##    .t2_pri_con_08     0.518    0.023   22.481    0.000    0.518    0.371
##    .t2_pri_con_09     0.424    0.019   22.382    0.000    0.424    0.359
##    .t3_pri_con_01     0.576    0.024   24.115    0.000    0.576    0.487
##    .t3_pri_con_02     0.509    0.021   23.879    0.000    0.509    0.482
##    .t3_pri_con_03     0.768    0.032   24.130    0.000    0.768    0.527
##    .t3_pri_con_04     0.359    0.017   21.645    0.000    0.359    0.318
##    .t3_pri_con_05     0.923    0.038   24.596    0.000    0.923    0.553
##    .t3_pri_con_06     0.528    0.023   23.357    0.000    0.528    0.397
##    .t3_pri_con_07     0.565    0.025   22.376    0.000    0.565    0.365
##    .t3_pri_con_08     0.486    0.022   22.211    0.000    0.486    0.359
##    .t3_pri_con_09     0.429    0.019   22.629    0.000    0.429    0.368
##     t1_pri_con_f      0.530    0.038   14.041    0.000    1.000    1.000
##     t2_pri_con_f      0.524    0.036   14.435    0.000    1.000    1.000
##     t3_pri_con_f      0.607    0.040   15.297    0.000    1.000    1.000
reliability(get(paste("fit", name, no, sep = "_")))
##        t1_pri_con_f t2_pri_con_f t3_pri_con_f
## alpha         0.911        0.918        0.921
## omega         0.911        0.918        0.921
## omega2        0.911        0.918        0.921
## omega3        0.902        0.915        0.920
## avevar        0.533        0.558        0.567

1.1.2.2 First-Order Model Constrained

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_01 + b2*t1_pri_con_02 + b3*t1_pri_con_03 + b4*t1_pri_con_04 + b5*t1_pri_con_05 + b6*t1_pri_con_06 + b7*t1_pri_con_07 + b8*t1_pri_con_08 + b9*t1_pri_con_09
t2_pri_con_f =~ 1*t2_pri_con_01 + b2*t2_pri_con_02 + b3*t2_pri_con_03 + b4*t2_pri_con_04 + b5*t2_pri_con_05 + b6*t2_pri_con_06 + b7*t2_pri_con_07 + b8*t2_pri_con_08 + b9*t2_pri_con_09
t3_pri_con_f =~ 1*t3_pri_con_01 + b2*t3_pri_con_02 + b3*t3_pri_con_03 + b4*t3_pri_con_04 + b5*t3_pri_con_05 + b6*t3_pri_con_06 + b7*t3_pri_con_07 + b8*t3_pri_con_08 + b9*t3_pri_con_09

# error covariances
t3_pri_con_01 ~~ t2_pri_con_01 + t1_pri_con_01
t3_pri_con_02 ~~ t2_pri_con_02 + t1_pri_con_02
t3_pri_con_03 ~~ t2_pri_con_03 + t1_pri_con_03
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_01 ~~ t1_pri_con_01
t2_pri_con_02 ~~ t1_pri_con_02 
t2_pri_con_03 ~~ t1_pri_con_03
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 91 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        111
##   Number of equality constraints                    16
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        29
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2742.286
##   Degrees of freedom                               310
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             29137.955
##   Degrees of freedom                               351
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.916
##   Tucker-Lewis Index (TLI)                       0.904
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -45203.335
##   Loglikelihood unrestricted model (H1)     -43832.192
##                                                       
##   Akaike (AIC)                               90596.670
##   Bayesian (BIC)                             91095.075
##   Sample-size adjusted Bayesian (BIC)        90793.295
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.075
##   90 Percent confidence interval - lower         0.072
##   90 Percent confidence interval - upper         0.077
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.052
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pr__01         1.000                               0.732    0.674
##     t1_pr__02 (b2)    0.942    0.027   35.461    0.000    0.689    0.683
##     t1_pr__03 (b3)    1.096    0.032   34.033    0.000    0.802    0.661
##     t1_pr__04 (b4)    1.168    0.028   41.826    0.000    0.855    0.799
##     t1_pr__05 (b5)    1.164    0.034   33.805    0.000    0.852    0.667
##     t1_pr__06 (b6)    1.198    0.031   38.839    0.000    0.877    0.751
##     t1_pr__07 (b7)    1.335    0.034   39.462    0.000    0.977    0.777
##     t1_pr__08 (b8)    1.242    0.032   39.320    0.000    0.909    0.769
##     t1_pr__09 (b9)    1.138    0.029   39.675    0.000    0.833    0.783
##   t2_pri_con_f =~                                                       
##     t2_pr__01         1.000                               0.747    0.695
##     t2_pr__02 (b2)    0.942    0.027   35.461    0.000    0.703    0.689
##     t2_pr__03 (b3)    1.096    0.032   34.033    0.000    0.818    0.684
##     t2_pr__04 (b4)    1.168    0.028   41.826    0.000    0.872    0.814
##     t2_pr__05 (b5)    1.164    0.034   33.805    0.000    0.869    0.675
##     t2_pr__06 (b6)    1.198    0.031   38.839    0.000    0.895    0.772
##     t2_pr__07 (b7)    1.335    0.034   39.462    0.000    0.997    0.802
##     t2_pr__08 (b8)    1.242    0.032   39.320    0.000    0.928    0.789
##     t2_pr__09 (b9)    1.138    0.029   39.675    0.000    0.850    0.792
##   t3_pri_con_f =~                                                       
##     t3_pr__01         1.000                               0.754    0.703
##     t3_pr__02 (b2)    0.942    0.027   35.461    0.000    0.710    0.703
##     t3_pr__03 (b3)    1.096    0.032   34.033    0.000    0.826    0.685
##     t3_pr__04 (b4)    1.168    0.028   41.826    0.000    0.881    0.826
##     t3_pr__05 (b5)    1.164    0.034   33.805    0.000    0.878    0.675
##     t3_pr__06 (b6)    1.198    0.031   38.839    0.000    0.904    0.780
##     t3_pr__07 (b7)    1.335    0.034   39.462    0.000    1.007    0.803
##     t3_pr__08 (b8)    1.242    0.032   39.320    0.000    0.937    0.804
##     t3_pr__09 (b9)    1.138    0.029   39.675    0.000    0.859    0.796
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.188    0.018   10.446    0.000    0.188    0.319
##  .t1_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.200    0.019   10.654    0.000    0.200    0.327
##  .t2_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.186    0.016   11.291    0.000    0.186    0.349
##  .t1_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.165    0.016   10.194    0.000    0.165    0.311
##  .t2_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.405    0.025   16.146    0.000    0.405    0.528
##  .t1_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.385    0.026   14.960    0.000    0.385    0.481
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.047    0.012    3.914    0.000    0.047    0.126
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.061    0.013    4.830    0.000    0.061    0.158
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.381    0.029   13.287    0.000    0.381    0.418
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.403    0.029   13.825    0.000    0.403    0.441
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.156    0.017    9.249    0.000    0.156    0.293
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.153    0.017    8.735    0.000    0.153    0.274
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.193    0.018   10.525    0.000    0.193    0.349
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.232    0.020   11.680    0.000    0.232    0.393
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.165    0.017    9.970    0.000    0.165    0.330
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.173    0.017   10.032    0.000    0.173    0.331
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.129    0.014    9.275    0.000    0.129    0.301
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.111    0.014    8.000    0.000    0.111    0.258
##  .t1_pri_con_01 ~~                                                      
##    .t2_pri_con_01     0.213    0.019   11.275    0.000    0.213    0.344
##  .t1_pri_con_02 ~~                                                      
##    .t2_pri_con_02     0.189    0.017   11.345    0.000    0.189    0.347
##  .t1_pri_con_03 ~~                                                      
##    .t2_pri_con_03     0.357    0.025   14.208    0.000    0.357    0.451
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.065    0.013    5.037    0.000    0.065    0.162
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.358    0.028   12.614    0.000    0.358    0.396
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.148    0.018    8.366    0.000    0.148    0.261
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.209    0.019   10.791    0.000    0.209    0.357
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.141    0.018    8.073    0.000    0.141    0.259
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.097    0.014    7.049    0.000    0.097    0.225
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.428    0.026   16.458    0.000    0.783    0.783
##     t3_pri_con_f      0.422    0.026   16.288    0.000    0.764    0.764
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.442    0.027   16.529    0.000    0.784    0.784
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     3.334    0.029  114.874    0.000    3.334    3.071
##    .t1_pri_con_02     3.834    0.027  142.129    0.000    3.834    3.801
##    .t1_pri_con_03     3.623    0.032  111.773    0.000    3.623    2.989
##    .t1_pri_con_04     3.745    0.029  130.858    0.000    3.745    3.498
##    .t1_pri_con_05     3.842    0.034  112.133    0.000    3.842    3.007
##    .t1_pri_con_06     3.314    0.031  106.100    0.000    3.314    2.837
##    .t1_pri_con_07     3.623    0.034  107.859    0.000    3.623    2.883
##    .t1_pri_con_08     3.624    0.032  114.692    0.000    3.624    3.066
##    .t1_pri_con_09     4.095    0.028  144.074    0.000    4.095    3.852
##    .t2_pri_con_01     3.334    0.029  116.232    0.000    3.334    3.106
##    .t2_pri_con_02     3.824    0.027  140.175    0.000    3.824    3.745
##    .t2_pri_con_03     3.577    0.032  111.955    0.000    3.577    2.991
##    .t2_pri_con_04     3.675    0.029  128.218    0.000    3.675    3.428
##    .t2_pri_con_05     3.784    0.034  109.689    0.000    3.784    2.940
##    .t2_pri_con_06     3.258    0.031  105.070    0.000    3.258    2.810
##    .t2_pri_con_07     3.555    0.033  107.036    0.000    3.555    2.861
##    .t2_pri_con_08     3.551    0.031  112.944    0.000    3.551    3.020
##    .t2_pri_con_09     3.994    0.029  139.243    0.000    3.994    3.721
##    .t3_pri_con_01     3.337    0.029  116.272    0.000    3.337    3.109
##    .t3_pri_con_02     3.770    0.027  139.573    0.000    3.770    3.733
##    .t3_pri_con_03     3.557    0.032  110.256    0.000    3.557    2.949
##    .t3_pri_con_04     3.664    0.029  128.465    0.000    3.664    3.435
##    .t3_pri_con_05     3.710    0.035  106.313    0.000    3.710    2.851
##    .t3_pri_con_06     3.255    0.031  105.108    0.000    3.255    2.811
##    .t3_pri_con_07     3.492    0.034  104.143    0.000    3.492    2.785
##    .t3_pri_con_08     3.560    0.031  114.166    0.000    3.560    3.054
##    .t3_pri_con_09     3.960    0.029  137.190    0.000    3.960    3.669
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     0.643    0.026   24.529    0.000    0.643    0.546
##    .t1_pri_con_02     0.543    0.022   24.367    0.000    0.543    0.533
##    .t1_pri_con_03     0.827    0.034   24.399    0.000    0.827    0.563
##    .t1_pri_con_04     0.415    0.019   22.280    0.000    0.415    0.362
##    .t1_pri_con_05     0.907    0.037   24.315    0.000    0.907    0.556
##    .t1_pri_con_06     0.595    0.025   23.518    0.000    0.595    0.436
##    .t1_pri_con_07     0.625    0.028   22.703    0.000    0.625    0.396
##    .t1_pri_con_08     0.571    0.025   22.838    0.000    0.571    0.408
##    .t1_pri_con_09     0.437    0.019   22.697    0.000    0.437    0.386
##    .t2_pri_con_01     0.595    0.024   24.560    0.000    0.595    0.516
##    .t2_pri_con_02     0.548    0.022   24.479    0.000    0.548    0.526
##    .t2_pri_con_03     0.760    0.031   24.346    0.000    0.760    0.532
##    .t2_pri_con_04     0.388    0.017   22.340    0.000    0.388    0.338
##    .t2_pri_con_05     0.901    0.037   24.475    0.000    0.901    0.544
##    .t2_pri_con_06     0.543    0.023   23.449    0.000    0.543    0.404
##    .t2_pri_con_07     0.550    0.024   22.548    0.000    0.550    0.356
##    .t2_pri_con_08     0.522    0.023   22.707    0.000    0.522    0.378
##    .t2_pri_con_09     0.430    0.019   22.703    0.000    0.430    0.373
##    .t3_pri_con_01     0.583    0.024   24.323    0.000    0.583    0.506
##    .t3_pri_con_02     0.516    0.021   24.116    0.000    0.516    0.506
##    .t3_pri_con_03     0.772    0.032   24.254    0.000    0.772    0.531
##    .t3_pri_con_04     0.361    0.016   21.902    0.000    0.361    0.318
##    .t3_pri_con_05     0.923    0.038   24.588    0.000    0.923    0.545
##    .t3_pri_con_06     0.525    0.022   23.386    0.000    0.525    0.391
##    .t3_pri_con_07     0.559    0.025   22.459    0.000    0.559    0.355
##    .t3_pri_con_08     0.481    0.022   22.322    0.000    0.481    0.354
##    .t3_pri_con_09     0.427    0.019   22.773    0.000    0.427    0.367
##     t1_pri_con_f      0.536    0.030   17.573    0.000    1.000    1.000
##     t2_pri_con_f      0.558    0.031   17.728    0.000    1.000    1.000
##     t3_pri_con_f      0.569    0.032   17.672    0.000    1.000    1.000

1.1.2.3 Second-Order Model Unconstrained

In what follows, we analyze a second-order solution of privacy concerns. Here, we distinguish between horizontal privacy concerns (items 4, 5, 6) and vertical privacy concerns (items 7, 8, 9). The resulting model fits the data better than the unidimensional one.

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_f1 + t1_pri_con_f2
t2_pri_con_f =~ 1*t2_pri_con_f1 + t2_pri_con_f2
t3_pri_con_f =~ 1*t3_pri_con_f1 + t3_pri_con_f2
t1_pri_con_f1 =~ 1*t1_pri_con_04 + t1_pri_con_05 + t1_pri_con_06
t1_pri_con_f2 =~ 1*t1_pri_con_07 + t1_pri_con_08 + t1_pri_con_09
t2_pri_con_f1 =~ 1*t2_pri_con_04 + t2_pri_con_05 + t2_pri_con_06
t2_pri_con_f2 =~ 1*t2_pri_con_07 + t2_pri_con_08 + t2_pri_con_09
t3_pri_con_f1 =~ 1*t3_pri_con_04 + t3_pri_con_05 + t3_pri_con_06
t3_pri_con_f2 =~ 1*t3_pri_con_07 + t3_pri_con_08 + t3_pri_con_09

# error covariances
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 83 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         81
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        26
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                               657.682
##   Degrees of freedom                               108
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             18770.022
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.970
##   Tucker-Lewis Index (TLI)                       0.958
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -30261.591
##   Loglikelihood unrestricted model (H1)     -29932.750
##                                                       
##   Akaike (AIC)                               60685.182
##   Bayesian (BIC)                             61110.138
##   Sample-size adjusted Bayesian (BIC)        60852.831
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.060
##   90 Percent confidence interval - lower         0.056
##   90 Percent confidence interval - upper         0.065
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.035
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pri_con_f1     1.000                               0.942    0.942
##     t1_pri_con_f2     1.213    0.048   25.484    0.000    0.951    0.951
##   t2_pri_con_f =~                                                       
##     t2_pri_con_f1     1.000                               0.962    0.962
##     t2_pri_con_f2     1.231    0.044   27.818    0.000    0.956    0.956
##   t3_pri_con_f =~                                                       
##     t3_pri_con_f1     1.000                               0.989    0.989
##     t3_pri_con_f2     1.195    0.042   28.147    0.000    0.952    0.952
##   t1_pri_con_f1 =~                                                      
##     t1_pri_con_04     1.000                               0.850    0.791
##     t1_pri_con_05     1.011    0.038   26.326    0.000    0.859    0.671
##     t1_pri_con_06     1.082    0.037   29.612    0.000    0.919    0.779
##   t1_pri_con_f2 =~                                                      
##     t1_pri_con_07     1.000                               1.021    0.819
##     t1_pri_con_08     0.971    0.027   36.207    0.000    0.991    0.843
##     t1_pri_con_09     0.839    0.024   34.422    0.000    0.857    0.822
##   t2_pri_con_f1 =~                                                      
##     t2_pri_con_04     1.000                               0.839    0.793
##     t2_pri_con_05     1.045    0.039   26.889    0.000    0.877    0.677
##     t2_pri_con_06     1.086    0.035   30.776    0.000    0.911    0.788
##   t2_pri_con_f2 =~                                                      
##     t2_pri_con_07     1.000                               1.040    0.839
##     t2_pri_con_08     0.969    0.025   39.030    0.000    1.007    0.855
##     t2_pri_con_09     0.871    0.023   37.594    0.000    0.906    0.839
##   t3_pri_con_f1 =~                                                      
##     t3_pri_con_04     1.000                               0.835    0.791
##     t3_pri_con_05     1.020    0.039   26.407    0.000    0.852    0.657
##     t3_pri_con_06     1.095    0.035   31.391    0.000    0.915    0.793
##   t3_pri_con_f2 =~                                                      
##     t3_pri_con_07     1.000                               1.037    0.841
##     t3_pri_con_08     0.972    0.024   40.887    0.000    1.008    0.868
##     t3_pri_con_09     0.865    0.023   37.695    0.000    0.897    0.832
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.073    0.014    5.089    0.000    0.073    0.176
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.094    0.015    6.273    0.000    0.094    0.223
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.433    0.031   14.123    0.000    0.433    0.464
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.454    0.031   14.641    0.000    0.454    0.489
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.166    0.018    9.428    0.000    0.166    0.332
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.160    0.018    8.817    0.000    0.160    0.309
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.157    0.017    9.446    0.000    0.157    0.349
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.170    0.018    9.690    0.000    0.170    0.358
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.109    0.014    8.034    0.000    0.109    0.309
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.099    0.014    7.167    0.000    0.099    0.272
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.107    0.013    8.438    0.000    0.107    0.305
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.069    0.012    5.546    0.000    0.069    0.195
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.090    0.015    5.985    0.000    0.090    0.213
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.401    0.030   13.362    0.000    0.401    0.443
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.157    0.019    8.467    0.000    0.157    0.298
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.156    0.018    8.914    0.000    0.156    0.325
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.092    0.014    6.402    0.000    0.092    0.238
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.074    0.012    5.978    0.000    0.074    0.213
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.508    0.031   16.209    0.000    0.786    0.786
##     t3_pri_con_f      0.511    0.031   16.327    0.000    0.772    0.772
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.525    0.031   16.806    0.000    0.787    0.787
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     3.745    0.029  130.430    0.000    3.745    3.487
##    .t1_pri_con_05     3.842    0.034  111.844    0.000    3.842    3.000
##    .t1_pri_con_06     3.314    0.032  105.077    0.000    3.314    2.809
##    .t1_pri_con_07     3.623    0.033  108.832    0.000    3.623    2.909
##    .t1_pri_con_08     3.624    0.031  115.296    0.000    3.624    3.082
##    .t1_pri_con_09     4.095    0.028  146.945    0.000    4.095    3.929
##    .t2_pri_con_04     3.675    0.028  129.967    0.000    3.675    3.475
##    .t2_pri_con_05     3.784    0.035  108.978    0.000    3.784    2.921
##    .t2_pri_con_06     3.258    0.031  105.353    0.000    3.258    2.818
##    .t2_pri_con_07     3.556    0.033  107.327    0.000    3.556    2.869
##    .t2_pri_con_08     3.551    0.032  112.679    0.000    3.551    3.012
##    .t2_pri_con_09     3.994    0.029  138.427    0.000    3.994    3.699
##    .t3_pri_con_04     3.664    0.028  129.676    0.000    3.664    3.468
##    .t3_pri_con_05     3.709    0.035  106.637    0.000    3.709    2.859
##    .t3_pri_con_06     3.256    0.031  105.607    0.000    3.256    2.824
##    .t3_pri_con_07     3.492    0.033  105.953    0.000    3.492    2.833
##    .t3_pri_con_08     3.560    0.031  114.604    0.000    3.560    3.065
##    .t3_pri_con_09     3.959    0.029  137.357    0.000    3.959    3.674
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
##    .t1_pri_con_f1     0.000                               0.000    0.000
##    .t1_pri_con_f2     0.000                               0.000    0.000
##    .t2_pri_con_f1     0.000                               0.000    0.000
##    .t2_pri_con_f2     0.000                               0.000    0.000
##    .t3_pri_con_f1     0.000                               0.000    0.000
##    .t3_pri_con_f2     0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     0.431    0.022   19.198    0.000    0.431    0.374
##    .t1_pri_con_05     0.902    0.040   22.711    0.000    0.902    0.550
##    .t1_pri_con_06     0.546    0.027   20.013    0.000    0.546    0.392
##    .t1_pri_con_07     0.509    0.026   19.666    0.000    0.509    0.328
##    .t1_pri_con_08     0.399    0.021   18.622    0.000    0.399    0.289
##    .t1_pri_con_09     0.353    0.018   19.768    0.000    0.353    0.325
##    .t2_pri_con_04     0.414    0.021   19.815    0.000    0.414    0.371
##    .t2_pri_con_05     0.910    0.039   23.075    0.000    0.910    0.542
##    .t2_pri_con_06     0.507    0.025   20.332    0.000    0.507    0.380
##    .t2_pri_con_07     0.455    0.023   19.557    0.000    0.455    0.296
##    .t2_pri_con_08     0.375    0.020   18.782    0.000    0.375    0.270
##    .t2_pri_con_09     0.345    0.018   19.456    0.000    0.345    0.296
##    .t3_pri_con_04     0.418    0.021   20.354    0.000    0.418    0.375
##    .t3_pri_con_05     0.956    0.041   23.557    0.000    0.956    0.568
##    .t3_pri_con_06     0.492    0.024   20.489    0.000    0.492    0.370
##    .t3_pri_con_07     0.444    0.022   19.740    0.000    0.444    0.292
##    .t3_pri_con_08     0.333    0.018   18.288    0.000    0.333    0.247
##    .t3_pri_con_09     0.357    0.018   20.263    0.000    0.357    0.307
##     t1_pri_con_f      0.641    0.043   15.025    0.000    1.000    1.000
##     t2_pri_con_f      0.652    0.041   15.720    0.000    1.000    1.000
##     t3_pri_con_f      0.683    0.042   16.106    0.000    1.000    1.000
##    .t1_pri_con_f1     0.081    0.015    5.266    0.000    0.112    0.112
##    .t1_pri_con_f2     0.099    0.021    4.818    0.000    0.095    0.095
##    .t2_pri_con_f1     0.052    0.014    3.831    0.000    0.074    0.074
##    .t2_pri_con_f2     0.094    0.019    5.012    0.000    0.087    0.087
##    .t3_pri_con_f1     0.015    0.013    1.199    0.230    0.022    0.022
##    .t3_pri_con_f2     0.101    0.018    5.558    0.000    0.094    0.094

1.1.2.4 Second-Order Model Constrained

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_f1 + a2*t1_pri_con_f2
t2_pri_con_f =~ 1*t2_pri_con_f1 + a2*t2_pri_con_f2
t3_pri_con_f =~ 1*t3_pri_con_f1 + a2*t3_pri_con_f2
t1_pri_con_f1 =~ 1*t1_pri_con_04 + b2*t1_pri_con_05 + b3*t1_pri_con_06
t1_pri_con_f2 =~ 1*t1_pri_con_07 + c2*t1_pri_con_08 + c3*t1_pri_con_09
t2_pri_con_f1 =~ 1*t2_pri_con_04 + b2*t2_pri_con_05 + b3*t2_pri_con_06
t2_pri_con_f2 =~ 1*t2_pri_con_07 + c2*t2_pri_con_08 + c3*t2_pri_con_09
t3_pri_con_f1 =~ 1*t3_pri_con_04 + b2*t3_pri_con_05 + b3*t3_pri_con_06
t3_pri_con_f2 =~ 1*t3_pri_con_07 + c2*t3_pri_con_08 + c3*t3_pri_con_09

# error covariances
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 86 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         81
##   Number of equality constraints                    10
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        26
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                               661.175
##   Degrees of freedom                               118
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             18770.022
##   Degrees of freedom                               153
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.971
##   Tucker-Lewis Index (TLI)                       0.962
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -30263.337
##   Loglikelihood unrestricted model (H1)     -29932.750
##                                                       
##   Akaike (AIC)                               60668.675
##   Bayesian (BIC)                             61041.167
##   Sample-size adjusted Bayesian (BIC)        60815.626
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.057
##   90 Percent confidence interval - lower         0.053
##   90 Percent confidence interval - upper         0.062
##   P-value RMSEA <= 0.05                          0.002
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.036
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pr_c_1         1.000                               0.942    0.942
##     t1_pr_c_2 (a2)    1.212    0.031   38.916    0.000    0.952    0.952
##   t2_pri_con_f =~                                                       
##     t2_pr_c_1         1.000                               0.966    0.966
##     t2_pr_c_2 (a2)    1.212    0.031   38.916    0.000    0.952    0.952
##   t3_pri_con_f =~                                                       
##     t3_pr_c_1         1.000                               0.986    0.986
##     t3_pr_c_2 (a2)    1.212    0.031   38.916    0.000    0.955    0.955
##   t1_pri_con_f1 =~                                                      
##     t1_pr__04         1.000                               0.845    0.789
##     t1_pr__05 (b2)    1.026    0.028   36.986    0.000    0.867    0.675
##     t1_pr__06 (b3)    1.088    0.024   44.494    0.000    0.919    0.779
##   t1_pri_con_f2 =~                                                      
##     t1_pr__07         1.000                               1.013    0.817
##     t1_pr__08 (c2)    0.971    0.018   55.102    0.000    0.984    0.841
##     t1_pr__09 (c3)    0.859    0.016   52.558    0.000    0.871    0.828
##   t2_pri_con_f1 =~                                                      
##     t2_pr__04         1.000                               0.846    0.796
##     t2_pr__05 (b2)    1.026    0.028   36.986    0.000    0.868    0.672
##     t2_pr__06 (b3)    1.088    0.024   44.494    0.000    0.920    0.791
##   t2_pri_con_f2 =~                                                      
##     t2_pr__07         1.000                               1.039    0.839
##     t2_pr__08 (c2)    0.971    0.018   55.102    0.000    1.009    0.855
##     t2_pr__09 (c3)    0.859    0.016   52.558    0.000    0.893    0.834
##   t3_pri_con_f1 =~                                                      
##     t3_pr__04         1.000                               0.833    0.790
##     t3_pr__05 (b2)    1.026    0.028   36.986    0.000    0.855    0.658
##     t3_pr__06 (b3)    1.088    0.024   44.494    0.000    0.906    0.791
##   t3_pri_con_f2 =~                                                      
##     t3_pr__07         1.000                               1.043    0.843
##     t3_pr__08 (c2)    0.971    0.018   55.102    0.000    1.013    0.869
##     t3_pr__09 (c3)    0.859    0.016   52.558    0.000    0.896    0.832
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.073    0.014    5.085    0.000    0.073    0.176
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.095    0.015    6.341    0.000    0.095    0.224
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.433    0.031   14.129    0.000    0.433    0.464
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.454    0.031   14.640    0.000    0.454    0.490
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.166    0.018    9.428    0.000    0.166    0.332
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.160    0.018    8.830    0.000    0.160    0.309
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.156    0.017    9.428    0.000    0.156    0.348
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.171    0.018    9.728    0.000    0.171    0.358
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.109    0.014    8.043    0.000    0.109    0.310
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.099    0.014    7.180    0.000    0.099    0.272
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.108    0.013    8.511    0.000    0.108    0.306
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.069    0.012    5.512    0.000    0.069    0.195
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.090    0.015    5.985    0.000    0.090    0.212
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.401    0.030   13.348    0.000    0.401    0.442
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.157    0.019    8.461    0.000    0.157    0.298
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.157    0.018    8.955    0.000    0.157    0.325
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.092    0.014    6.430    0.000    0.092    0.239
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.074    0.012    5.999    0.000    0.074    0.214
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.511    0.030   17.157    0.000    0.786    0.786
##     t3_pri_con_f      0.505    0.029   17.166    0.000    0.772    0.772
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.528    0.030   17.351    0.000    0.786    0.786
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     3.745    0.029  130.814    0.000    3.745    3.498
##    .t1_pri_con_05     3.842    0.034  111.479    0.000    3.842    2.990
##    .t1_pri_con_06     3.314    0.032  105.073    0.000    3.314    2.809
##    .t1_pri_con_07     3.623    0.033  109.216    0.000    3.623    2.920
##    .t1_pri_con_08     3.624    0.031  115.845    0.000    3.624    3.097
##    .t1_pri_con_09     4.095    0.028  145.606    0.000    4.095    3.893
##    .t2_pri_con_04     3.675    0.028  129.357    0.000    3.675    3.459
##    .t2_pri_con_05     3.784    0.035  109.375    0.000    3.784    2.932
##    .t2_pri_con_06     3.258    0.031  104.716    0.000    3.258    2.801
##    .t2_pri_con_07     3.556    0.033  107.425    0.000    3.556    2.872
##    .t2_pri_con_08     3.551    0.032  112.593    0.000    3.551    3.010
##    .t2_pri_con_09     3.994    0.029  139.662    0.000    3.994    3.732
##    .t3_pri_con_04     3.664    0.028  129.881    0.000    3.664    3.473
##    .t3_pri_con_05     3.709    0.035  106.555    0.000    3.709    2.857
##    .t3_pri_con_06     3.256    0.031  106.189    0.000    3.256    2.839
##    .t3_pri_con_07     3.492    0.033  105.575    0.000    3.492    2.823
##    .t3_pri_con_08     3.560    0.031  114.210    0.000    3.560    3.055
##    .t3_pri_con_09     3.959    0.029  137.398    0.000    3.959    3.675
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
##    .t1_pri_con_f1     0.000                               0.000    0.000
##    .t1_pri_con_f2     0.000                               0.000    0.000
##    .t2_pri_con_f1     0.000                               0.000    0.000
##    .t2_pri_con_f2     0.000                               0.000    0.000
##    .t3_pri_con_f1     0.000                               0.000    0.000
##    .t3_pri_con_f2     0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     0.433    0.022   19.819    0.000    0.433    0.377
##    .t1_pri_con_05     0.900    0.040   22.779    0.000    0.900    0.545
##    .t1_pri_con_06     0.546    0.027   20.364    0.000    0.546    0.392
##    .t1_pri_con_07     0.513    0.025   20.282    0.000    0.513    0.333
##    .t1_pri_con_08     0.401    0.021   19.096    0.000    0.401    0.293
##    .t1_pri_con_09     0.349    0.017   19.948    0.000    0.349    0.315
##    .t2_pri_con_04     0.413    0.020   20.196    0.000    0.413    0.366
##    .t2_pri_con_05     0.913    0.039   23.235    0.000    0.913    0.548
##    .t2_pri_con_06     0.506    0.025   20.513    0.000    0.506    0.374
##    .t2_pri_con_07     0.453    0.023   19.877    0.000    0.453    0.296
##    .t2_pri_con_08     0.373    0.020   18.959    0.000    0.373    0.268
##    .t2_pri_con_09     0.348    0.017   19.944    0.000    0.348    0.304
##    .t3_pri_con_04     0.419    0.020   20.670    0.000    0.419    0.376
##    .t3_pri_con_05     0.955    0.040   23.579    0.000    0.955    0.567
##    .t3_pri_con_06     0.493    0.024   20.717    0.000    0.493    0.375
##    .t3_pri_con_07     0.443    0.022   20.042    0.000    0.443    0.289
##    .t3_pri_con_08     0.333    0.018   18.506    0.000    0.333    0.245
##    .t3_pri_con_09     0.358    0.017   20.632    0.000    0.358    0.308
##     t1_pri_con_f      0.633    0.035   18.237    0.000    1.000    1.000
##     t2_pri_con_f      0.667    0.036   18.585    0.000    1.000    1.000
##     t3_pri_con_f      0.675    0.036   18.769    0.000    1.000    1.000
##    .t1_pri_con_f1     0.081    0.014    5.626    0.000    0.113    0.113
##    .t1_pri_con_f2     0.097    0.019    5.195    0.000    0.094    0.094
##    .t2_pri_con_f1     0.048    0.013    3.735    0.000    0.067    0.067
##    .t2_pri_con_f2     0.100    0.018    5.713    0.000    0.093    0.093
##    .t3_pri_con_f1     0.019    0.012    1.569    0.117    0.027    0.027
##    .t3_pri_con_f2     0.097    0.017    5.669    0.000    0.089    0.089

1.1.3 Reliability

reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t1", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.852          0.946          0.896
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t2", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.870          0.956          0.905
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t3", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.880          0.966          0.906

1.1.4 Longitudinal Invariance

(anova(get(paste("fit", name, no - 1, sep = "_")), get(paste("fit", name, no, sep = "_"))))

1.2 Attitude Toward Online Sharing of Personal Information

1.2.1 EFA

no <- 0
name <- "inf_sha_att"
d_tmp <- select(d_wide, contains(paste0("t1_", name)), -contains("_m"))
model <- fa.parallel(d_tmp, fa = "fa", fm = "ml")

## Parallel analysis suggests that the number of factors =  5  and the number of components =  NA
factan <- fa(d_tmp, fm = "ml", nfactors = model$nfact, rotate = "promax")
print(factan, sort = TRUE, cut = 0.3)
## Factor Analysis using method =  ml
## Call: fa(r = d_tmp, nfactors = model$nfact, rotate = "promax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                   item   ML1   ML4   ML2   ML3   ML5   h2     u2 com
## t1_inf_sha_att_06    7  1.06                         0.86 0.1400 1.0
## t1_inf_sha_att_05    6  0.95                         0.88 0.1179 1.1
## t1_inf_sha_att_03    4  0.64                    0.40 0.82 0.1788 1.7
## t1_inf_sha_att_08    9  0.63                         0.51 0.4885 1.4
## t1_inf_sha_att_fs    1  0.58                         1.00 0.0044 1.9
## t1_inf_sha_att_10   11        0.99                   0.89 0.1130 1.0
## t1_inf_sha_att_11   12        0.98                   0.87 0.1290 1.0
## t1_inf_sha_att_09   10        0.47                   0.24 0.7619 1.1
## t1_inf_sha_att_01    2              1.06             1.00 0.0050 1.1
## t1_inf_sha_att_02    3              0.54             0.34 0.6614 1.1
## t1_inf_sha_att_07    8                    1.01       1.00 0.0050 1.0
## t1_inf_sha_att_04    5  0.32                    0.74 0.97 0.0320 1.4
## 
##                        ML1  ML4  ML2  ML3  ML5
## SS loadings           3.54 2.18 1.38 1.08 1.19
## Proportion Var        0.30 0.18 0.11 0.09 0.10
## Cumulative Var        0.30 0.48 0.59 0.68 0.78
## Proportion Explained  0.38 0.23 0.15 0.12 0.13
## Cumulative Proportion 0.38 0.61 0.76 0.87 1.00
## 
##  With factor correlations of 
##      ML1  ML4  ML2  ML3  ML5
## ML1 1.00 0.48 0.43 0.66 0.52
## ML4 0.48 1.00 0.29 0.47 0.40
## ML2 0.43 0.29 1.00 0.34 0.21
## ML3 0.66 0.47 0.34 1.00 0.37
## ML5 0.52 0.40 0.21 0.37 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 5 factors are sufficient.
## 
## The degrees of freedom for the null model are  66  and the objective function was  12.7 with Chi Square of  17754
## The degrees of freedom for the model are 16  and the objective function was  1.58 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.04 
## 
## The harmonic number of observations is  1396 with the empirical chi square  61.6  with prob <  2.8e-07 
## The total number of observations was  1403  with Likelihood Chi Square =  2196  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.49
## RMSEA index =  0.312  and the 90 % confidence intervals are  0.301 0.323
## BIC =  2080
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    ML1  ML4  ML2  ML3  ML5
## Correlation of (regression) scores with factors   0.99 0.98 1.00 1.00 0.97
## Multiple R square of scores with factors          0.98 0.96 1.00 0.99 0.94
## Minimum correlation of possible factor scores     0.95 0.91 0.99 0.99 0.88

1.2.2 CFA

1.2.2.1 First-Order Model Unconstrained

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_01 + t1_pri_con_02 + t1_pri_con_03 + t1_pri_con_04 + t1_pri_con_05 + t1_pri_con_06 + t1_pri_con_07 + t1_pri_con_08 + t1_pri_con_09
t2_pri_con_f =~ 1*t2_pri_con_01 + t2_pri_con_02 + t2_pri_con_03 + t2_pri_con_04 + t2_pri_con_05 + t2_pri_con_06 + t2_pri_con_07 + t2_pri_con_08 + t2_pri_con_09
t3_pri_con_f =~ 1*t3_pri_con_01 + t3_pri_con_02 + t3_pri_con_03 + t3_pri_con_04 + t3_pri_con_05 + t3_pri_con_06 + t3_pri_con_07 + t3_pri_con_08 + t3_pri_con_09

# error covariances
t3_pri_con_01 ~~ t2_pri_con_01 + t1_pri_con_01
t3_pri_con_02 ~~ t2_pri_con_02 + t1_pri_con_02
t3_pri_con_03 ~~ t2_pri_con_03 + t1_pri_con_03
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_01 ~~ t1_pri_con_01
t2_pri_con_02 ~~ t1_pri_con_02 
t2_pri_con_03 ~~ t1_pri_con_03
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 101 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        111
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        29
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2726.529
##   Degrees of freedom                               294
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             29137.955
##   Degrees of freedom                               351
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.915
##   Tucker-Lewis Index (TLI)                       0.899
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -45195.456
##   Loglikelihood unrestricted model (H1)     -43832.192
##                                                       
##   Akaike (AIC)                               90612.913
##   Bayesian (BIC)                             91195.260
##   Sample-size adjusted Bayesian (BIC)        90842.654
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.077
##   90 Percent confidence interval - lower         0.074
##   90 Percent confidence interval - upper         0.079
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.051
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pri_con_01     1.000                               0.728    0.672
##     t1_pri_con_02     0.927    0.039   23.800    0.000    0.675    0.675
##     t1_pri_con_03     1.103    0.047   23.669    0.000    0.803    0.662
##     t1_pri_con_04     1.198    0.043   27.544    0.000    0.872    0.806
##     t1_pri_con_05     1.176    0.050   23.621    0.000    0.857    0.669
##     t1_pri_con_06     1.226    0.047   25.980    0.000    0.892    0.757
##     t1_pri_con_07     1.343    0.050   26.665    0.000    0.978    0.777
##     t1_pri_con_08     1.243    0.048   26.133    0.000    0.905    0.767
##     t1_pri_con_09     1.115    0.042   26.333    0.000    0.812    0.774
##   t2_pri_con_f =~                                                       
##     t2_pri_con_01     1.000                               0.724    0.683
##     t2_pri_con_02     0.944    0.039   24.509    0.000    0.684    0.677
##     t2_pri_con_03     1.126    0.045   24.972    0.000    0.815    0.682
##     t2_pri_con_04     1.192    0.042   28.303    0.000    0.863    0.810
##     t2_pri_con_05     1.215    0.050   24.474    0.000    0.879    0.680
##     t2_pri_con_06     1.230    0.045   27.083    0.000    0.891    0.770
##     t2_pri_con_07     1.395    0.049   28.252    0.000    1.010    0.807
##     t2_pri_con_08     1.293    0.047   27.719    0.000    0.936    0.793
##     t2_pri_con_09     1.202    0.043   27.945    0.000    0.870    0.801
##   t3_pri_con_f =~                                                       
##     t3_pri_con_01     1.000                               0.779    0.716
##     t3_pri_con_02     0.949    0.035   27.110    0.000    0.740    0.720
##     t3_pri_con_03     1.065    0.040   26.378    0.000    0.830    0.688
##     t3_pri_con_04     1.126    0.037   30.533    0.000    0.878    0.826
##     t3_pri_con_05     1.108    0.044   25.221    0.000    0.863    0.668
##     t3_pri_con_06     1.148    0.040   28.735    0.000    0.895    0.776
##     t3_pri_con_07     1.273    0.043   29.592    0.000    0.992    0.797
##     t3_pri_con_08     1.194    0.040   29.630    0.000    0.931    0.800
##     t3_pri_con_09     1.101    0.038   29.296    0.000    0.858    0.795
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.188    0.018   10.432    0.000    0.188    0.319
##  .t1_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.198    0.019   10.556    0.000    0.198    0.324
##  .t2_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.186    0.016   11.324    0.000    0.186    0.351
##  .t1_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.164    0.016   10.173    0.000    0.164    0.311
##  .t2_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.405    0.025   16.132    0.000    0.405    0.528
##  .t1_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.383    0.026   14.928    0.000    0.383    0.481
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.047    0.012    3.894    0.000    0.047    0.126
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.059    0.013    4.709    0.000    0.059    0.155
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.381    0.029   13.280    0.000    0.381    0.418
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.402    0.029   13.809    0.000    0.402    0.440
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.157    0.017    9.272    0.000    0.157    0.293
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.153    0.018    8.736    0.000    0.153    0.274
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.195    0.018   10.585    0.000    0.195    0.351
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.235    0.020   11.730    0.000    0.235    0.395
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.166    0.017    9.991    0.000    0.166    0.331
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.175    0.017   10.092    0.000    0.175    0.332
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.129    0.014    9.247    0.000    0.129    0.301
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.113    0.014    8.049    0.000    0.113    0.259
##  .t1_pri_con_01 ~~                                                      
##    .t2_pri_con_01     0.215    0.019   11.310    0.000    0.215    0.346
##  .t1_pri_con_02 ~~                                                      
##    .t2_pri_con_02     0.191    0.017   11.391    0.000    0.191    0.348
##  .t1_pri_con_03 ~~                                                      
##    .t2_pri_con_03     0.358    0.025   14.190    0.000    0.358    0.450
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.065    0.013    5.034    0.000    0.065    0.163
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.358    0.028   12.611    0.000    0.358    0.397
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.149    0.018    8.377    0.000    0.149    0.262
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.210    0.019   10.796    0.000    0.210    0.358
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.141    0.017    8.085    0.000    0.141    0.260
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.097    0.014    7.036    0.000    0.097    0.225
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.413    0.027   15.322    0.000    0.783    0.783
##     t3_pri_con_f      0.434    0.028   15.608    0.000    0.764    0.764
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.443    0.028   15.956    0.000    0.785    0.785
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     3.334    0.029  115.127    0.000    3.334    3.078
##    .t1_pri_con_02     3.834    0.027  143.391    0.000    3.834    3.835
##    .t1_pri_con_03     3.623    0.032  111.778    0.000    3.623    2.989
##    .t1_pri_con_04     3.745    0.029  129.436    0.000    3.745    3.460
##    .t1_pri_con_05     3.842    0.034  111.938    0.000    3.842    3.002
##    .t1_pri_con_06     3.314    0.032  105.186    0.000    3.314    2.812
##    .t1_pri_con_07     3.623    0.034  107.747    0.000    3.623    2.880
##    .t1_pri_con_08     3.624    0.032  114.843    0.000    3.624    3.070
##    .t1_pri_con_09     4.095    0.028  146.054    0.000    4.095    3.905
##    .t2_pri_con_01     3.334    0.028  117.727    0.000    3.334    3.146
##    .t2_pri_con_02     3.824    0.027  141.720    0.000    3.824    3.787
##    .t2_pri_con_03     3.577    0.032  112.037    0.000    3.577    2.994
##    .t2_pri_con_04     3.675    0.028  128.972    0.000    3.675    3.448
##    .t2_pri_con_05     3.784    0.035  109.118    0.000    3.784    2.925
##    .t2_pri_con_06     3.258    0.031  105.352    0.000    3.258    2.818
##    .t2_pri_con_07     3.555    0.033  106.315    0.000    3.555    2.842
##    .t2_pri_con_08     3.550    0.032  112.492    0.000    3.550    3.007
##    .t2_pri_con_09     3.994    0.029  137.529    0.000    3.994    3.675
##    .t3_pri_con_01     3.337    0.029  114.707    0.000    3.337    3.068
##    .t3_pri_con_02     3.770    0.027  137.192    0.000    3.770    3.669
##    .t3_pri_con_03     3.557    0.032  110.186    0.000    3.557    2.947
##    .t3_pri_con_04     3.664    0.028  128.933    0.000    3.664    3.448
##    .t3_pri_con_05     3.710    0.035  107.098    0.000    3.710    2.872
##    .t3_pri_con_06     3.255    0.031  105.623    0.000    3.255    2.824
##    .t3_pri_con_07     3.492    0.033  104.929    0.000    3.492    2.806
##    .t3_pri_con_08     3.560    0.031  114.458    0.000    3.560    3.061
##    .t3_pri_con_09     3.960    0.029  137.133    0.000    3.960    3.668
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     0.643    0.026   24.370    0.000    0.643    0.548
##    .t1_pri_con_02     0.544    0.022   24.301    0.000    0.544    0.544
##    .t1_pri_con_03     0.825    0.034   24.259    0.000    0.825    0.561
##    .t1_pri_con_04     0.411    0.019   21.877    0.000    0.411    0.351
##    .t1_pri_con_05     0.904    0.037   24.229    0.000    0.904    0.552
##    .t1_pri_con_06     0.592    0.025   23.324    0.000    0.592    0.426
##    .t1_pri_con_07     0.626    0.028   22.490    0.000    0.626    0.396
##    .t1_pri_con_08     0.574    0.025   22.683    0.000    0.574    0.412
##    .t1_pri_con_09     0.440    0.019   22.680    0.000    0.440    0.400
##    .t2_pri_con_01     0.600    0.024   24.517    0.000    0.600    0.534
##    .t2_pri_con_02     0.552    0.023   24.417    0.000    0.552    0.542
##    .t2_pri_con_03     0.764    0.031   24.251    0.000    0.764    0.535
##    .t2_pri_con_04     0.391    0.018   22.204    0.000    0.391    0.345
##    .t2_pri_con_05     0.901    0.037   24.409    0.000    0.901    0.538
##    .t2_pri_con_06     0.544    0.023   23.388    0.000    0.544    0.407
##    .t2_pri_con_07     0.546    0.024   22.352    0.000    0.546    0.349
##    .t2_pri_con_08     0.518    0.023   22.481    0.000    0.518    0.371
##    .t2_pri_con_09     0.424    0.019   22.382    0.000    0.424    0.359
##    .t3_pri_con_01     0.576    0.024   24.115    0.000    0.576    0.487
##    .t3_pri_con_02     0.509    0.021   23.879    0.000    0.509    0.482
##    .t3_pri_con_03     0.768    0.032   24.130    0.000    0.768    0.527
##    .t3_pri_con_04     0.359    0.017   21.645    0.000    0.359    0.318
##    .t3_pri_con_05     0.923    0.038   24.596    0.000    0.923    0.553
##    .t3_pri_con_06     0.528    0.023   23.357    0.000    0.528    0.397
##    .t3_pri_con_07     0.565    0.025   22.376    0.000    0.565    0.365
##    .t3_pri_con_08     0.486    0.022   22.211    0.000    0.486    0.359
##    .t3_pri_con_09     0.429    0.019   22.629    0.000    0.429    0.368
##     t1_pri_con_f      0.530    0.038   14.041    0.000    1.000    1.000
##     t2_pri_con_f      0.524    0.036   14.435    0.000    1.000    1.000
##     t3_pri_con_f      0.607    0.040   15.297    0.000    1.000    1.000

1.2.2.2 First-Order Model Constrained

model <- '
# create factors
t1_pri_con_f =~ 1*t1_pri_con_01 + a2*t1_pri_con_02 + a3*t1_pri_con_03 + a4*t1_pri_con_04 + a5*t1_pri_con_05 + a6*t1_pri_con_06 + a7*t1_pri_con_07 + a8*t1_pri_con_08 + a9*t1_pri_con_09
t2_pri_con_f =~ 1*t2_pri_con_01 + a2*t2_pri_con_02 + a3*t2_pri_con_03 + a4*t2_pri_con_04 + a5*t2_pri_con_05 + a6*t2_pri_con_06 + a7*t2_pri_con_07 + a8*t2_pri_con_08 + a9*t2_pri_con_09
t3_pri_con_f =~ 1*t3_pri_con_01 + a2*t3_pri_con_02 + a3*t3_pri_con_03 + a4*t3_pri_con_04 + a5*t3_pri_con_05 + a6*t3_pri_con_06 + a7*t3_pri_con_07 + a8*t3_pri_con_08 + a9*t3_pri_con_09

# error covariances
t3_pri_con_01 ~~ t2_pri_con_01 + t1_pri_con_01
t3_pri_con_02 ~~ t2_pri_con_02 + t1_pri_con_02
t3_pri_con_03 ~~ t2_pri_con_03 + t1_pri_con_03
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_01 ~~ t1_pri_con_01
t2_pri_con_02 ~~ t1_pri_con_02 
t2_pri_con_03 ~~ t1_pri_con_03
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 91 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        111
##   Number of equality constraints                    16
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        29
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2742.286
##   Degrees of freedom                               310
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             29137.955
##   Degrees of freedom                               351
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.916
##   Tucker-Lewis Index (TLI)                       0.904
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -45203.335
##   Loglikelihood unrestricted model (H1)     -43832.192
##                                                       
##   Akaike (AIC)                               90596.670
##   Bayesian (BIC)                             91095.075
##   Sample-size adjusted Bayesian (BIC)        90793.295
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.075
##   90 Percent confidence interval - lower         0.072
##   90 Percent confidence interval - upper         0.077
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.052
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                       
##     t1_pr__01         1.000                               0.732    0.674
##     t1_pr__02 (a2)    0.942    0.027   35.461    0.000    0.689    0.683
##     t1_pr__03 (a3)    1.096    0.032   34.033    0.000    0.802    0.661
##     t1_pr__04 (a4)    1.168    0.028   41.826    0.000    0.855    0.799
##     t1_pr__05 (a5)    1.164    0.034   33.805    0.000    0.852    0.667
##     t1_pr__06 (a6)    1.198    0.031   38.839    0.000    0.877    0.751
##     t1_pr__07 (a7)    1.335    0.034   39.462    0.000    0.977    0.777
##     t1_pr__08 (a8)    1.242    0.032   39.320    0.000    0.909    0.769
##     t1_pr__09 (a9)    1.138    0.029   39.675    0.000    0.833    0.783
##   t2_pri_con_f =~                                                       
##     t2_pr__01         1.000                               0.747    0.695
##     t2_pr__02 (a2)    0.942    0.027   35.461    0.000    0.703    0.689
##     t2_pr__03 (a3)    1.096    0.032   34.033    0.000    0.818    0.684
##     t2_pr__04 (a4)    1.168    0.028   41.826    0.000    0.872    0.814
##     t2_pr__05 (a5)    1.164    0.034   33.805    0.000    0.869    0.675
##     t2_pr__06 (a6)    1.198    0.031   38.839    0.000    0.895    0.772
##     t2_pr__07 (a7)    1.335    0.034   39.462    0.000    0.997    0.802
##     t2_pr__08 (a8)    1.242    0.032   39.320    0.000    0.928    0.789
##     t2_pr__09 (a9)    1.138    0.029   39.675    0.000    0.850    0.792
##   t3_pri_con_f =~                                                       
##     t3_pr__01         1.000                               0.754    0.703
##     t3_pr__02 (a2)    0.942    0.027   35.461    0.000    0.710    0.703
##     t3_pr__03 (a3)    1.096    0.032   34.033    0.000    0.826    0.685
##     t3_pr__04 (a4)    1.168    0.028   41.826    0.000    0.881    0.826
##     t3_pr__05 (a5)    1.164    0.034   33.805    0.000    0.878    0.675
##     t3_pr__06 (a6)    1.198    0.031   38.839    0.000    0.904    0.780
##     t3_pr__07 (a7)    1.335    0.034   39.462    0.000    1.007    0.803
##     t3_pr__08 (a8)    1.242    0.032   39.320    0.000    0.937    0.804
##     t3_pr__09 (a9)    1.138    0.029   39.675    0.000    0.859    0.796
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.188    0.018   10.446    0.000    0.188    0.319
##  .t1_pri_con_01 ~~                                                      
##    .t3_pri_con_01     0.200    0.019   10.654    0.000    0.200    0.327
##  .t2_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.186    0.016   11.291    0.000    0.186    0.349
##  .t1_pri_con_02 ~~                                                      
##    .t3_pri_con_02     0.165    0.016   10.194    0.000    0.165    0.311
##  .t2_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.405    0.025   16.146    0.000    0.405    0.528
##  .t1_pri_con_03 ~~                                                      
##    .t3_pri_con_03     0.385    0.026   14.960    0.000    0.385    0.481
##  .t2_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.047    0.012    3.914    0.000    0.047    0.126
##  .t1_pri_con_04 ~~                                                      
##    .t3_pri_con_04     0.061    0.013    4.830    0.000    0.061    0.158
##  .t2_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.381    0.029   13.287    0.000    0.381    0.418
##  .t1_pri_con_05 ~~                                                      
##    .t3_pri_con_05     0.403    0.029   13.825    0.000    0.403    0.441
##  .t2_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.156    0.017    9.249    0.000    0.156    0.293
##  .t1_pri_con_06 ~~                                                      
##    .t3_pri_con_06     0.153    0.017    8.735    0.000    0.153    0.274
##  .t2_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.193    0.018   10.525    0.000    0.193    0.349
##  .t1_pri_con_07 ~~                                                      
##    .t3_pri_con_07     0.232    0.020   11.680    0.000    0.232    0.393
##  .t2_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.165    0.017    9.970    0.000    0.165    0.330
##  .t1_pri_con_08 ~~                                                      
##    .t3_pri_con_08     0.173    0.017   10.032    0.000    0.173    0.331
##  .t2_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.129    0.014    9.275    0.000    0.129    0.301
##  .t1_pri_con_09 ~~                                                      
##    .t3_pri_con_09     0.111    0.014    8.000    0.000    0.111    0.258
##  .t1_pri_con_01 ~~                                                      
##    .t2_pri_con_01     0.213    0.019   11.275    0.000    0.213    0.344
##  .t1_pri_con_02 ~~                                                      
##    .t2_pri_con_02     0.189    0.017   11.345    0.000    0.189    0.347
##  .t1_pri_con_03 ~~                                                      
##    .t2_pri_con_03     0.357    0.025   14.208    0.000    0.357    0.451
##  .t1_pri_con_04 ~~                                                      
##    .t2_pri_con_04     0.065    0.013    5.037    0.000    0.065    0.162
##  .t1_pri_con_05 ~~                                                      
##    .t2_pri_con_05     0.358    0.028   12.614    0.000    0.358    0.396
##  .t1_pri_con_06 ~~                                                      
##    .t2_pri_con_06     0.148    0.018    8.366    0.000    0.148    0.261
##  .t1_pri_con_07 ~~                                                      
##    .t2_pri_con_07     0.209    0.019   10.791    0.000    0.209    0.357
##  .t1_pri_con_08 ~~                                                      
##    .t2_pri_con_08     0.141    0.018    8.073    0.000    0.141    0.259
##  .t1_pri_con_09 ~~                                                      
##    .t2_pri_con_09     0.097    0.014    7.049    0.000    0.097    0.225
##   t1_pri_con_f ~~                                                       
##     t2_pri_con_f      0.428    0.026   16.458    0.000    0.783    0.783
##     t3_pri_con_f      0.422    0.026   16.288    0.000    0.764    0.764
##   t2_pri_con_f ~~                                                       
##     t3_pri_con_f      0.442    0.027   16.529    0.000    0.784    0.784
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     3.334    0.029  114.874    0.000    3.334    3.071
##    .t1_pri_con_02     3.834    0.027  142.129    0.000    3.834    3.801
##    .t1_pri_con_03     3.623    0.032  111.773    0.000    3.623    2.989
##    .t1_pri_con_04     3.745    0.029  130.858    0.000    3.745    3.498
##    .t1_pri_con_05     3.842    0.034  112.133    0.000    3.842    3.007
##    .t1_pri_con_06     3.314    0.031  106.100    0.000    3.314    2.837
##    .t1_pri_con_07     3.623    0.034  107.859    0.000    3.623    2.883
##    .t1_pri_con_08     3.624    0.032  114.692    0.000    3.624    3.066
##    .t1_pri_con_09     4.095    0.028  144.074    0.000    4.095    3.852
##    .t2_pri_con_01     3.334    0.029  116.232    0.000    3.334    3.106
##    .t2_pri_con_02     3.824    0.027  140.175    0.000    3.824    3.745
##    .t2_pri_con_03     3.577    0.032  111.955    0.000    3.577    2.991
##    .t2_pri_con_04     3.675    0.029  128.218    0.000    3.675    3.428
##    .t2_pri_con_05     3.784    0.034  109.689    0.000    3.784    2.940
##    .t2_pri_con_06     3.258    0.031  105.070    0.000    3.258    2.810
##    .t2_pri_con_07     3.555    0.033  107.036    0.000    3.555    2.861
##    .t2_pri_con_08     3.551    0.031  112.944    0.000    3.551    3.020
##    .t2_pri_con_09     3.994    0.029  139.243    0.000    3.994    3.721
##    .t3_pri_con_01     3.337    0.029  116.272    0.000    3.337    3.109
##    .t3_pri_con_02     3.770    0.027  139.573    0.000    3.770    3.733
##    .t3_pri_con_03     3.557    0.032  110.256    0.000    3.557    2.949
##    .t3_pri_con_04     3.664    0.029  128.465    0.000    3.664    3.435
##    .t3_pri_con_05     3.710    0.035  106.313    0.000    3.710    2.851
##    .t3_pri_con_06     3.255    0.031  105.108    0.000    3.255    2.811
##    .t3_pri_con_07     3.492    0.034  104.143    0.000    3.492    2.785
##    .t3_pri_con_08     3.560    0.031  114.166    0.000    3.560    3.054
##    .t3_pri_con_09     3.960    0.029  137.190    0.000    3.960    3.669
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_01     0.643    0.026   24.529    0.000    0.643    0.546
##    .t1_pri_con_02     0.543    0.022   24.367    0.000    0.543    0.533
##    .t1_pri_con_03     0.827    0.034   24.399    0.000    0.827    0.563
##    .t1_pri_con_04     0.415    0.019   22.280    0.000    0.415    0.362
##    .t1_pri_con_05     0.907    0.037   24.315    0.000    0.907    0.556
##    .t1_pri_con_06     0.595    0.025   23.518    0.000    0.595    0.436
##    .t1_pri_con_07     0.625    0.028   22.703    0.000    0.625    0.396
##    .t1_pri_con_08     0.571    0.025   22.838    0.000    0.571    0.408
##    .t1_pri_con_09     0.437    0.019   22.697    0.000    0.437    0.386
##    .t2_pri_con_01     0.595    0.024   24.560    0.000    0.595    0.516
##    .t2_pri_con_02     0.548    0.022   24.479    0.000    0.548    0.526
##    .t2_pri_con_03     0.760    0.031   24.346    0.000    0.760    0.532
##    .t2_pri_con_04     0.388    0.017   22.340    0.000    0.388    0.338
##    .t2_pri_con_05     0.901    0.037   24.475    0.000    0.901    0.544
##    .t2_pri_con_06     0.543    0.023   23.449    0.000    0.543    0.404
##    .t2_pri_con_07     0.550    0.024   22.548    0.000    0.550    0.356
##    .t2_pri_con_08     0.522    0.023   22.707    0.000    0.522    0.378
##    .t2_pri_con_09     0.430    0.019   22.703    0.000    0.430    0.373
##    .t3_pri_con_01     0.583    0.024   24.323    0.000    0.583    0.506
##    .t3_pri_con_02     0.516    0.021   24.116    0.000    0.516    0.506
##    .t3_pri_con_03     0.772    0.032   24.254    0.000    0.772    0.531
##    .t3_pri_con_04     0.361    0.016   21.902    0.000    0.361    0.318
##    .t3_pri_con_05     0.923    0.038   24.588    0.000    0.923    0.545
##    .t3_pri_con_06     0.525    0.022   23.386    0.000    0.525    0.391
##    .t3_pri_con_07     0.559    0.025   22.459    0.000    0.559    0.355
##    .t3_pri_con_08     0.481    0.022   22.322    0.000    0.481    0.354
##    .t3_pri_con_09     0.427    0.019   22.773    0.000    0.427    0.367
##     t1_pri_con_f      0.536    0.030   17.573    0.000    1.000    1.000
##     t2_pri_con_f      0.558    0.031   17.728    0.000    1.000    1.000
##     t3_pri_con_f      0.569    0.032   17.672    0.000    1.000    1.000

1.2.2.3 Second-Order Model Unconstrained

We again run models in which we build sub-dimensions referring to the empirical EFA results and theoretical considerations. Resulting model fits the data better than unidimensional one.

model <- '
# create factors
t1_inf_sha_att_f =~ 1*t1_inf_sha_att_f1 + t1_inf_sha_att_f2 + t1_inf_sha_att_f3 + t1_inf_sha_att_f4 + t1_inf_sha_att_f5
t2_inf_sha_att_f =~ 1*t2_inf_sha_att_f1 + t2_inf_sha_att_f2 + t2_inf_sha_att_f3 + t2_inf_sha_att_f4 + t2_inf_sha_att_f5
t3_inf_sha_att_f =~ 1*t3_inf_sha_att_f1 + t3_inf_sha_att_f2 + t3_inf_sha_att_f3 + t3_inf_sha_att_f4 + t3_inf_sha_att_f5
t1_inf_sha_att_f1 =~ 1*t1_inf_sha_att_01 + t1_inf_sha_att_02
t1_inf_sha_att_f2 =~ 1*t1_inf_sha_att_03 + t1_inf_sha_att_04
t1_inf_sha_att_f3 =~ 1*t1_inf_sha_att_05 + t1_inf_sha_att_06
t1_inf_sha_att_f4 =~ 1*t1_inf_sha_att_07 + t1_inf_sha_att_08
t1_inf_sha_att_f5 =~ 1*t1_inf_sha_att_10 + t1_inf_sha_att_11
t2_inf_sha_att_f1 =~ 1*t2_inf_sha_att_01 + t2_inf_sha_att_02
t2_inf_sha_att_f2 =~ 1*t2_inf_sha_att_03 + t2_inf_sha_att_04
t2_inf_sha_att_f3 =~ 1*t2_inf_sha_att_05 + t2_inf_sha_att_06
t2_inf_sha_att_f4 =~ 1*t2_inf_sha_att_07 + t2_inf_sha_att_08
t2_inf_sha_att_f5 =~ 1*t2_inf_sha_att_10 + t2_inf_sha_att_11
t3_inf_sha_att_f1 =~ 1*t3_inf_sha_att_01 + t3_inf_sha_att_02
t3_inf_sha_att_f2 =~ 1*t3_inf_sha_att_03 + t3_inf_sha_att_04
t3_inf_sha_att_f3 =~ 1*t3_inf_sha_att_05 + t3_inf_sha_att_06
t3_inf_sha_att_f4 =~ 1*t3_inf_sha_att_07 + t3_inf_sha_att_08
t3_inf_sha_att_f5 =~ 1*t3_inf_sha_att_10 + t3_inf_sha_att_11

# factor covariance
t1_inf_sha_att_f ~~ t2_inf_sha_att_f + t3_inf_sha_att_f
t2_inf_sha_att_f ~~ t3_inf_sha_att_f

# item error covariance
t1_inf_sha_att_01 ~~ t2_inf_sha_att_01 + t3_inf_sha_att_01
t2_inf_sha_att_01 ~~ t3_inf_sha_att_01
t1_inf_sha_att_02 ~~ t2_inf_sha_att_02 + t3_inf_sha_att_02
t2_inf_sha_att_02 ~~ t3_inf_sha_att_02
t1_inf_sha_att_03 ~~ t2_inf_sha_att_03 + t3_inf_sha_att_03
t2_inf_sha_att_03 ~~ t3_inf_sha_att_03
t1_inf_sha_att_04 ~~ t2_inf_sha_att_04 + t3_inf_sha_att_04
t2_inf_sha_att_04 ~~ t3_inf_sha_att_04
t1_inf_sha_att_05 ~~ t2_inf_sha_att_05 + t3_inf_sha_att_05
t2_inf_sha_att_05 ~~ t3_inf_sha_att_05
t1_inf_sha_att_06 ~~ t2_inf_sha_att_06 + t3_inf_sha_att_06
t2_inf_sha_att_06 ~~ t3_inf_sha_att_06
t1_inf_sha_att_07 ~~ t2_inf_sha_att_07 + t3_inf_sha_att_07
t2_inf_sha_att_07 ~~ t3_inf_sha_att_07
t1_inf_sha_att_08 ~~ t2_inf_sha_att_08 + t3_inf_sha_att_08
t2_inf_sha_att_08 ~~ t3_inf_sha_att_08
t1_inf_sha_att_10 ~~ t2_inf_sha_att_10 + t3_inf_sha_att_10
t2_inf_sha_att_10 ~~ t3_inf_sha_att_10
t1_inf_sha_att_11 ~~ t2_inf_sha_att_11 + t3_inf_sha_att_11
t2_inf_sha_att_11 ~~ t3_inf_sha_att_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 182 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        138
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        43
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2673.738
##   Degrees of freedom                               357
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             34051.217
##   Degrees of freedom                               435
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.931
##   Tucker-Lewis Index (TLI)                       0.916
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -47028.014
##   Loglikelihood unrestricted model (H1)     -45691.145
##                                                       
##   Akaike (AIC)                               94332.028
##   Bayesian (BIC)                             95056.027
##   Sample-size adjusted Bayesian (BIC)        94617.652
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.068
##   90 Percent confidence interval - lower         0.066
##   90 Percent confidence interval - upper         0.070
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.080
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_att_f =~                                                       
##     t1_nf_sh_tt_f1        1.000                               0.397    0.397
##     t1_nf_sh_tt_f2        3.125    0.297   10.528    0.000    0.951    0.951
##     t1_nf_sh_tt_f3        3.047    0.289   10.531    0.000    0.934    0.934
##     t1_nf_sh_tt_f4        2.315    0.226   10.222    0.000    0.875    0.875
##     t1_nf_sh_tt_f5        1.469    0.163    9.037    0.000    0.460    0.460
##   t2_inf_sha_att_f =~                                                       
##     t2_nf_sh_tt_f1        1.000                               0.439    0.439
##     t2_nf_sh_tt_f2        2.946    0.269   10.948    0.000    0.959    0.959
##     t2_nf_sh_tt_f3        2.948    0.269   10.940    0.000    0.948    0.948
##     t2_nf_sh_tt_f4        2.172    0.206   10.561    0.000    0.905    0.905
##     t2_nf_sh_tt_f5        1.445    0.153    9.440    0.000    0.479    0.479
##   t3_inf_sha_att_f =~                                                       
##     t3_nf_sh_tt_f1        1.000                               0.446    0.446
##     t3_nf_sh_tt_f2        2.798    0.250   11.195    0.000    0.931    0.931
##     t3_nf_sh_tt_f3        2.710    0.243   11.164    0.000    0.920    0.920
##     t3_nf_sh_tt_f4        2.117    0.195   10.833    0.000    0.893    0.893
##     t3_nf_sh_tt_f5        1.534    0.155    9.869    0.000    0.513    0.513
##   t1_inf_sha_att_f1 =~                                                      
##     t1_nf_sh_tt_01        1.000                               0.779    0.700
##     t1_nf_sh_tt_02        0.866    0.090    9.652    0.000    0.675    0.615
##   t1_inf_sha_att_f2 =~                                                      
##     t1_nf_sh_tt_03        1.000                               1.018    0.923
##     t1_nf_sh_tt_04        0.934    0.017   53.982    0.000    0.951    0.895
##   t1_inf_sha_att_f3 =~                                                      
##     t1_nf_sh_tt_05        1.000                               1.010    0.944
##     t1_nf_sh_tt_06        0.946    0.017   55.477    0.000    0.955    0.879
##   t1_inf_sha_att_f4 =~                                                      
##     t1_nf_sh_tt_07        1.000                               0.820    0.747
##     t1_nf_sh_tt_08        0.902    0.036   25.388    0.000    0.739    0.693
##   t1_inf_sha_att_f5 =~                                                      
##     t1_nf_sh_tt_10        1.000                               0.988    0.936
##     t1_nf_sh_tt_11        0.968    0.034   28.783    0.000    0.957    0.913
##   t2_inf_sha_att_f1 =~                                                      
##     t2_nf_sh_tt_01        1.000                               0.739    0.650
##     t2_nf_sh_tt_02        0.888    0.088   10.091    0.000    0.657    0.604
##   t2_inf_sha_att_f2 =~                                                      
##     t2_nf_sh_tt_03        1.000                               0.996    0.917
##     t2_nf_sh_tt_04        0.955    0.018   53.384    0.000    0.951    0.888
##   t2_inf_sha_att_f3 =~                                                      
##     t2_nf_sh_tt_05        1.000                               1.008    0.946
##     t2_nf_sh_tt_06        0.941    0.017   54.045    0.000    0.949    0.866
##   t2_inf_sha_att_f4 =~                                                      
##     t2_nf_sh_tt_07        1.000                               0.778    0.719
##     t2_nf_sh_tt_08        0.921    0.038   24.499    0.000    0.716    0.671
##   t2_inf_sha_att_f5 =~                                                      
##     t2_nf_sh_tt_10        1.000                               0.978    0.940
##     t2_nf_sh_tt_11        0.999    0.031   32.366    0.000    0.976    0.929
##   t3_inf_sha_att_f1 =~                                                      
##     t3_nf_sh_tt_01        1.000                               0.744    0.657
##     t3_nf_sh_tt_02        0.885    0.084   10.536    0.000    0.659    0.618
##   t3_inf_sha_att_f2 =~                                                      
##     t3_nf_sh_tt_03        1.000                               0.998    0.933
##     t3_nf_sh_tt_04        0.935    0.018   53.069    0.000    0.933    0.886
##   t3_inf_sha_att_f3 =~                                                      
##     t3_nf_sh_tt_05        1.000                               0.978    0.934
##     t3_nf_sh_tt_06        0.949    0.019   50.701    0.000    0.928    0.872
##   t3_inf_sha_att_f4 =~                                                      
##     t3_nf_sh_tt_07        1.000                               0.787    0.752
##     t3_nf_sh_tt_08        0.882    0.035   25.094    0.000    0.694    0.674
##   t3_inf_sha_att_f5 =~                                                      
##     t3_nf_sh_tt_10        1.000                               0.993    0.950
##     t3_nf_sh_tt_11        0.959    0.029   33.537    0.000    0.953    0.915
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_att_f ~~                                                       
##     t2_inf_sh_tt_f        0.058    0.009    6.663    0.000    0.574    0.574
##     t3_inf_sh_tt_f        0.058    0.009    6.710    0.000    0.561    0.561
##   t2_inf_sha_att_f ~~                                                       
##     t3_inf_sh_tt_f        0.068    0.010    6.846    0.000    0.634    0.634
##  .t1_inf_sha_att_01 ~~                                                      
##    .t2_nf_sh_tt_01        0.293    0.029    9.950    0.000    0.293    0.426
##    .t3_nf_sh_tt_01        0.306    0.029   10.516    0.000    0.306    0.451
##  .t2_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_tt_01        0.339    0.031   11.031    0.000    0.339    0.460
##  .t1_inf_sha_att_02 ~~                                                      
##    .t2_nf_sh_tt_02        0.345    0.029   12.033    0.000    0.345    0.461
##    .t3_nf_sh_tt_02        0.326    0.028   11.694    0.000    0.326    0.451
##  .t2_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_tt_02        0.393    0.029   13.749    0.000    0.393    0.542
##  .t1_inf_sha_att_03 ~~                                                      
##    .t2_nf_sh_tt_03        0.071    0.009    8.018    0.000    0.071    0.385
##    .t3_nf_sh_tt_03        0.065    0.009    7.654    0.000    0.065    0.399
##  .t2_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_tt_03        0.067    0.009    7.888    0.000    0.067    0.405
##  .t1_inf_sha_att_04 ~~                                                      
##    .t2_nf_sh_tt_04        0.088    0.009    9.418    0.000    0.088    0.378
##    .t3_nf_sh_tt_04        0.074    0.009    8.031    0.000    0.074    0.318
##  .t2_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_tt_04        0.098    0.010   10.194    0.000    0.098    0.408
##  .t1_inf_sha_att_05 ~~                                                      
##    .t2_nf_sh_tt_05        0.032    0.008    4.320    0.000    0.032    0.264
##    .t3_nf_sh_tt_05        0.036    0.008    4.669    0.000    0.036    0.275
##  .t2_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_tt_05        0.027    0.008    3.518    0.000    0.027    0.207
##  .t1_inf_sha_att_06 ~~                                                      
##    .t2_nf_sh_tt_06        0.152    0.011   13.978    0.000    0.152    0.536
##    .t3_nf_sh_tt_06        0.129    0.010   12.355    0.000    0.129    0.477
##  .t2_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_tt_06        0.137    0.011   12.677    0.000    0.137    0.478
##  .t1_inf_sha_att_07 ~~                                                      
##    .t2_nf_sh_tt_07        0.269    0.020   13.335    0.000    0.269    0.490
##    .t3_nf_sh_tt_07        0.240    0.019   12.636    0.000    0.240    0.476
##  .t2_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_tt_07        0.279    0.020   14.312    0.000    0.279    0.537
##  .t1_inf_sha_att_08 ~~                                                      
##    .t2_nf_sh_tt_08        0.260    0.021   12.509    0.000    0.260    0.427
##    .t3_nf_sh_tt_08        0.275    0.020   13.608    0.000    0.275    0.469
##  .t2_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_tt_08        0.267    0.020   13.031    0.000    0.267    0.442
##  .t1_inf_sha_att_10 ~~                                                      
##    .t2_nf_sh_tt_10        0.032    0.011    3.002    0.003    0.032    0.243
##    .t3_nf_sh_tt_10        0.008    0.011    0.742    0.458    0.008    0.066
##  .t2_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_tt_10        0.006    0.010    0.543    0.587    0.006    0.049
##  .t1_inf_sha_att_11 ~~                                                      
##    .t2_nf_sh_tt_11        0.037    0.011    3.417    0.001    0.037    0.222
##    .t3_nf_sh_tt_11        0.051    0.011    4.794    0.000    0.051    0.286
##  .t2_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_tt_11        0.046    0.010    4.391    0.000    0.046    0.280
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_tt_01    1.704    0.030   57.252    0.000    1.704    1.530
##    .t1_nf_sh_tt_02    1.900    0.029   64.798    0.000    1.900    1.732
##    .t1_nf_sh_tt_03    2.788    0.029   94.585    0.000    2.788    2.527
##    .t1_nf_sh_tt_04    2.940    0.028  103.535    0.000    2.940    2.766
##    .t1_nf_sh_tt_05    2.626    0.029   91.827    0.000    2.626    2.453
##    .t1_nf_sh_tt_06    2.373    0.029   81.700    0.000    2.373    2.183
##    .t1_nf_sh_tt_07    3.010    0.029  102.640    0.000    3.010    2.742
##    .t1_nf_sh_tt_08    2.294    0.029   80.462    0.000    2.294    2.150
##    .t1_nf_sh_tt_10    2.249    0.028   79.658    0.000    2.249    2.129
##    .t1_nf_sh_tt_11    2.295    0.028   81.956    0.000    2.295    2.191
##    .t2_nf_sh_tt_01    1.763    0.030   57.925    0.000    1.763    1.551
##    .t2_nf_sh_tt_02    1.931    0.029   66.323    0.000    1.931    1.777
##    .t2_nf_sh_tt_03    2.904    0.029   99.901    0.000    2.904    2.673
##    .t2_nf_sh_tt_04    2.999    0.029  104.561    0.000    2.999    2.799
##    .t2_nf_sh_tt_05    2.711    0.029   95.014    0.000    2.711    2.543
##    .t2_nf_sh_tt_06    2.428    0.029   82.780    0.000    2.428    2.216
##    .t2_nf_sh_tt_07    3.119    0.029  107.573    0.000    3.119    2.881
##    .t2_nf_sh_tt_08    2.332    0.029   81.491    0.000    2.332    2.182
##    .t2_nf_sh_tt_10    2.271    0.028   81.411    0.000    2.271    2.183
##    .t2_nf_sh_tt_11    2.363    0.028   83.883    0.000    2.363    2.249
##    .t3_nf_sh_tt_01    1.777    0.030   58.735    0.000    1.777    1.569
##    .t3_nf_sh_tt_02    1.887    0.028   66.336    0.000    1.887    1.771
##    .t3_nf_sh_tt_03    2.951    0.029  103.343    0.000    2.951    2.759
##    .t3_nf_sh_tt_04    3.057    0.028  108.669    0.000    3.057    2.901
##    .t3_nf_sh_tt_05    2.737    0.028   97.897    0.000    2.737    2.614
##    .t3_nf_sh_tt_06    2.473    0.028   87.000    0.000    2.473    2.323
##    .t3_nf_sh_tt_07    3.103    0.028  110.981    0.000    3.103    2.965
##    .t3_nf_sh_tt_08    2.367    0.028   85.984    0.000    2.367    2.297
##    .t3_nf_sh_tt_10    2.297    0.028   82.238    0.000    2.297    2.197
##    .t3_nf_sh_tt_11    2.366    0.028   85.092    0.000    2.366    2.272
##     t1_inf_sh_tt_f    0.000                               0.000    0.000
##     t2_inf_sh_tt_f    0.000                               0.000    0.000
##     t3_inf_sh_tt_f    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_tt_01    0.633    0.067    9.405    0.000    0.633    0.510
##    .t1_nf_sh_tt_02    0.748    0.055   13.493    0.000    0.748    0.621
##    .t1_nf_sh_tt_03    0.181    0.013   13.828    0.000    0.181    0.148
##    .t1_nf_sh_tt_04    0.225    0.013   17.462    0.000    0.225    0.199
##    .t1_nf_sh_tt_05    0.125    0.012   10.754    0.000    0.125    0.109
##    .t1_nf_sh_tt_06    0.268    0.014   19.042    0.000    0.268    0.227
##    .t1_nf_sh_tt_07    0.533    0.029   18.143    0.000    0.533    0.442
##    .t1_nf_sh_tt_08    0.591    0.029   20.714    0.000    0.591    0.520
##    .t1_nf_sh_tt_10    0.139    0.031    4.444    0.000    0.139    0.125
##    .t1_nf_sh_tt_11    0.182    0.029    6.191    0.000    0.182    0.166
##    .t2_nf_sh_tt_01    0.746    0.062   12.115    0.000    0.746    0.577
##    .t2_nf_sh_tt_02    0.750    0.052   14.432    0.000    0.750    0.635
##    .t2_nf_sh_tt_03    0.188    0.013   14.749    0.000    0.188    0.159
##    .t2_nf_sh_tt_04    0.243    0.013   18.270    0.000    0.243    0.212
##    .t2_nf_sh_tt_05    0.120    0.011   10.654    0.000    0.120    0.106
##    .t2_nf_sh_tt_06    0.300    0.015   20.340    0.000    0.300    0.250
##    .t2_nf_sh_tt_07    0.567    0.030   19.101    0.000    0.567    0.483
##    .t2_nf_sh_tt_08    0.628    0.029   21.368    0.000    0.628    0.550
##    .t2_nf_sh_tt_10    0.127    0.027    4.711    0.000    0.127    0.117
##    .t2_nf_sh_tt_11    0.151    0.027    5.620    0.000    0.151    0.137
##    .t3_nf_sh_tt_01    0.730    0.060   12.180    0.000    0.730    0.569
##    .t3_nf_sh_tt_02    0.701    0.050   14.131    0.000    0.701    0.618
##    .t3_nf_sh_tt_03    0.148    0.013   11.737    0.000    0.148    0.129
##    .t3_nf_sh_tt_04    0.239    0.013   17.962    0.000    0.239    0.215
##    .t3_nf_sh_tt_05    0.140    0.013   11.159    0.000    0.140    0.127
##    .t3_nf_sh_tt_06    0.273    0.015   18.789    0.000    0.273    0.240
##    .t3_nf_sh_tt_07    0.476    0.027   17.545    0.000    0.476    0.435
##    .t3_nf_sh_tt_08    0.580    0.027   21.640    0.000    0.580    0.546
##    .t3_nf_sh_tt_10    0.107    0.026    4.062    0.000    0.107    0.098
##    .t3_nf_sh_tt_11    0.176    0.025    7.192    0.000    0.176    0.163
##     t1_inf_sh_tt_f    0.096    0.018    5.241    0.000    1.000    1.000
##     t2_inf_sh_tt_f    0.105    0.019    5.434    0.000    1.000    1.000
##     t3_inf_sh_tt_f    0.110    0.020    5.572    0.000    1.000    1.000
##    .t1_nf_sh_tt_f1    0.511    0.064    7.962    0.000    0.842    0.842
##    .t1_nf_sh_tt_f2    0.100    0.015    6.739    0.000    0.096    0.096
##    .t1_nf_sh_tt_f3    0.130    0.015    8.721    0.000    0.127    0.127
##    .t1_nf_sh_tt_f4    0.158    0.021    7.662    0.000    0.235    0.235
##    .t1_nf_sh_tt_f5    0.769    0.043   17.844    0.000    0.788    0.788
##    .t2_nf_sh_tt_f1    0.441    0.056    7.932    0.000    0.808    0.808
##    .t2_nf_sh_tt_f2    0.080    0.013    6.130    0.000    0.081    0.081
##    .t2_nf_sh_tt_f3    0.103    0.014    7.475    0.000    0.101    0.101
##    .t2_nf_sh_tt_f4    0.110    0.019    5.889    0.000    0.181    0.181
##    .t2_nf_sh_tt_f5    0.737    0.039   18.807    0.000    0.770    0.770
##    .t3_nf_sh_tt_f1    0.444    0.054    8.242    0.000    0.801    0.801
##    .t3_nf_sh_tt_f2    0.134    0.015    8.649    0.000    0.134    0.134
##    .t3_nf_sh_tt_f3    0.147    0.016    9.452    0.000    0.154    0.154
##    .t3_nf_sh_tt_f4    0.125    0.019    6.681    0.000    0.203    0.203
##    .t3_nf_sh_tt_f5    0.727    0.039   18.732    0.000    0.737    0.737

1.2.2.4 Second-Order Model at All Waves Constrained

model <- '
# create factors
t1_inf_sha_att_f =~ 1*t1_inf_sha_att_f1 + o2*t1_inf_sha_att_f2 + o3*t1_inf_sha_att_f3 + o4*t1_inf_sha_att_f4 + o5*t1_inf_sha_att_f5
t2_inf_sha_att_f =~ 1*t2_inf_sha_att_f1 + o2*t2_inf_sha_att_f2 + o3*t2_inf_sha_att_f3 + o4*t2_inf_sha_att_f4 + o5*t2_inf_sha_att_f5
t3_inf_sha_att_f =~ 1*t3_inf_sha_att_f1 + o2*t3_inf_sha_att_f2 + o3*t3_inf_sha_att_f3 + o4*t3_inf_sha_att_f4 + o5*t3_inf_sha_att_f5
t1_inf_sha_att_f1 =~ 1*t1_inf_sha_att_01 + j2*t1_inf_sha_att_02
t1_inf_sha_att_f2 =~ 1*t1_inf_sha_att_03 + k2*t1_inf_sha_att_04
t1_inf_sha_att_f3 =~ 1*t1_inf_sha_att_05 + l2*t1_inf_sha_att_06
t1_inf_sha_att_f4 =~ 1*t1_inf_sha_att_07 + m2*t1_inf_sha_att_08
t1_inf_sha_att_f5 =~ 1*t1_inf_sha_att_10 + n2*t1_inf_sha_att_11
t2_inf_sha_att_f1 =~ 1*t2_inf_sha_att_01 + j2*t2_inf_sha_att_02
t2_inf_sha_att_f2 =~ 1*t2_inf_sha_att_03 + k2*t2_inf_sha_att_04
t2_inf_sha_att_f3 =~ 1*t2_inf_sha_att_05 + l2*t2_inf_sha_att_06
t2_inf_sha_att_f4 =~ 1*t2_inf_sha_att_07 + m2*t2_inf_sha_att_08
t2_inf_sha_att_f5 =~ 1*t2_inf_sha_att_10 + n2*t2_inf_sha_att_11
t3_inf_sha_att_f1 =~ 1*t3_inf_sha_att_01 + j2*t3_inf_sha_att_02
t3_inf_sha_att_f2 =~ 1*t3_inf_sha_att_03 + k2*t3_inf_sha_att_04
t3_inf_sha_att_f3 =~ 1*t3_inf_sha_att_05 + l2*t3_inf_sha_att_06
t3_inf_sha_att_f4 =~ 1*t3_inf_sha_att_07 + m2*t3_inf_sha_att_08
t3_inf_sha_att_f5 =~ 1*t3_inf_sha_att_10 + n2*t3_inf_sha_att_11

# factor covariance
t1_inf_sha_att_f ~~ t2_inf_sha_att_f + t3_inf_sha_att_f
t2_inf_sha_att_f ~~ t3_inf_sha_att_f

# item error covariance
t1_inf_sha_att_01 ~~ t2_inf_sha_att_01 + t3_inf_sha_att_01
t2_inf_sha_att_01 ~~ t3_inf_sha_att_01
t1_inf_sha_att_02 ~~ t2_inf_sha_att_02 + t3_inf_sha_att_02
t2_inf_sha_att_02 ~~ t3_inf_sha_att_02
t1_inf_sha_att_03 ~~ t2_inf_sha_att_03 + t3_inf_sha_att_03
t2_inf_sha_att_03 ~~ t3_inf_sha_att_03
t1_inf_sha_att_04 ~~ t2_inf_sha_att_04 + t3_inf_sha_att_04
t2_inf_sha_att_04 ~~ t3_inf_sha_att_04
t1_inf_sha_att_05 ~~ t2_inf_sha_att_05 + t3_inf_sha_att_05
t2_inf_sha_att_05 ~~ t3_inf_sha_att_05
t1_inf_sha_att_06 ~~ t2_inf_sha_att_06 + t3_inf_sha_att_06
t2_inf_sha_att_06 ~~ t3_inf_sha_att_06
t1_inf_sha_att_07 ~~ t2_inf_sha_att_07 + t3_inf_sha_att_07
t2_inf_sha_att_07 ~~ t3_inf_sha_att_07
t1_inf_sha_att_08 ~~ t2_inf_sha_att_08 + t3_inf_sha_att_08
t2_inf_sha_att_08 ~~ t3_inf_sha_att_08
t1_inf_sha_att_10 ~~ t2_inf_sha_att_10 + t3_inf_sha_att_10
t2_inf_sha_att_10 ~~ t3_inf_sha_att_10
t1_inf_sha_att_11 ~~ t2_inf_sha_att_11 + t3_inf_sha_att_11
t2_inf_sha_att_11 ~~ t3_inf_sha_att_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 146 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        138
##   Number of equality constraints                    18
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        43
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2683.427
##   Degrees of freedom                               375
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             34051.217
##   Degrees of freedom                               435
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.931
##   Tucker-Lewis Index (TLI)                       0.920
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -47032.859
##   Loglikelihood unrestricted model (H1)     -45691.145
##                                                       
##   Akaike (AIC)                               94305.718
##   Bayesian (BIC)                             94935.282
##   Sample-size adjusted Bayesian (BIC)        94554.087
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.066
##   90 Percent confidence interval - lower         0.064
##   90 Percent confidence interval - upper         0.069
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.080
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_att_f =~                                                       
##     t1_nf___1             1.000                               0.417    0.417
##     t1_nf___2 (o2)        2.954    0.179   16.540    0.000    0.950    0.950
##     t1_nf___3 (o3)        2.902    0.175   16.543    0.000    0.934    0.934
##     t1_nf___4 (o4)        2.201    0.138   15.934    0.000    0.875    0.875
##     t1_nf___5 (o5)        1.483    0.101   14.749    0.000    0.484    0.484
##   t2_inf_sha_att_f =~                                                       
##     t2_nf___1             1.000                               0.439    0.439
##     t2_nf___2 (o2)        2.954    0.179   16.540    0.000    0.960    0.960
##     t2_nf___3 (o3)        2.902    0.175   16.543    0.000    0.946    0.946
##     t2_nf___4 (o4)        2.201    0.138   15.934    0.000    0.907    0.907
##     t2_nf___5 (o5)        1.483    0.101   14.749    0.000    0.487    0.487
##   t3_inf_sha_att_f =~                                                       
##     t3_nf___1             1.000                               0.425    0.425
##     t3_nf___2 (o2)        2.954    0.179   16.540    0.000    0.931    0.931
##     t3_nf___3 (o3)        2.902    0.175   16.543    0.000    0.924    0.924
##     t3_nf___4 (o4)        2.201    0.138   15.934    0.000    0.891    0.891
##     t3_nf___5 (o5)        1.483    0.101   14.749    0.000    0.481    0.481
##   t1_inf_sha_att_f1 =~                                                      
##     t1_n___01             1.000                               0.780    0.698
##     t1_n___02 (j2)        0.881    0.062   14.292    0.000    0.687    0.624
##   t1_inf_sha_att_f2 =~                                                      
##     t1_n___03             1.000                               1.012    0.921
##     t1_n___04 (k2)        0.941    0.012   77.226    0.000    0.952    0.896
##   t1_inf_sha_att_f3 =~                                                      
##     t1_n___05             1.000                               1.011    0.944
##     t1_n___06 (l2)        0.945    0.012   75.718    0.000    0.955    0.879
##   t1_inf_sha_att_f4 =~                                                      
##     t1_n___07             1.000                               0.819    0.747
##     t1_n___08 (m2)        0.901    0.026   35.176    0.000    0.737    0.692
##   t1_inf_sha_att_f5 =~                                                      
##     t1_n___10             1.000                               0.997    0.934
##     t1_n___11 (n2)        0.976    0.020   49.065    0.000    0.973    0.918
##   t2_inf_sha_att_f1 =~                                                      
##     t2_n___01             1.000                               0.743    0.653
##     t2_n___02 (j2)        0.881    0.062   14.292    0.000    0.654    0.602
##   t2_inf_sha_att_f2 =~                                                      
##     t2_n___03             1.000                               1.004    0.919
##     t2_n___04 (k2)        0.941    0.012   77.226    0.000    0.945    0.886
##   t2_inf_sha_att_f3 =~                                                      
##     t2_n___05             1.000                               1.001    0.944
##     t2_n___06 (l2)        0.945    0.012   75.718    0.000    0.946    0.866
##   t2_inf_sha_att_f4 =~                                                      
##     t2_n___07             1.000                               0.792    0.726
##     t2_n___08 (m2)        0.901    0.026   35.176    0.000    0.713    0.668
##   t2_inf_sha_att_f5 =~                                                      
##     t2_n___10             1.000                               0.994    0.949
##     t2_n___11 (n2)        0.976    0.020   49.065    0.000    0.969    0.921
##   t3_inf_sha_att_f1 =~                                                      
##     t3_n___01             1.000                               0.739    0.655
##     t3_n___02 (j2)        0.881    0.062   14.292    0.000    0.651    0.613
##   t3_inf_sha_att_f2 =~                                                      
##     t3_n___03             1.000                               0.997    0.933
##     t3_n___04 (k2)        0.941    0.012   77.226    0.000    0.939    0.887
##   t3_inf_sha_att_f3 =~                                                      
##     t3_n___05             1.000                               0.987    0.936
##     t3_n___06 (l2)        0.945    0.012   75.718    0.000    0.933    0.872
##   t3_inf_sha_att_f4 =~                                                      
##     t3_n___07             1.000                               0.776    0.746
##     t3_n___08 (m2)        0.901    0.026   35.176    0.000    0.699    0.677
##   t3_inf_sha_att_f5 =~                                                      
##     t3_n___10             1.000                               0.968    0.942
##     t3_n___11 (n2)        0.976    0.020   49.065    0.000    0.944    0.919
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_att_f ~~                                                       
##     t2_inf_sh_tt_f        0.061    0.008    7.555    0.000    0.574    0.574
##     t3_inf_sh_tt_f        0.057    0.008    7.535    0.000    0.561    0.561
##   t2_inf_sha_att_f ~~                                                       
##     t3_inf_sh_tt_f        0.065    0.008    7.664    0.000    0.634    0.634
##  .t1_inf_sha_att_01 ~~                                                      
##    .t2_nf_sh_tt_01        0.292    0.029    9.940    0.000    0.292    0.423
##    .t3_nf_sh_tt_01        0.306    0.029   10.517    0.000    0.306    0.449
##  .t2_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_tt_01        0.339    0.031   11.038    0.000    0.339    0.462
##  .t1_inf_sha_att_02 ~~                                                      
##    .t2_nf_sh_tt_02        0.345    0.029   12.034    0.000    0.345    0.462
##    .t3_nf_sh_tt_02        0.326    0.028   11.683    0.000    0.326    0.451
##  .t2_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_tt_02        0.393    0.029   13.745    0.000    0.393    0.540
##  .t1_inf_sha_att_03 ~~                                                      
##    .t2_nf_sh_tt_03        0.071    0.009    7.984    0.000    0.071    0.384
##    .t3_nf_sh_tt_03        0.065    0.009    7.655    0.000    0.065    0.395
##  .t2_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_tt_03        0.067    0.009    7.854    0.000    0.067    0.404
##  .t1_inf_sha_att_04 ~~                                                      
##    .t2_nf_sh_tt_04        0.088    0.009    9.414    0.000    0.088    0.377
##    .t3_nf_sh_tt_04        0.074    0.009    8.046    0.000    0.074    0.321
##  .t2_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_tt_04        0.098    0.010   10.200    0.000    0.098    0.407
##  .t1_inf_sha_att_05 ~~                                                      
##    .t2_nf_sh_tt_05        0.033    0.008    4.332    0.000    0.033    0.264
##    .t3_nf_sh_tt_05        0.037    0.008    4.697    0.000    0.037    0.278
##  .t2_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_tt_05        0.027    0.008    3.517    0.000    0.027    0.207
##  .t1_inf_sha_att_06 ~~                                                      
##    .t2_nf_sh_tt_06        0.152    0.011   13.980    0.000    0.152    0.537
##    .t3_nf_sh_tt_06        0.129    0.010   12.344    0.000    0.129    0.476
##  .t2_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_tt_06        0.137    0.011   12.677    0.000    0.137    0.478
##  .t1_inf_sha_att_07 ~~                                                      
##    .t2_nf_sh_tt_07        0.268    0.020   13.318    0.000    0.268    0.491
##    .t3_nf_sh_tt_07        0.241    0.019   12.677    0.000    0.241    0.475
##  .t2_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_tt_07        0.279    0.019   14.313    0.000    0.279    0.536
##  .t1_inf_sha_att_08 ~~                                                      
##    .t2_nf_sh_tt_08        0.260    0.021   12.518    0.000    0.260    0.426
##    .t3_nf_sh_tt_08        0.275    0.020   13.608    0.000    0.275    0.470
##  .t2_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_tt_08        0.267    0.020   13.034    0.000    0.267    0.442
##  .t1_inf_sha_att_10 ~~                                                      
##    .t2_nf_sh_tt_10        0.031    0.011    2.932    0.003    0.031    0.250
##    .t3_nf_sh_tt_10        0.009    0.011    0.833    0.405    0.009    0.069
##  .t2_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_tt_10        0.006    0.010    0.554    0.579    0.006    0.051
##  .t1_inf_sha_att_11 ~~                                                      
##    .t2_nf_sh_tt_11        0.038    0.011    3.499    0.000    0.038    0.218
##    .t3_nf_sh_tt_11        0.051    0.011    4.737    0.000    0.051    0.297
##  .t2_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_tt_11        0.046    0.010    4.387    0.000    0.046    0.275
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_tt_01    1.704    0.030   57.045    0.000    1.704    1.524
##    .t1_nf_sh_tt_02    1.900    0.029   64.555    0.000    1.900    1.726
##    .t1_nf_sh_tt_03    2.788    0.029   95.014    0.000    2.788    2.538
##    .t1_nf_sh_tt_04    2.940    0.028  103.517    0.000    2.940    2.765
##    .t1_nf_sh_tt_05    2.626    0.029   91.815    0.000    2.626    2.453
##    .t1_nf_sh_tt_06    2.373    0.029   81.724    0.000    2.373    2.184
##    .t1_nf_sh_tt_07    3.010    0.029  102.744    0.000    3.010    2.745
##    .t1_nf_sh_tt_08    2.294    0.028   80.559    0.000    2.294    2.153
##    .t1_nf_sh_tt_10    2.249    0.029   78.816    0.000    2.249    2.107
##    .t1_nf_sh_tt_11    2.295    0.028   81.021    0.000    2.295    2.166
##    .t2_nf_sh_tt_01    1.763    0.030   57.906    0.000    1.763    1.551
##    .t2_nf_sh_tt_02    1.931    0.029   66.338    0.000    1.931    1.777
##    .t2_nf_sh_tt_03    2.904    0.029   99.355    0.000    2.904    2.659
##    .t2_nf_sh_tt_04    2.999    0.029  105.004    0.000    2.999    2.811
##    .t2_nf_sh_tt_05    2.711    0.028   95.577    0.000    2.711    2.558
##    .t2_nf_sh_tt_06    2.428    0.029   83.016    0.000    2.428    2.222
##    .t2_nf_sh_tt_07    3.119    0.029  106.837    0.000    3.119    2.861
##    .t2_nf_sh_tt_08    2.332    0.029   81.536    0.000    2.332    2.183
##    .t2_nf_sh_tt_10    2.271    0.028   80.899    0.000    2.271    2.169
##    .t2_nf_sh_tt_11    2.363    0.028   83.753    0.000    2.363    2.245
##    .t3_nf_sh_tt_01    1.777    0.030   58.962    0.000    1.777    1.575
##    .t3_nf_sh_tt_02    1.887    0.028   66.581    0.000    1.887    1.778
##    .t3_nf_sh_tt_03    2.951    0.029  103.374    0.000    2.951    2.760
##    .t3_nf_sh_tt_04    3.057    0.028  108.245    0.000    3.057    2.890
##    .t3_nf_sh_tt_05    2.737    0.028   97.145    0.000    2.737    2.594
##    .t3_nf_sh_tt_06    2.473    0.029   86.630    0.000    2.473    2.313
##    .t3_nf_sh_tt_07    3.103    0.028  111.586    0.000    3.103    2.981
##    .t3_nf_sh_tt_08    2.367    0.028   85.840    0.000    2.367    2.293
##    .t3_nf_sh_tt_10    2.297    0.027   83.630    0.000    2.297    2.234
##    .t3_nf_sh_tt_11    2.366    0.027   86.179    0.000    2.366    2.301
##     t1_inf_sh_tt_f    0.000                               0.000    0.000
##     t2_inf_sh_tt_f    0.000                               0.000    0.000
##     t3_inf_sh_tt_f    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_tt_01    0.641    0.053   11.993    0.000    0.641    0.513
##    .t1_nf_sh_tt_02    0.740    0.047   15.886    0.000    0.740    0.611
##    .t1_nf_sh_tt_03    0.183    0.013   14.444    0.000    0.183    0.151
##    .t1_nf_sh_tt_04    0.223    0.013   17.744    0.000    0.223    0.198
##    .t1_nf_sh_tt_05    0.125    0.011   11.153    0.000    0.125    0.109
##    .t1_nf_sh_tt_06    0.269    0.014   19.433    0.000    0.269    0.228
##    .t1_nf_sh_tt_07    0.532    0.029   18.583    0.000    0.532    0.443
##    .t1_nf_sh_tt_08    0.591    0.028   21.016    0.000    0.591    0.521
##    .t1_nf_sh_tt_10    0.145    0.022    6.677    0.000    0.145    0.127
##    .t1_nf_sh_tt_11    0.176    0.021    8.457    0.000    0.176    0.157
##    .t2_nf_sh_tt_01    0.742    0.053   14.027    0.000    0.742    0.574
##    .t2_nf_sh_tt_02    0.753    0.045   16.555    0.000    0.753    0.638
##    .t2_nf_sh_tt_03    0.185    0.012   14.846    0.000    0.185    0.155
##    .t2_nf_sh_tt_04    0.245    0.013   18.747    0.000    0.245    0.216
##    .t2_nf_sh_tt_05    0.121    0.011   11.118    0.000    0.121    0.108
##    .t2_nf_sh_tt_06    0.299    0.015   20.526    0.000    0.299    0.251
##    .t2_nf_sh_tt_07    0.562    0.029   19.212    0.000    0.562    0.473
##    .t2_nf_sh_tt_08    0.632    0.029   21.753    0.000    0.632    0.554
##    .t2_nf_sh_tt_10    0.109    0.021    5.281    0.000    0.109    0.099
##    .t2_nf_sh_tt_11    0.168    0.020    8.300    0.000    0.168    0.152
##    .t3_nf_sh_tt_01    0.728    0.052   13.883    0.000    0.728    0.571
##    .t3_nf_sh_tt_02    0.703    0.044   15.940    0.000    0.703    0.624
##    .t3_nf_sh_tt_03    0.149    0.012   12.426    0.000    0.149    0.130
##    .t3_nf_sh_tt_04    0.238    0.013   18.434    0.000    0.238    0.213
##    .t3_nf_sh_tt_05    0.139    0.012   11.682    0.000    0.139    0.125
##    .t3_nf_sh_tt_06    0.273    0.014   19.345    0.000    0.273    0.239
##    .t3_nf_sh_tt_07    0.481    0.026   18.238    0.000    0.481    0.444
##    .t3_nf_sh_tt_08    0.577    0.027   21.748    0.000    0.577    0.541
##    .t3_nf_sh_tt_10    0.119    0.021    5.768    0.000    0.119    0.113
##    .t3_nf_sh_tt_11    0.165    0.020    8.276    0.000    0.165    0.156
##     t1_inf_sh_tt_f    0.106    0.013    7.964    0.000    1.000    1.000
##     t2_inf_sh_tt_f    0.106    0.013    7.966    0.000    1.000    1.000
##     t3_inf_sh_tt_f    0.099    0.012    7.950    0.000    1.000    1.000
##    .t1_nf_sh_tt_f1    0.502    0.050   10.036    0.000    0.826    0.826
##    .t1_nf_sh_tt_f2    0.100    0.014    7.293    0.000    0.098    0.098
##    .t1_nf_sh_tt_f3    0.131    0.014    9.214    0.000    0.128    0.128
##    .t1_nf_sh_tt_f4    0.158    0.020    7.918    0.000    0.235    0.235
##    .t1_nf_sh_tt_f5    0.761    0.037   20.692    0.000    0.766    0.766
##    .t2_nf_sh_tt_f1    0.445    0.046    9.577    0.000    0.807    0.807
##    .t2_nf_sh_tt_f2    0.080    0.013    6.275    0.000    0.079    0.079
##    .t2_nf_sh_tt_f3    0.106    0.013    8.100    0.000    0.106    0.106
##    .t2_nf_sh_tt_f4    0.111    0.019    5.994    0.000    0.177    0.177
##    .t2_nf_sh_tt_f5    0.753    0.036   20.917    0.000    0.763    0.763
##    .t3_nf_sh_tt_f1    0.447    0.046    9.745    0.000    0.819    0.819
##    .t3_nf_sh_tt_f2    0.133    0.014    9.181    0.000    0.134    0.134
##    .t3_nf_sh_tt_f3    0.143    0.015    9.645    0.000    0.147    0.147
##    .t3_nf_sh_tt_f4    0.124    0.018    6.981    0.000    0.206    0.206
##    .t3_nf_sh_tt_f5    0.720    0.035   20.713    0.000    0.768    0.768

1.2.3 Reliability

reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t1", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.817          0.877          0.924
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t2", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.824          0.888          0.920
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t3", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.812          0.875          0.920

1.2.4 Longitudinal Invariance

(anova(get(paste("fit", name, no - 1, sep = "_")), get(paste("fit", name, no, sep = "_"))))

1.3 Online Sharing of Personal Information

1.3.1 EFA

no <- 0
name <- "inf_sha_beh"
d_tmp <- select(d_wide, contains(paste0("t1_", name)), -contains("_m"))
model <- fa.parallel(d_tmp, fa = "fa", fm = "ml")

## Parallel analysis suggests that the number of factors =  4  and the number of components =  NA
factan <- fa(d_tmp, fm = "ml", nfactors = model$nfact, rotate = "promax")
print(factan, sort = TRUE, cut = 0.3)
## Factor Analysis using method =  ml
## Call: fa(r = d_tmp, nfactors = model$nfact, rotate = "promax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                   item   ML1   ML2   ML4   ML3   h2     u2 com
## t1_inf_sha_beh_03    4  1.03                   0.94 0.0591 1.0
## t1_inf_sha_beh_04    5  1.02                   0.94 0.0555 1.0
## t1_inf_sha_beh_05    6  0.89              0.43 1.00 0.0049 1.5
## t1_inf_sha_beh_fs    1  0.83                   1.00 0.0039 1.2
## t1_inf_sha_beh_07    8  0.82                   0.72 0.2835 1.0
## t1_inf_sha_beh_06    7  0.81              0.33 0.82 0.1771 1.3
## t1_inf_sha_beh_08    9  0.52                   0.48 0.5224 1.4
## t1_inf_sha_beh_10   11        1.07             1.00 0.0050 1.0
## t1_inf_sha_beh_11   12        0.79             0.65 0.3544 1.0
## t1_inf_sha_beh_09   10        0.42             0.22 0.7824 1.0
## t1_inf_sha_beh_01    2              0.81       0.63 0.3750 1.0
## t1_inf_sha_beh_02    3              0.49       0.24 0.7597 1.1
## 
##                        ML1  ML2  ML4  ML3
## SS loadings           5.31 1.98 0.89 0.44
## Proportion Var        0.44 0.17 0.07 0.04
## Cumulative Var        0.44 0.61 0.68 0.72
## Proportion Explained  0.62 0.23 0.10 0.05
## Cumulative Proportion 0.62 0.85 0.95 1.00
## 
##  With factor correlations of 
##      ML1  ML2  ML4  ML3
## ML1 1.00 0.56 0.47 0.18
## ML2 0.56 1.00 0.41 0.12
## ML4 0.47 0.41 1.00 0.27
## ML3 0.18 0.12 0.27 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 4 factors are sufficient.
## 
## The degrees of freedom for the null model are  66  and the objective function was  15.1 with Chi Square of  21047
## The degrees of freedom for the model are 24  and the objective function was  1.85 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.05 
## 
## The harmonic number of observations is  1398 with the empirical chi square  198  with prob <  2.9e-29 
## The total number of observations was  1403  with Likelihood Chi Square =  2575  with prob <  0 
## 
## Tucker Lewis Index of factoring reliability =  0.665
## RMSEA index =  0.275  and the 90 % confidence intervals are  0.266 0.284
## BIC =  2401
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                    ML1  ML2  ML4  ML3
## Correlation of (regression) scores with factors   1.00 1.00 0.89 0.95
## Multiple R square of scores with factors          0.99 0.99 0.79 0.91
## Minimum correlation of possible factor scores     0.98 0.99 0.58 0.82

1.3.2 CFA

1.3.2.1 First-Order Model Unconstrained

First-order model shows poor fit. Needs to be adapted (see second order model).

model <- '
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_01 + t1_inf_sha_beh_02 + t1_inf_sha_beh_03 + t1_inf_sha_beh_04 + t1_inf_sha_beh_05 + t1_inf_sha_beh_06 + t1_inf_sha_beh_07 + t1_inf_sha_beh_08 + t1_inf_sha_beh_09 + t1_inf_sha_beh_10 + t1_inf_sha_beh_11
t2_inf_sha_beh_f =~ 1*t2_inf_sha_beh_01 + t2_inf_sha_beh_02 + t2_inf_sha_beh_03 + t2_inf_sha_beh_04 + t2_inf_sha_beh_05 + t2_inf_sha_beh_06 + t2_inf_sha_beh_07 + t2_inf_sha_beh_08 + t2_inf_sha_beh_09 + t2_inf_sha_beh_10 + t2_inf_sha_beh_11
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_01 + t3_inf_sha_beh_02 + t3_inf_sha_beh_03 + t3_inf_sha_beh_04 + t3_inf_sha_beh_05 + t3_inf_sha_beh_06 + t3_inf_sha_beh_07 + t3_inf_sha_beh_08 + t3_inf_sha_beh_09 + t3_inf_sha_beh_10 + t3_inf_sha_beh_11

# factor covariance
t1_inf_sha_beh_f ~~ t2_inf_sha_beh_f + t3_inf_sha_beh_f
t2_inf_sha_beh_f ~~ t3_inf_sha_beh_f

# item error covariance
t1_inf_sha_beh_01 ~~ t2_inf_sha_beh_01 + t3_inf_sha_beh_01
t2_inf_sha_beh_01 ~~ t3_inf_sha_beh_01
t1_inf_sha_beh_02 ~~ t2_inf_sha_beh_02 + t3_inf_sha_beh_02
t2_inf_sha_beh_02 ~~ t3_inf_sha_beh_02
t1_inf_sha_beh_03 ~~ t2_inf_sha_beh_03 + t3_inf_sha_beh_03
t2_inf_sha_beh_03 ~~ t3_inf_sha_beh_03
t1_inf_sha_beh_04 ~~ t2_inf_sha_beh_04 + t3_inf_sha_beh_04
t2_inf_sha_beh_04 ~~ t3_inf_sha_beh_04
t1_inf_sha_beh_05 ~~ t2_inf_sha_beh_05 + t3_inf_sha_beh_05
t2_inf_sha_beh_05 ~~ t3_inf_sha_beh_05
t1_inf_sha_beh_06 ~~ t2_inf_sha_beh_06 + t3_inf_sha_beh_06
t2_inf_sha_beh_06 ~~ t3_inf_sha_beh_06
t1_inf_sha_beh_07 ~~ t2_inf_sha_beh_07 + t3_inf_sha_beh_07
t2_inf_sha_beh_07 ~~ t3_inf_sha_beh_07
t1_inf_sha_beh_08 ~~ t2_inf_sha_beh_08 + t3_inf_sha_beh_08
t2_inf_sha_beh_08 ~~ t3_inf_sha_beh_08
t1_inf_sha_beh_09 ~~ t2_inf_sha_beh_09 + t3_inf_sha_beh_09
t2_inf_sha_beh_09 ~~ t3_inf_sha_beh_09
t1_inf_sha_beh_10 ~~ t2_inf_sha_beh_10 + t3_inf_sha_beh_10
t2_inf_sha_beh_10 ~~ t3_inf_sha_beh_10
t1_inf_sha_beh_11 ~~ t2_inf_sha_beh_11 + t3_inf_sha_beh_11
t2_inf_sha_beh_11 ~~ t3_inf_sha_beh_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 194 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        135
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        40
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              8471.050
##   Degrees of freedom                               459
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             41941.362
##   Degrees of freedom                               528
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.807
##   Tucker-Lewis Index (TLI)                       0.777
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -43502.943
##   Loglikelihood unrestricted model (H1)     -39267.418
##                                                       
##   Akaike (AIC)                               87275.886
##   Bayesian (BIC)                             87984.145
##   Sample-size adjusted Bayesian (BIC)        87555.300
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.112
##   90 Percent confidence interval - lower         0.109
##   90 Percent confidence interval - upper         0.114
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f =~                                                      
##     t1_nf_sh_bh_01       1.000                               0.316    0.291
##     t1_nf_sh_bh_02       0.353    0.056    6.286    0.000    0.111    0.189
##     t1_nf_sh_bh_03       3.219    0.267   12.046    0.000    1.016    0.953
##     t1_nf_sh_bh_04       3.198    0.266   12.042    0.000    1.010    0.951
##     t1_nf_sh_bh_05       2.843    0.237   12.007    0.000    0.898    0.910
##     t1_nf_sh_bh_06       2.633    0.221   11.933    0.000    0.832    0.850
##     t1_nf_sh_bh_07       2.683    0.227   11.829    0.000    0.847    0.811
##     t1_nf_sh_bh_08       1.902    0.167   11.364    0.000    0.601    0.634
##     t1_nf_sh_bh_09       0.560    0.068    8.189    0.000    0.177    0.252
##     t1_nf_sh_bh_10       1.228    0.119   10.312    0.000    0.388    0.442
##     t1_nf_sh_bh_11       1.092    0.108   10.123    0.000    0.345    0.409
##   t2_inf_sha_beh_f =~                                                      
##     t2_nf_sh_bh_01       1.000                               0.319    0.299
##     t2_nf_sh_bh_02       0.269    0.044    6.058    0.000    0.086    0.177
##     t2_nf_sh_bh_03       3.078    0.245   12.537    0.000    0.982    0.947
##     t2_nf_sh_bh_04       3.103    0.248   12.521    0.000    0.991    0.938
##     t2_nf_sh_bh_05       2.684    0.216   12.438    0.000    0.857    0.887
##     t2_nf_sh_bh_06       2.488    0.201   12.358    0.000    0.794    0.829
##     t2_nf_sh_bh_07       2.590    0.211   12.256    0.000    0.827    0.798
##     t2_nf_sh_bh_08       1.907    0.162   11.790    0.000    0.609    0.636
##     t2_nf_sh_bh_09       0.557    0.066    8.499    0.000    0.178    0.256
##     t2_nf_sh_bh_10       1.285    0.118   10.897    0.000    0.410    0.478
##     t2_nf_sh_bh_11       1.041    0.101   10.346    0.000    0.332    0.406
##   t3_inf_sha_beh_f =~                                                      
##     t3_nf_sh_bh_01       1.000                               0.301    0.282
##     t3_nf_sh_bh_02       0.320    0.051    6.264    0.000    0.096    0.188
##     t3_nf_sh_bh_03       3.136    0.266   11.796    0.000    0.943    0.953
##     t3_nf_sh_bh_04       3.161    0.268   11.776    0.000    0.951    0.938
##     t3_nf_sh_bh_05       2.820    0.240   11.732    0.000    0.848    0.906
##     t3_nf_sh_bh_06       2.551    0.219   11.643    0.000    0.767    0.836
##     t3_nf_sh_bh_07       2.613    0.227   11.487    0.000    0.786    0.770
##     t3_nf_sh_bh_08       1.890    0.170   11.090    0.000    0.569    0.622
##     t3_nf_sh_bh_09       0.543    0.069    7.850    0.000    0.163    0.232
##     t3_nf_sh_bh_10       1.217    0.121   10.064    0.000    0.366    0.429
##     t3_nf_sh_bh_11       0.931    0.099    9.410    0.000    0.280    0.358
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f ~~                                                       
##     t2_inf_sh_bh_f        0.061    0.008    7.330    0.000    0.606    0.606
##     t3_inf_sh_bh_f        0.057    0.008    7.168    0.000    0.595    0.595
##   t2_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.058    0.008    7.171    0.000    0.609    0.609
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.415    0.031   13.580    0.000    0.415    0.393
##    .t3_nf_sh_bh_01        0.396    0.030   13.017    0.000    0.396    0.373
##  .t2_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.455    0.031   14.844    0.000    0.455    0.436
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.069    0.008    9.056    0.000    0.069    0.250
##    .t3_nf_sh_bh_02        0.069    0.008    8.593    0.000    0.069    0.237
##  .t2_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.069    0.007   10.315    0.000    0.069    0.287
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.030    0.005    6.400    0.000    0.030    0.279
##    .t3_nf_sh_bh_03        0.029    0.004    6.769    0.000    0.029    0.305
##  .t2_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.044    0.005    9.416    0.000    0.044    0.440
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.043    0.005    8.559    0.000    0.043    0.361
##    .t3_nf_sh_bh_04        0.034    0.005    7.150    0.000    0.034    0.298
##  .t2_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.062    0.005   11.292    0.000    0.062    0.478
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.043    0.006    6.814    0.000    0.043    0.235
##    .t3_nf_sh_bh_05        0.046    0.006    8.030    0.000    0.046    0.287
##  .t2_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.038    0.006    6.087    0.000    0.038    0.215
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.114    0.009   12.443    0.000    0.114    0.412
##    .t3_nf_sh_bh_06        0.104    0.009   12.156    0.000    0.104    0.401
##  .t2_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.104    0.009   11.697    0.000    0.104    0.387
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.137    0.012   11.642    0.000    0.137    0.359
##    .t3_nf_sh_bh_07        0.110    0.012    9.292    0.000    0.110    0.277
##  .t2_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.105    0.012    8.542    0.000    0.105    0.259
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.210    0.016   13.060    0.000    0.210    0.388
##    .t3_nf_sh_bh_08        0.175    0.015   11.442    0.000    0.175    0.334
##  .t2_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.200    0.016   12.776    0.000    0.200    0.379
##  .t1_inf_sha_beh_09 ~~                                                      
##    .t2_nf_sh_bh_09        0.232    0.014   16.841    0.000    0.232    0.507
##    .t3_nf_sh_bh_09        0.238    0.014   16.895    0.000    0.238    0.512
##  .t2_inf_sha_beh_09 ~~                                                      
##    .t3_nf_sh_bh_09        0.258    0.014   18.225    0.000    0.258    0.562
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.232    0.017   13.425    0.000    0.232    0.392
##    .t3_nf_sh_bh_10        0.236    0.018   13.329    0.000    0.236    0.390
##  .t2_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.240    0.017   14.007    0.000    0.240    0.412
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.266    0.017   15.515    0.000    0.266    0.462
##    .t3_nf_sh_bh_11        0.235    0.016   14.234    0.000    0.235    0.418
##  .t2_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.221    0.016   13.844    0.000    0.221    0.404
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.713    0.029   59.112    0.000    1.713    1.579
##    .t1_nf_sh_bh_02    1.244    0.016   78.926    0.000    1.244    2.109
##    .t1_nf_sh_bh_03    2.671    0.028   93.816    0.000    2.671    2.505
##    .t1_nf_sh_bh_04    2.725    0.028   96.157    0.000    2.725    2.567
##    .t1_nf_sh_bh_05    2.546    0.026   96.663    0.000    2.546    2.581
##    .t1_nf_sh_bh_06    2.431    0.026   93.023    0.000    2.431    2.484
##    .t1_nf_sh_bh_07    2.878    0.028  103.197    0.000    2.878    2.755
##    .t1_nf_sh_bh_08    2.194    0.025   86.676    0.000    2.194    2.317
##    .t1_nf_sh_bh_09    1.408    0.019   75.047    0.000    1.408    2.004
##    .t1_nf_sh_bh_10    1.793    0.023   76.561    0.000    1.793    2.046
##    .t1_nf_sh_bh_11    1.738    0.023   77.086    0.000    1.738    2.060
##    .t2_nf_sh_bh_01    1.712    0.029   59.960    0.000    1.712    1.604
##    .t2_nf_sh_bh_02    1.214    0.013   93.688    0.000    1.214    2.503
##    .t2_nf_sh_bh_03    2.682    0.028   96.818    0.000    2.682    2.586
##    .t2_nf_sh_bh_04    2.765    0.028   98.003    0.000    2.765    2.618
##    .t2_nf_sh_bh_05    2.558    0.026   99.193    0.000    2.558    2.650
##    .t2_nf_sh_bh_06    2.434    0.026   95.109    0.000    2.434    2.541
##    .t2_nf_sh_bh_07    2.923    0.028  105.656    0.000    2.923    2.822
##    .t2_nf_sh_bh_08    2.239    0.026   87.551    0.000    2.239    2.339
##    .t2_nf_sh_bh_09    1.415    0.019   76.180    0.000    1.415    2.036
##    .t2_nf_sh_bh_10    1.806    0.023   78.643    0.000    1.806    2.102
##    .t2_nf_sh_bh_11    1.734    0.022   79.224    0.000    1.734    2.117
##    .t3_nf_sh_bh_01    1.702    0.028   59.727    0.000    1.702    1.595
##    .t3_nf_sh_bh_02    1.227    0.014   89.831    0.000    1.227    2.400
##    .t3_nf_sh_bh_03    2.627    0.026   99.428    0.000    2.627    2.654
##    .t3_nf_sh_bh_04    2.692    0.027   99.520    0.000    2.692    2.657
##    .t3_nf_sh_bh_05    2.510    0.025  100.439    0.000    2.510    2.682
##    .t3_nf_sh_bh_06    2.395    0.025   97.705    0.000    2.395    2.609
##    .t3_nf_sh_bh_07    2.864    0.027  105.061    0.000    2.864    2.806
##    .t3_nf_sh_bh_08    2.177    0.024   89.089    0.000    2.177    2.382
##    .t3_nf_sh_bh_09    1.418    0.019   75.548    0.000    1.418    2.018
##    .t3_nf_sh_bh_10    1.777    0.023   77.948    0.000    1.777    2.082
##    .t3_nf_sh_bh_11    1.713    0.021   82.030    0.000    1.713    2.192
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t2_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.076    0.041   26.354    0.000    1.076    0.915
##    .t1_nf_sh_bh_02    0.336    0.013   26.424    0.000    0.336    0.964
##    .t1_nf_sh_bh_03    0.104    0.006   16.331    0.000    0.104    0.091
##    .t1_nf_sh_bh_04    0.107    0.006   16.489    0.000    0.107    0.095
##    .t1_nf_sh_bh_05    0.166    0.008   20.107    0.000    0.166    0.171
##    .t1_nf_sh_bh_06    0.266    0.012   22.561    0.000    0.266    0.278
##    .t1_nf_sh_bh_07    0.373    0.015   24.535    0.000    0.373    0.342
##    .t1_nf_sh_bh_08    0.536    0.021   25.573    0.000    0.536    0.598
##    .t1_nf_sh_bh_09    0.462    0.018   26.371    0.000    0.462    0.937
##    .t1_nf_sh_bh_10    0.618    0.024   26.095    0.000    0.618    0.804
##    .t1_nf_sh_bh_11    0.592    0.023   26.147    0.000    0.592    0.833
##    .t2_nf_sh_bh_01    1.038    0.040   26.268    0.000    1.038    0.911
##    .t2_nf_sh_bh_02    0.228    0.009   26.435    0.000    0.228    0.969
##    .t2_nf_sh_bh_03    0.110    0.007   16.487    0.000    0.110    0.103
##    .t2_nf_sh_bh_04    0.134    0.007   17.962    0.000    0.134    0.120
##    .t2_nf_sh_bh_05    0.198    0.009   21.058    0.000    0.198    0.213
##    .t2_nf_sh_bh_06    0.286    0.013   22.827    0.000    0.286    0.312
##    .t2_nf_sh_bh_07    0.389    0.016   24.287    0.000    0.389    0.363
##    .t2_nf_sh_bh_08    0.546    0.021   25.491    0.000    0.546    0.596
##    .t2_nf_sh_bh_09    0.452    0.017   26.275    0.000    0.452    0.935
##    .t2_nf_sh_bh_10    0.570    0.022   26.023    0.000    0.570    0.772
##    .t2_nf_sh_bh_11    0.561    0.021   26.183    0.000    0.561    0.836
##    .t3_nf_sh_bh_01    1.048    0.040   26.367    0.000    1.048    0.921
##    .t3_nf_sh_bh_02    0.252    0.010   26.425    0.000    0.252    0.964
##    .t3_nf_sh_bh_03    0.089    0.006   15.523    0.000    0.089    0.091
##    .t3_nf_sh_bh_04    0.123    0.007   17.878    0.000    0.123    0.120
##    .t3_nf_sh_bh_05    0.156    0.008   20.002    0.000    0.156    0.179
##    .t3_nf_sh_bh_06    0.254    0.011   22.708    0.000    0.254    0.301
##    .t3_nf_sh_bh_07    0.425    0.017   24.845    0.000    0.425    0.407
##    .t3_nf_sh_bh_08    0.512    0.020   25.550    0.000    0.512    0.613
##    .t3_nf_sh_bh_09    0.467    0.018   26.339    0.000    0.467    0.946
##    .t3_nf_sh_bh_10    0.594    0.023   26.140    0.000    0.594    0.816
##    .t3_nf_sh_bh_11    0.533    0.020   26.248    0.000    0.533    0.872
##     t1_inf_sh_bh_f    0.100    0.017    5.906    0.000    1.000    1.000
##     t2_inf_sh_bh_f    0.102    0.017    6.136    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.090    0.016    5.784    0.000    1.000    1.000

1.3.2.2 First-Order Model Constrained

model <- '
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_01 + c2*t1_inf_sha_beh_02 + c3*t1_inf_sha_beh_03 + c4*t1_inf_sha_beh_04 + c5*t1_inf_sha_beh_05 + c6*t1_inf_sha_beh_06 + c7*t1_inf_sha_beh_07 + c8*t1_inf_sha_beh_08 + c9*t1_inf_sha_beh_09 + c10*t1_inf_sha_beh_10 + c11*t1_inf_sha_beh_11
t2_inf_sha_beh_f =~ 1*t2_inf_sha_beh_01 + c2*t2_inf_sha_beh_02 + c3*t2_inf_sha_beh_03 + c4*t2_inf_sha_beh_04 + c5*t2_inf_sha_beh_05 + c6*t2_inf_sha_beh_06 + c7*t2_inf_sha_beh_07 + c8*t2_inf_sha_beh_08 + c9*t2_inf_sha_beh_09 + c10*t2_inf_sha_beh_10 + c11*t2_inf_sha_beh_11
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_01 + c2*t3_inf_sha_beh_02 + c3*t3_inf_sha_beh_03 + c4*t3_inf_sha_beh_04 + c5*t3_inf_sha_beh_05 + c6*t3_inf_sha_beh_06 + c7*t3_inf_sha_beh_07 + c8*t3_inf_sha_beh_08 + c9*t3_inf_sha_beh_09 + c10*t3_inf_sha_beh_10 + c11*t3_inf_sha_beh_11

# factor covariance
t1_inf_sha_beh_f ~~ t2_inf_sha_beh_f + t3_inf_sha_beh_f
t2_inf_sha_beh_f ~~ t3_inf_sha_beh_f

# item error covariance
t1_inf_sha_beh_01 ~~ t2_inf_sha_beh_01 + t3_inf_sha_beh_01
t2_inf_sha_beh_01 ~~ t3_inf_sha_beh_01
t1_inf_sha_beh_02 ~~ t2_inf_sha_beh_02 + t3_inf_sha_beh_02
t2_inf_sha_beh_02 ~~ t3_inf_sha_beh_02
t1_inf_sha_beh_03 ~~ t2_inf_sha_beh_03 + t3_inf_sha_beh_03
t2_inf_sha_beh_03 ~~ t3_inf_sha_beh_03
t1_inf_sha_beh_04 ~~ t2_inf_sha_beh_04 + t3_inf_sha_beh_04
t2_inf_sha_beh_04 ~~ t3_inf_sha_beh_04
t1_inf_sha_beh_05 ~~ t2_inf_sha_beh_05 + t3_inf_sha_beh_05
t2_inf_sha_beh_05 ~~ t3_inf_sha_beh_05
t1_inf_sha_beh_06 ~~ t2_inf_sha_beh_06 + t3_inf_sha_beh_06
t2_inf_sha_beh_06 ~~ t3_inf_sha_beh_06
t1_inf_sha_beh_07 ~~ t2_inf_sha_beh_07 + t3_inf_sha_beh_07
t2_inf_sha_beh_07 ~~ t3_inf_sha_beh_07
t1_inf_sha_beh_08 ~~ t2_inf_sha_beh_08 + t3_inf_sha_beh_08
t2_inf_sha_beh_08 ~~ t3_inf_sha_beh_08
t1_inf_sha_beh_09 ~~ t2_inf_sha_beh_09 + t3_inf_sha_beh_09
t2_inf_sha_beh_09 ~~ t3_inf_sha_beh_09
t1_inf_sha_beh_10 ~~ t2_inf_sha_beh_10 + t3_inf_sha_beh_10
t2_inf_sha_beh_10 ~~ t3_inf_sha_beh_10
t1_inf_sha_beh_11 ~~ t2_inf_sha_beh_11 + t3_inf_sha_beh_11
t2_inf_sha_beh_11 ~~ t3_inf_sha_beh_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 148 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        135
##   Number of equality constraints                    20
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        40
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              8485.780
##   Degrees of freedom                               479
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             41941.362
##   Degrees of freedom                               528
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.807
##   Tucker-Lewis Index (TLI)                       0.787
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -43510.308
##   Loglikelihood unrestricted model (H1)     -39267.418
##                                                       
##   Akaike (AIC)                               87250.615
##   Bayesian (BIC)                             87853.948
##   Sample-size adjusted Bayesian (BIC)        87488.635
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.109
##   90 Percent confidence interval - lower         0.107
##   90 Percent confidence interval - upper         0.111
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f =~                                                      
##     t1____01             1.000                               0.322    0.297
##     t1____02  (c2)       0.309    0.033    9.310    0.000    0.099    0.169
##     t1____03  (c3)       3.144    0.179   17.589    0.000    1.013    0.953
##     t1____04  (c4)       3.151    0.179   17.568    0.000    1.015    0.952
##     t1____05  (c5)       2.784    0.159   17.523    0.000    0.897    0.910
##     t1____06  (c6)       2.559    0.147   17.387    0.000    0.824    0.847
##     t1____07  (c7)       2.629    0.153   17.236    0.000    0.847    0.811
##     t1____08  (c8)       1.898    0.114   16.588    0.000    0.612    0.641
##     t1____09  (c9)       0.553    0.048   11.623    0.000    0.178    0.254
##     t1____10 (c10)       1.245    0.082   15.123    0.000    0.401    0.455
##     t1____11 (c11)       1.022    0.071   14.406    0.000    0.329    0.393
##   t2_inf_sha_beh_f =~                                                      
##     t2____01             1.000                               0.313    0.294
##     t2____02  (c2)       0.309    0.033    9.310    0.000    0.097    0.198
##     t2____03  (c3)       3.144    0.179   17.589    0.000    0.984    0.947
##     t2____04  (c4)       3.151    0.179   17.568    0.000    0.986    0.937
##     t2____05  (c5)       2.784    0.159   17.523    0.000    0.871    0.891
##     t2____06  (c6)       2.559    0.147   17.387    0.000    0.801    0.832
##     t2____07  (c7)       2.629    0.153   17.236    0.000    0.823    0.796
##     t2____08  (c8)       1.898    0.114   16.588    0.000    0.594    0.626
##     t2____09  (c9)       0.553    0.048   11.623    0.000    0.173    0.249
##     t2____10 (c10)       1.245    0.082   15.123    0.000    0.390    0.458
##     t2____11 (c11)       1.022    0.071   14.406    0.000    0.320    0.392
##   t3_inf_sha_beh_f =~                                                      
##     t3____01             1.000                               0.301    0.282
##     t3____02  (c2)       0.309    0.033    9.310    0.000    0.093    0.182
##     t3____03  (c3)       3.144    0.179   17.589    0.000    0.946    0.954
##     t3____04  (c4)       3.151    0.179   17.568    0.000    0.948    0.938
##     t3____05  (c5)       2.784    0.159   17.523    0.000    0.837    0.904
##     t3____06  (c6)       2.559    0.147   17.387    0.000    0.770    0.836
##     t3____07  (c7)       2.629    0.153   17.236    0.000    0.791    0.772
##     t3____08  (c8)       1.898    0.114   16.588    0.000    0.571    0.624
##     t3____09  (c9)       0.553    0.048   11.623    0.000    0.166    0.237
##     t3____10 (c10)       1.245    0.082   15.123    0.000    0.375    0.437
##     t3____11 (c11)       1.022    0.071   14.406    0.000    0.307    0.389
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f ~~                                                       
##     t2_inf_sh_bh_f        0.061    0.008    8.007    0.000    0.606    0.606
##     t3_inf_sh_bh_f        0.058    0.007    7.989    0.000    0.595    0.595
##   t2_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.057    0.007    8.006    0.000    0.609    0.609
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.415    0.031   13.585    0.000    0.415    0.393
##    .t3_nf_sh_bh_01        0.396    0.030   13.015    0.000    0.396    0.373
##  .t2_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.456    0.031   14.867    0.000    0.456    0.437
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.069    0.008    9.060    0.000    0.069    0.250
##    .t3_nf_sh_bh_02        0.069    0.008    8.575    0.000    0.069    0.236
##  .t2_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.069    0.007   10.295    0.000    0.069    0.287
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.030    0.005    6.382    0.000    0.030    0.278
##    .t3_nf_sh_bh_03        0.029    0.004    6.769    0.000    0.029    0.304
##  .t2_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.044    0.005    9.390    0.000    0.044    0.441
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.044    0.005    8.605    0.000    0.044    0.363
##    .t3_nf_sh_bh_04        0.034    0.005    7.186    0.000    0.034    0.299
##  .t2_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.062    0.005   11.317    0.000    0.062    0.477
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.042    0.006    6.760    0.000    0.042    0.234
##    .t3_nf_sh_bh_05        0.047    0.006    8.113    0.000    0.047    0.288
##  .t2_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.037    0.006    6.016    0.000    0.037    0.212
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.114    0.009   12.446    0.000    0.114    0.413
##    .t3_nf_sh_bh_06        0.104    0.009   12.179    0.000    0.104    0.401
##  .t2_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.104    0.009   11.675    0.000    0.104    0.386
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.137    0.012   11.699    0.000    0.137    0.360
##    .t3_nf_sh_bh_07        0.110    0.012    9.303    0.000    0.110    0.277
##  .t2_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.106    0.012    8.622    0.000    0.106    0.260
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.210    0.016   13.062    0.000    0.210    0.387
##    .t3_nf_sh_bh_08        0.174    0.015   11.418    0.000    0.174    0.333
##  .t2_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.201    0.016   12.815    0.000    0.201    0.380
##  .t1_inf_sha_beh_09 ~~                                                      
##    .t2_nf_sh_bh_09        0.232    0.014   16.859    0.000    0.232    0.508
##    .t3_nf_sh_bh_09        0.238    0.014   16.904    0.000    0.238    0.512
##  .t2_inf_sha_beh_09 ~~                                                      
##    .t3_nf_sh_bh_09        0.258    0.014   18.254    0.000    0.258    0.562
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.232    0.017   13.427    0.000    0.232    0.391
##    .t3_nf_sh_bh_10        0.234    0.018   13.302    0.000    0.234    0.388
##  .t2_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.241    0.017   14.051    0.000    0.241    0.413
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.268    0.017   15.563    0.000    0.268    0.463
##    .t3_nf_sh_bh_11        0.235    0.016   14.255    0.000    0.235    0.418
##  .t2_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.220    0.016   13.813    0.000    0.220    0.403
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.713    0.029   59.015    0.000    1.713    1.577
##    .t1_nf_sh_bh_02    1.244    0.016   79.196    0.000    1.244    2.116
##    .t1_nf_sh_bh_03    2.671    0.028   94.126    0.000    2.671    2.513
##    .t1_nf_sh_bh_04    2.725    0.028   95.736    0.000    2.725    2.556
##    .t1_nf_sh_bh_05    2.546    0.026   96.720    0.000    2.546    2.583
##    .t1_nf_sh_bh_06    2.431    0.026   93.573    0.000    2.431    2.499
##    .t1_nf_sh_bh_07    2.878    0.028  103.235    0.000    2.878    2.756
##    .t1_nf_sh_bh_08    2.194    0.025   86.068    0.000    2.194    2.301
##    .t1_nf_sh_bh_09    1.408    0.019   75.010    0.000    1.408    2.003
##    .t1_nf_sh_bh_10    1.793    0.024   76.090    0.000    1.793    2.034
##    .t1_nf_sh_bh_11    1.738    0.022   77.564    0.000    1.738    2.073
##    .t2_nf_sh_bh_01    1.712    0.029   60.055    0.000    1.712    1.606
##    .t2_nf_sh_bh_02    1.214    0.013   93.290    0.000    1.214    2.492
##    .t2_nf_sh_bh_03    2.682    0.028   96.694    0.000    2.682    2.583
##    .t2_nf_sh_bh_04    2.765    0.028   98.365    0.000    2.765    2.627
##    .t2_nf_sh_bh_05    2.558    0.026   98.002    0.000    2.558    2.618
##    .t2_nf_sh_bh_06    2.434    0.026   94.691    0.000    2.434    2.530
##    .t2_nf_sh_bh_07    2.923    0.028  105.941    0.000    2.923    2.830
##    .t2_nf_sh_bh_08    2.239    0.025   88.343    0.000    2.239    2.360
##    .t2_nf_sh_bh_09    1.415    0.019   76.256    0.000    1.415    2.038
##    .t2_nf_sh_bh_10    1.806    0.023   79.384    0.000    1.806    2.122
##    .t2_nf_sh_bh_11    1.734    0.022   79.611    0.000    1.734    2.127
##    .t3_nf_sh_bh_01    1.702    0.028   59.728    0.000    1.702    1.595
##    .t3_nf_sh_bh_02    1.226    0.014   89.943    0.000    1.226    2.403
##    .t3_nf_sh_bh_03    2.627    0.026   99.211    0.000    2.627    2.649
##    .t3_nf_sh_bh_04    2.692    0.027   99.785    0.000    2.692    2.664
##    .t3_nf_sh_bh_05    2.510    0.025  101.426    0.000    2.510    2.708
##    .t3_nf_sh_bh_06    2.395    0.025   97.478    0.000    2.395    2.603
##    .t3_nf_sh_bh_07    2.864    0.027  104.702    0.000    2.864    2.796
##    .t3_nf_sh_bh_08    2.177    0.024   88.954    0.000    2.177    2.379
##    .t3_nf_sh_bh_09    1.418    0.019   75.487    0.000    1.418    2.017
##    .t3_nf_sh_bh_10    1.777    0.023   77.681    0.000    1.777    2.075
##    .t3_nf_sh_bh_11    1.713    0.021   81.057    0.000    1.713    2.166
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t2_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.076    0.041   26.370    0.000    1.076    0.912
##    .t1_nf_sh_bh_02    0.336    0.013   26.427    0.000    0.336    0.971
##    .t1_nf_sh_bh_03    0.104    0.006   16.704    0.000    0.104    0.092
##    .t1_nf_sh_bh_04    0.106    0.006   16.721    0.000    0.106    0.093
##    .t1_nf_sh_bh_05    0.167    0.008   20.487    0.000    0.167    0.172
##    .t1_nf_sh_bh_06    0.267    0.012   22.813    0.000    0.267    0.282
##    .t1_nf_sh_bh_07    0.373    0.015   24.662    0.000    0.373    0.342
##    .t1_nf_sh_bh_08    0.536    0.021   25.638    0.000    0.536    0.589
##    .t1_nf_sh_bh_09    0.462    0.018   26.398    0.000    0.462    0.936
##    .t1_nf_sh_bh_10    0.617    0.024   26.174    0.000    0.617    0.793
##    .t1_nf_sh_bh_11    0.594    0.023   26.186    0.000    0.594    0.846
##    .t2_nf_sh_bh_01    1.038    0.039   26.297    0.000    1.038    0.914
##    .t2_nf_sh_bh_02    0.228    0.009   26.425    0.000    0.228    0.961
##    .t2_nf_sh_bh_03    0.111    0.007   16.632    0.000    0.111    0.103
##    .t2_nf_sh_bh_04    0.136    0.007   18.215    0.000    0.136    0.122
##    .t2_nf_sh_bh_05    0.196    0.009   21.123    0.000    0.196    0.206
##    .t2_nf_sh_bh_06    0.284    0.012   22.881    0.000    0.284    0.307
##    .t2_nf_sh_bh_07    0.391    0.016   24.460    0.000    0.391    0.366
##    .t2_nf_sh_bh_08    0.547    0.021   25.574    0.000    0.547    0.608
##    .t2_nf_sh_bh_09    0.452    0.017   26.321    0.000    0.452    0.938
##    .t2_nf_sh_bh_10    0.572    0.022   26.064    0.000    0.572    0.790
##    .t2_nf_sh_bh_11    0.563    0.021   26.216    0.000    0.563    0.846
##    .t3_nf_sh_bh_01    1.048    0.040   26.380    0.000    1.048    0.921
##    .t3_nf_sh_bh_02    0.252    0.010   26.426    0.000    0.252    0.967
##    .t3_nf_sh_bh_03    0.089    0.006   15.822    0.000    0.089    0.091
##    .t3_nf_sh_bh_04    0.123    0.007   18.263    0.000    0.123    0.120
##    .t3_nf_sh_bh_05    0.157    0.008   20.520    0.000    0.157    0.183
##    .t3_nf_sh_bh_06    0.255    0.011   22.955    0.000    0.255    0.301
##    .t3_nf_sh_bh_07    0.424    0.017   24.942    0.000    0.424    0.404
##    .t3_nf_sh_bh_08    0.512    0.020   25.612    0.000    0.512    0.611
##    .t3_nf_sh_bh_09    0.467    0.018   26.349    0.000    0.467    0.944
##    .t3_nf_sh_bh_10    0.593    0.023   26.181    0.000    0.593    0.809
##    .t3_nf_sh_bh_11    0.531    0.020   26.267    0.000    0.531    0.849
##     t1_inf_sh_bh_f    0.104    0.012    8.373    0.000    1.000    1.000
##     t2_inf_sh_bh_f    0.098    0.012    8.369    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.090    0.011    8.370    0.000    1.000    1.000

1.3.2.3 Second-Order Model Unconstrained

Second-order model shows much improved fit.

model <- '
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_f1 + t1_inf_sha_beh_f2 + t1_inf_sha_beh_f3 + t1_inf_sha_beh_f4 + t1_inf_sha_beh_f5
t2_inf_sha_beh_f =~ 1*t2_inf_sha_beh_f1 + t2_inf_sha_beh_f2 + t2_inf_sha_beh_f3 + t2_inf_sha_beh_f4 + t2_inf_sha_beh_f5
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_f1 + t3_inf_sha_beh_f2 + t3_inf_sha_beh_f3 + t3_inf_sha_beh_f4 + t3_inf_sha_beh_f5
t1_inf_sha_beh_f1 =~ 1*t1_inf_sha_beh_01 + t1_inf_sha_beh_02
t1_inf_sha_beh_f2 =~ 1*t1_inf_sha_beh_03 + t1_inf_sha_beh_04
t1_inf_sha_beh_f3 =~ 1*t1_inf_sha_beh_05 + t1_inf_sha_beh_06
t1_inf_sha_beh_f4 =~ 1*t1_inf_sha_beh_07 + t1_inf_sha_beh_08
t1_inf_sha_beh_f5 =~ 1*t1_inf_sha_beh_10 + t1_inf_sha_beh_11
t2_inf_sha_beh_f1 =~ 1*t2_inf_sha_beh_01 + t2_inf_sha_beh_02
t2_inf_sha_beh_f2 =~ 1*t2_inf_sha_beh_03 + t2_inf_sha_beh_04
t2_inf_sha_beh_f3 =~ 1*t2_inf_sha_beh_05 + t2_inf_sha_beh_06
t2_inf_sha_beh_f4 =~ 1*t2_inf_sha_beh_07 + t2_inf_sha_beh_08
t2_inf_sha_beh_f5 =~ 1*t2_inf_sha_beh_10 + t2_inf_sha_beh_11
t3_inf_sha_beh_f1 =~ 1*t3_inf_sha_beh_01 + t3_inf_sha_beh_02
t3_inf_sha_beh_f2 =~ 1*t3_inf_sha_beh_03 + t3_inf_sha_beh_04
t3_inf_sha_beh_f3 =~ 1*t3_inf_sha_beh_05 + t3_inf_sha_beh_06
t3_inf_sha_beh_f4 =~ 1*t3_inf_sha_beh_07 + t3_inf_sha_beh_08
t3_inf_sha_beh_f5 =~ 1*t3_inf_sha_beh_10 + t3_inf_sha_beh_11

# factor covariance
t1_inf_sha_beh_f ~~ t2_inf_sha_beh_f + t3_inf_sha_beh_f
t2_inf_sha_beh_f ~~ t3_inf_sha_beh_f

# item error covariance
t1_inf_sha_beh_01 ~~ t2_inf_sha_beh_01 + t3_inf_sha_beh_01
t2_inf_sha_beh_01 ~~ t3_inf_sha_beh_01
t1_inf_sha_beh_02 ~~ t2_inf_sha_beh_02 + t3_inf_sha_beh_02
t2_inf_sha_beh_02 ~~ t3_inf_sha_beh_02
t1_inf_sha_beh_03 ~~ t2_inf_sha_beh_03 + t3_inf_sha_beh_03
t2_inf_sha_beh_03 ~~ t3_inf_sha_beh_03
t1_inf_sha_beh_04 ~~ t2_inf_sha_beh_04 + t3_inf_sha_beh_04
t2_inf_sha_beh_04 ~~ t3_inf_sha_beh_04
t1_inf_sha_beh_05 ~~ t2_inf_sha_beh_05 + t3_inf_sha_beh_05
t2_inf_sha_beh_05 ~~ t3_inf_sha_beh_05
t1_inf_sha_beh_06 ~~ t2_inf_sha_beh_06 + t3_inf_sha_beh_06
t2_inf_sha_beh_06 ~~ t3_inf_sha_beh_06
t1_inf_sha_beh_07 ~~ t2_inf_sha_beh_07 + t3_inf_sha_beh_07
t2_inf_sha_beh_07 ~~ t3_inf_sha_beh_07
t1_inf_sha_beh_08 ~~ t2_inf_sha_beh_08 + t3_inf_sha_beh_08
t2_inf_sha_beh_08 ~~ t3_inf_sha_beh_08
t1_inf_sha_beh_10 ~~ t2_inf_sha_beh_10 + t3_inf_sha_beh_10
t2_inf_sha_beh_10 ~~ t3_inf_sha_beh_10
t1_inf_sha_beh_11 ~~ t2_inf_sha_beh_11 + t3_inf_sha_beh_11
t2_inf_sha_beh_11 ~~ t3_inf_sha_beh_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 234 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        138
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        38
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2510.346
##   Degrees of freedom                               357
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             39663.809
##   Degrees of freedom                               435
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.945
##   Tucker-Lewis Index (TLI)                       0.933
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -37156.335
##   Loglikelihood unrestricted model (H1)     -35901.162
##                                                       
##   Akaike (AIC)                               74588.669
##   Bayesian (BIC)                             75312.668
##   Sample-size adjusted Bayesian (BIC)        74874.293
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.066
##   90 Percent confidence interval - lower         0.063
##   90 Percent confidence interval - upper         0.068
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.062
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f =~                                                       
##     t1_nf_sh_bh_f1        1.000                               0.465    0.465
##     t1_nf_sh_bh_f2        2.974    0.241   12.321    0.000    0.961    0.961
##     t1_nf_sh_bh_f3        2.734    0.221   12.346    0.000    0.941    0.941
##     t1_nf_sh_bh_f4        2.627    0.216   12.188    0.000    0.957    0.957
##     t1_nf_sh_bh_f5        1.298    0.122   10.626    0.000    0.537    0.537
##   t2_inf_sha_beh_f =~                                                       
##     t2_nf_sh_bh_f1        1.000                               0.539    0.539
##     t2_nf_sh_bh_f2        2.845    0.222   12.832    0.000    0.964    0.964
##     t2_nf_sh_bh_f3        2.564    0.200   12.788    0.000    0.920    0.920
##     t2_nf_sh_bh_f4        2.539    0.201   12.662    0.000    0.947    0.947
##     t2_nf_sh_bh_f5        1.311    0.118   11.131    0.000    0.543    0.543
##   t3_inf_sha_beh_f =~                                                       
##     t3_nf_sh_bh_f1        1.000                               0.465    0.465
##     t3_nf_sh_bh_f2        2.893    0.239   12.094    0.000    0.956    0.956
##     t3_nf_sh_bh_f3        2.715    0.225   12.067    0.000    0.939    0.939
##     t3_nf_sh_bh_f4        2.556    0.215   11.862    0.000    0.930    0.930
##     t3_nf_sh_bh_f5        1.252    0.122   10.306    0.000    0.483    0.483
##   t1_inf_sha_beh_f1 =~                                                      
##     t1_nf_sh_bh_01        1.000                               0.712    0.659
##     t1_nf_sh_bh_02        0.346    0.047    7.302    0.000    0.246    0.421
##   t1_inf_sha_beh_f2 =~                                                      
##     t1_nf_sh_bh_03        1.000                               1.025    0.965
##     t1_nf_sh_bh_04        0.992    0.010   94.723    0.000    1.017    0.964
##   t1_inf_sha_beh_f3 =~                                                      
##     t1_nf_sh_bh_05        1.000                               0.962    0.974
##     t1_nf_sh_bh_06        0.920    0.013   70.754    0.000    0.884    0.907
##   t1_inf_sha_beh_f4 =~                                                      
##     t1_nf_sh_bh_07        1.000                               0.909    0.860
##     t1_nf_sh_bh_08        0.722    0.023   30.797    0.000    0.656    0.688
##   t1_inf_sha_beh_f5 =~                                                      
##     t1_nf_sh_bh_10        1.000                               0.801    0.907
##     t1_nf_sh_bh_11        0.888    0.034   25.947    0.000    0.711    0.848
##   t2_inf_sha_beh_f1 =~                                                      
##     t2_nf_sh_bh_01        1.000                               0.621    0.584
##     t2_nf_sh_bh_02        0.268    0.039    6.801    0.000    0.167    0.344
##   t2_inf_sha_beh_f2 =~                                                      
##     t2_nf_sh_bh_03        1.000                               0.987    0.958
##     t2_nf_sh_bh_04        1.006    0.012   84.635    0.000    0.992    0.949
##   t2_inf_sha_beh_f3 =~                                                      
##     t2_nf_sh_bh_05        1.000                               0.932    0.965
##     t2_nf_sh_bh_06        0.926    0.014   64.893    0.000    0.863    0.904
##   t2_inf_sha_beh_f4 =~                                                      
##     t2_nf_sh_bh_07        1.000                               0.896    0.857
##     t2_nf_sh_bh_08        0.749    0.024   30.868    0.000    0.671    0.692
##   t2_inf_sha_beh_f5 =~                                                      
##     t2_nf_sh_bh_10        1.000                               0.807    0.942
##     t2_nf_sh_bh_11        0.818    0.031   26.022    0.000    0.660    0.817
##   t3_inf_sha_beh_f1 =~                                                      
##     t3_nf_sh_bh_01        1.000                               0.677    0.642
##     t3_nf_sh_bh_02        0.316    0.043    7.265    0.000    0.214    0.419
##   t3_inf_sha_beh_f2 =~                                                      
##     t3_nf_sh_bh_03        1.000                               0.953    0.967
##     t3_nf_sh_bh_04        1.002    0.011   89.521    0.000    0.955    0.949
##   t3_inf_sha_beh_f3 =~                                                      
##     t3_nf_sh_bh_05        1.000                               0.910    0.972
##     t3_nf_sh_bh_06        0.900    0.014   65.819    0.000    0.819    0.898
##   t3_inf_sha_beh_f4 =~                                                      
##     t3_nf_sh_bh_07        1.000                               0.865    0.839
##     t3_nf_sh_bh_08        0.739    0.025   29.436    0.000    0.639    0.693
##   t3_inf_sha_beh_f5 =~                                                      
##     t3_nf_sh_bh_10        1.000                               0.817    0.962
##     t3_nf_sh_bh_11        0.784    0.032   24.681    0.000    0.640    0.827
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f ~~                                                       
##     t2_inf_sh_bh_f        0.070    0.009    7.506    0.000    0.634    0.634
##     t3_inf_sh_bh_f        0.065    0.009    7.370    0.000    0.623    0.623
##   t2_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.067    0.009    7.348    0.000    0.642    0.642
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.388    0.029   13.343    0.000    0.388    0.553
##    .t3_nf_sh_bh_01        0.353    0.028   12.458    0.000    0.353    0.536
##  .t2_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.424    0.029   14.607    0.000    0.424    0.606
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.060    0.007    8.248    0.000    0.060    0.249
##    .t3_nf_sh_bh_02        0.058    0.008    7.677    0.000    0.058    0.234
##  .t2_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.065    0.006   10.151    0.000    0.065    0.309
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.028    0.004    6.407    0.000    0.028    0.340
##    .t3_nf_sh_bh_03        0.032    0.004    8.046    0.000    0.032    0.459
##  .t2_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.041    0.004    9.282    0.000    0.041    0.557
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.042    0.005    9.001    0.000    0.042    0.445
##    .t3_nf_sh_bh_04        0.031    0.004    7.293    0.000    0.031    0.351
##  .t2_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.055    0.005   10.873    0.000    0.055    0.522
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.016    0.004    3.659    0.000    0.016    0.287
##    .t3_nf_sh_bh_05        0.020    0.004    4.884    0.000    0.020    0.409
##  .t2_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.012    0.004    2.701    0.007    0.012    0.216
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.078    0.006   12.530    0.000    0.078    0.466
##    .t3_nf_sh_bh_06        0.064    0.006   10.955    0.000    0.064    0.391
##  .t2_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.073    0.006   12.165    0.000    0.073    0.446
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.142    0.012   12.280    0.000    0.142    0.489
##    .t3_nf_sh_bh_07        0.119    0.012   10.125    0.000    0.119    0.393
##  .t2_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.119    0.012    9.841    0.000    0.119    0.393
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.200    0.015   13.031    0.000    0.200    0.412
##    .t3_nf_sh_bh_08        0.171    0.015   11.738    0.000    0.171    0.370
##  .t2_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.204    0.015   13.550    0.000    0.204    0.437
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.021    0.009    2.259    0.024    0.021    0.198
##    .t3_nf_sh_bh_10        0.034    0.009    3.789    0.000    0.034    0.396
##  .t2_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.057    0.009    6.680    0.000    0.057    0.865
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.071    0.009    8.058    0.000    0.071    0.340
##    .t3_nf_sh_bh_11        0.044    0.008    5.393    0.000    0.044    0.228
##  .t2_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.036    0.008    4.516    0.000    0.036    0.177
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.712    0.029   59.284    0.000    1.712    1.584
##    .t1_nf_sh_bh_02    1.244    0.016   79.577    0.000    1.244    2.126
##    .t1_nf_sh_bh_03    2.672    0.028   94.195    0.000    2.672    2.515
##    .t1_nf_sh_bh_04    2.725    0.028   96.736    0.000    2.725    2.583
##    .t1_nf_sh_bh_05    2.545    0.026   96.580    0.000    2.545    2.579
##    .t1_nf_sh_bh_06    2.431    0.026   93.391    0.000    2.431    2.494
##    .t1_nf_sh_bh_07    2.878    0.028  101.990    0.000    2.878    2.723
##    .t1_nf_sh_bh_08    2.194    0.025   86.085    0.000    2.194    2.301
##    .t1_nf_sh_bh_10    1.794    0.024   75.976    0.000    1.794    2.031
##    .t1_nf_sh_bh_11    1.739    0.022   77.543    0.000    1.739    2.072
##    .t2_nf_sh_bh_01    1.712    0.028   60.234    0.000    1.712    1.611
##    .t2_nf_sh_bh_02    1.214    0.013   93.902    0.000    1.214    2.508
##    .t2_nf_sh_bh_03    2.682    0.028   97.488    0.000    2.682    2.604
##    .t2_nf_sh_bh_04    2.764    0.028   98.933    0.000    2.764    2.643
##    .t2_nf_sh_bh_05    2.558    0.026   99.185    0.000    2.558    2.649
##    .t2_nf_sh_bh_06    2.434    0.026   95.404    0.000    2.434    2.549
##    .t2_nf_sh_bh_07    2.923    0.028  104.656    0.000    2.923    2.795
##    .t2_nf_sh_bh_08    2.239    0.026   86.402    0.000    2.239    2.308
##    .t2_nf_sh_bh_10    1.805    0.023   78.878    0.000    1.805    2.108
##    .t2_nf_sh_bh_11    1.735    0.022   80.298    0.000    1.735    2.145
##    .t3_nf_sh_bh_01    1.702    0.028   60.385    0.000    1.702    1.613
##    .t3_nf_sh_bh_02    1.227    0.014   90.023    0.000    1.227    2.405
##    .t3_nf_sh_bh_03    2.627    0.026   99.825    0.000    2.627    2.665
##    .t3_nf_sh_bh_04    2.692    0.027  100.265    0.000    2.692    2.677
##    .t3_nf_sh_bh_05    2.509    0.025  100.441    0.000    2.509    2.682
##    .t3_nf_sh_bh_06    2.395    0.024   98.403    0.000    2.395    2.628
##    .t3_nf_sh_bh_07    2.864    0.028  104.096    0.000    2.864    2.780
##    .t3_nf_sh_bh_08    2.178    0.025   88.269    0.000    2.178    2.360
##    .t3_nf_sh_bh_10    1.776    0.023   78.316    0.000    1.776    2.092
##    .t3_nf_sh_bh_11    1.715    0.021   82.955    0.000    1.715    2.216
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t2_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    0.662    0.075    8.863    0.000    0.662    0.566
##    .t1_nf_sh_bh_02    0.281    0.013   21.026    0.000    0.281    0.823
##    .t1_nf_sh_bh_03    0.078    0.006   13.449    0.000    0.078    0.069
##    .t1_nf_sh_bh_04    0.079    0.006   13.720    0.000    0.079    0.071
##    .t1_nf_sh_bh_05    0.050    0.007    7.567    0.000    0.050    0.051
##    .t1_nf_sh_bh_06    0.168    0.008   20.668    0.000    0.168    0.177
##    .t1_nf_sh_bh_07    0.291    0.019   15.143    0.000    0.291    0.261
##    .t1_nf_sh_bh_08    0.479    0.020   23.684    0.000    0.479    0.527
##    .t1_nf_sh_bh_10    0.139    0.022    6.200    0.000    0.139    0.178
##    .t1_nf_sh_bh_11    0.198    0.019   10.641    0.000    0.198    0.282
##    .t2_nf_sh_bh_01    0.745    0.067   11.112    0.000    0.745    0.659
##    .t2_nf_sh_bh_02    0.207    0.009   23.266    0.000    0.207    0.882
##    .t2_nf_sh_bh_03    0.087    0.007   13.044    0.000    0.087    0.082
##    .t2_nf_sh_bh_04    0.110    0.007   15.106    0.000    0.110    0.100
##    .t2_nf_sh_bh_05    0.064    0.007    8.561    0.000    0.064    0.069
##    .t2_nf_sh_bh_06    0.167    0.009   19.166    0.000    0.167    0.183
##    .t2_nf_sh_bh_07    0.291    0.019   14.921    0.000    0.291    0.266
##    .t2_nf_sh_bh_08    0.491    0.021   23.560    0.000    0.491    0.522
##    .t2_nf_sh_bh_10    0.082    0.022    3.694    0.000    0.082    0.112
##    .t2_nf_sh_bh_11    0.218    0.017   13.197    0.000    0.218    0.333
##    .t3_nf_sh_bh_01    0.655    0.069    9.474    0.000    0.655    0.588
##    .t3_nf_sh_bh_02    0.214    0.010   21.037    0.000    0.214    0.824
##    .t3_nf_sh_bh_03    0.064    0.006   11.384    0.000    0.064    0.065
##    .t3_nf_sh_bh_04    0.100    0.006   15.955    0.000    0.100    0.099
##    .t3_nf_sh_bh_05    0.048    0.007    7.310    0.000    0.048    0.055
##    .t3_nf_sh_bh_06    0.161    0.008   20.827    0.000    0.161    0.193
##    .t3_nf_sh_bh_07    0.314    0.020   15.452    0.000    0.314    0.295
##    .t3_nf_sh_bh_08    0.443    0.019   22.956    0.000    0.443    0.520
##    .t3_nf_sh_bh_10    0.053    0.025    2.168    0.030    0.053    0.074
##    .t3_nf_sh_bh_11    0.189    0.016   11.637    0.000    0.189    0.316
##     t1_inf_sh_bh_f    0.110    0.018    6.071    0.000    1.000    1.000
##     t2_inf_sh_bh_f    0.112    0.018    6.317    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.099    0.017    5.957    0.000    1.000    1.000
##    .t1_nf_sh_bh_f1    0.398    0.070    5.707    0.000    0.784    0.784
##    .t1_nf_sh_bh_f2    0.080    0.009    9.037    0.000    0.076    0.076
##    .t1_nf_sh_bh_f3    0.105    0.009   11.092    0.000    0.114    0.114
##    .t1_nf_sh_bh_f4    0.069    0.016    4.421    0.000    0.084    0.084
##    .t1_nf_sh_bh_f5    0.457    0.029   15.986    0.000    0.712    0.712
##    .t2_nf_sh_bh_f1    0.273    0.059    4.673    0.000    0.710    0.710
##    .t2_nf_sh_bh_f2    0.070    0.009    7.583    0.000    0.071    0.071
##    .t2_nf_sh_bh_f3    0.134    0.010   12.782    0.000    0.154    0.154
##    .t2_nf_sh_bh_f4    0.083    0.016    5.251    0.000    0.103    0.103
##    .t2_nf_sh_bh_f5    0.459    0.029   15.984    0.000    0.705    0.705
##    .t3_nf_sh_bh_f1    0.360    0.063    5.697    0.000    0.784    0.784
##    .t3_nf_sh_bh_f2    0.079    0.009    9.168    0.000    0.087    0.087
##    .t3_nf_sh_bh_f3    0.097    0.009   10.421    0.000    0.117    0.117
##    .t3_nf_sh_bh_f4    0.101    0.016    6.127    0.000    0.135    0.135
##    .t3_nf_sh_bh_f5    0.512    0.032   16.139    0.000    0.767    0.767

1.3.2.4 Second-Order Model Constrained

model <- '
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_f1 + o2*t1_inf_sha_beh_f2 + o3*t1_inf_sha_beh_f3 + o4*t1_inf_sha_beh_f4 + o5*t1_inf_sha_beh_f5
t2_inf_sha_beh_f =~ 1*t2_inf_sha_beh_f1 + o2*t2_inf_sha_beh_f2 + o3*t2_inf_sha_beh_f3 + o4*t2_inf_sha_beh_f4 + o5*t2_inf_sha_beh_f5
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_f1 + o2*t3_inf_sha_beh_f2 + o3*t3_inf_sha_beh_f3 + o4*t3_inf_sha_beh_f4 + o5*t3_inf_sha_beh_f5
t1_inf_sha_beh_f1 =~ 1*t1_inf_sha_beh_01 + j2*t1_inf_sha_beh_02
t1_inf_sha_beh_f2 =~ 1*t1_inf_sha_beh_03 + k2*t1_inf_sha_beh_04
t1_inf_sha_beh_f3 =~ 1*t1_inf_sha_beh_05 + l2*t1_inf_sha_beh_06
t1_inf_sha_beh_f4 =~ 1*t1_inf_sha_beh_07 + m2*t1_inf_sha_beh_08
t1_inf_sha_beh_f5 =~ 1*t1_inf_sha_beh_10 + n2*t1_inf_sha_beh_11
t2_inf_sha_beh_f1 =~ 1*t2_inf_sha_beh_01 + j2*t2_inf_sha_beh_02
t2_inf_sha_beh_f2 =~ 1*t2_inf_sha_beh_03 + k2*t2_inf_sha_beh_04
t2_inf_sha_beh_f3 =~ 1*t2_inf_sha_beh_05 + l2*t2_inf_sha_beh_06
t2_inf_sha_beh_f4 =~ 1*t2_inf_sha_beh_07 + m2*t2_inf_sha_beh_08
t2_inf_sha_beh_f5 =~ 1*t2_inf_sha_beh_10 + n2*t2_inf_sha_beh_11
t3_inf_sha_beh_f1 =~ 1*t3_inf_sha_beh_01 + j2*t3_inf_sha_beh_02
t3_inf_sha_beh_f2 =~ 1*t3_inf_sha_beh_03 + k2*t3_inf_sha_beh_04
t3_inf_sha_beh_f3 =~ 1*t3_inf_sha_beh_05 + l2*t3_inf_sha_beh_06
t3_inf_sha_beh_f4 =~ 1*t3_inf_sha_beh_07 + m2*t3_inf_sha_beh_08
t3_inf_sha_beh_f5 =~ 1*t3_inf_sha_beh_10 + n2*t3_inf_sha_beh_11

# factor covariance
t1_inf_sha_beh_f ~~ t2_inf_sha_beh_f + t3_inf_sha_beh_f
t2_inf_sha_beh_f ~~ t3_inf_sha_beh_f

# item error covariance
t1_inf_sha_beh_01 ~~ t2_inf_sha_beh_01 + t3_inf_sha_beh_01
t2_inf_sha_beh_01 ~~ t3_inf_sha_beh_01
t1_inf_sha_beh_02 ~~ t2_inf_sha_beh_02 + t3_inf_sha_beh_02
t2_inf_sha_beh_02 ~~ t3_inf_sha_beh_02
t1_inf_sha_beh_03 ~~ t2_inf_sha_beh_03 + t3_inf_sha_beh_03
t2_inf_sha_beh_03 ~~ t3_inf_sha_beh_03
t1_inf_sha_beh_04 ~~ t2_inf_sha_beh_04 + t3_inf_sha_beh_04
t2_inf_sha_beh_04 ~~ t3_inf_sha_beh_04
t1_inf_sha_beh_05 ~~ t2_inf_sha_beh_05 + t3_inf_sha_beh_05
t2_inf_sha_beh_05 ~~ t3_inf_sha_beh_05
t1_inf_sha_beh_06 ~~ t2_inf_sha_beh_06 + t3_inf_sha_beh_06
t2_inf_sha_beh_06 ~~ t3_inf_sha_beh_06
t1_inf_sha_beh_07 ~~ t2_inf_sha_beh_07 + t3_inf_sha_beh_07
t2_inf_sha_beh_07 ~~ t3_inf_sha_beh_07
t1_inf_sha_beh_08 ~~ t2_inf_sha_beh_08 + t3_inf_sha_beh_08
t2_inf_sha_beh_08 ~~ t3_inf_sha_beh_08
t1_inf_sha_beh_10 ~~ t2_inf_sha_beh_10 + t3_inf_sha_beh_10
t2_inf_sha_beh_10 ~~ t3_inf_sha_beh_10
t1_inf_sha_beh_11 ~~ t2_inf_sha_beh_11 + t3_inf_sha_beh_11
t2_inf_sha_beh_11 ~~ t3_inf_sha_beh_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 184 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        138
##   Number of equality constraints                    18
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                        38
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2527.695
##   Degrees of freedom                               375
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             39663.809
##   Degrees of freedom                               435
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.945
##   Tucker-Lewis Index (TLI)                       0.936
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -37165.009
##   Loglikelihood unrestricted model (H1)     -35901.162
##                                                       
##   Akaike (AIC)                               74570.018
##   Bayesian (BIC)                             75199.583
##   Sample-size adjusted Bayesian (BIC)        74818.387
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.064
##   90 Percent confidence interval - lower         0.062
##   90 Percent confidence interval - upper         0.066
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.063
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f =~                                                       
##     t1_nf___1             1.000                               0.449    0.449
##     t1_nf___2 (o2)        2.913    0.163   17.902    0.000    0.961    0.961
##     t1_nf___3 (o3)        2.681    0.150   17.926    0.000    0.941    0.941
##     t1_nf___4 (o4)        2.582    0.146   17.666    0.000    0.958    0.958
##     t1_nf___5 (o5)        1.292    0.081   15.942    0.000    0.528    0.528
##   t2_inf_sha_beh_f =~                                                       
##     t2_nf___1             1.000                               0.556    0.556
##     t2_nf___2 (o2)        2.913    0.163   17.902    0.000    0.963    0.963
##     t2_nf___3 (o3)        2.681    0.150   17.926    0.000    0.923    0.923
##     t2_nf___4 (o4)        2.582    0.146   17.666    0.000    0.944    0.944
##     t2_nf___5 (o5)        1.292    0.081   15.942    0.000    0.530    0.530
##   t3_inf_sha_beh_f =~                                                       
##     t3_nf___1             1.000                               0.459    0.459
##     t3_nf___2 (o2)        2.913    0.163   17.902    0.000    0.956    0.956
##     t3_nf___3 (o3)        2.681    0.150   17.926    0.000    0.938    0.938
##     t3_nf___4 (o4)        2.582    0.146   17.666    0.000    0.931    0.931
##     t3_nf___5 (o5)        1.292    0.081   15.942    0.000    0.504    0.504
##   t1_inf_sha_beh_f1 =~                                                      
##     t1_n___01             1.000                               0.750    0.693
##     t1_n___02 (j2)        0.307    0.029   10.437    0.000    0.230    0.395
##   t1_inf_sha_beh_f2 =~                                                      
##     t1_n___03             1.000                               1.021    0.964
##     t1_n___04 (k2)        0.999    0.008  125.373    0.000    1.020    0.964
##   t1_inf_sha_beh_f3 =~                                                      
##     t1_n___05             1.000                               0.960    0.974
##     t1_n___06 (l2)        0.916    0.010   95.266    0.000    0.879    0.906
##   t1_inf_sha_beh_f4 =~                                                      
##     t1_n___07             1.000                               0.908    0.859
##     t1_n___08 (m2)        0.735    0.017   43.185    0.000    0.668    0.695
##   t1_inf_sha_beh_f5 =~                                                      
##     t1_n___10             1.000                               0.825    0.931
##     t1_n___11 (n2)        0.827    0.022   38.213    0.000    0.682    0.822
##   t2_inf_sha_beh_f1 =~                                                      
##     t2_n___01             1.000                               0.587    0.553
##     t2_n___02 (j2)        0.307    0.029   10.437    0.000    0.180    0.371
##   t2_inf_sha_beh_f2 =~                                                      
##     t2_n___03             1.000                               0.987    0.959
##     t2_n___04 (k2)        0.999    0.008  125.373    0.000    0.986    0.948
##   t2_inf_sha_beh_f3 =~                                                      
##     t2_n___05             1.000                               0.948    0.967
##     t2_n___06 (l2)        0.916    0.010   95.266    0.000    0.868    0.904
##   t2_inf_sha_beh_f4 =~                                                      
##     t2_n___07             1.000                               0.892    0.856
##     t2_n___08 (m2)        0.735    0.017   43.185    0.000    0.656    0.683
##   t2_inf_sha_beh_f5 =~                                                      
##     t2_n___10             1.000                               0.796    0.937
##     t2_n___11 (n2)        0.827    0.022   38.213    0.000    0.658    0.818
##   t3_inf_sha_beh_f1 =~                                                      
##     t3_n___01             1.000                               0.684    0.648
##     t3_n___02 (j2)        0.307    0.029   10.437    0.000    0.210    0.413
##   t3_inf_sha_beh_f2 =~                                                      
##     t3_n___03             1.000                               0.956    0.967
##     t3_n___04 (k2)        0.999    0.008  125.373    0.000    0.955    0.949
##   t3_inf_sha_beh_f3 =~                                                      
##     t3_n___05             1.000                               0.897    0.970
##     t3_n___06 (l2)        0.916    0.010   95.266    0.000    0.822    0.900
##   t3_inf_sha_beh_f4 =~                                                      
##     t3_n___07             1.000                               0.870    0.841
##     t3_n___08 (m2)        0.735    0.017   43.185    0.000    0.640    0.693
##   t3_inf_sha_beh_f5 =~                                                      
##     t3_n___10             1.000                               0.806    0.943
##     t3_n___11 (n2)        0.827    0.022   38.213    0.000    0.666    0.849
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_inf_sha_beh_f ~~                                                       
##     t2_inf_sh_bh_f        0.070    0.009    8.178    0.000    0.634    0.634
##     t3_inf_sh_bh_f        0.066    0.008    8.160    0.000    0.624    0.624
##   t2_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.066    0.008    8.180    0.000    0.642    0.642
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.389    0.029   13.353    0.000    0.389    0.563
##    .t3_nf_sh_bh_01        0.352    0.028   12.450    0.000    0.352    0.561
##  .t2_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.424    0.029   14.629    0.000    0.424    0.598
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.060    0.007    8.257    0.000    0.060    0.248
##    .t3_nf_sh_bh_02        0.057    0.007    7.651    0.000    0.057    0.231
##  .t2_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.065    0.006   10.141    0.000    0.065    0.311
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.028    0.004    6.384    0.000    0.028    0.338
##    .t3_nf_sh_bh_03        0.032    0.004    8.013    0.000    0.032    0.456
##  .t2_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.041    0.004    9.275    0.000    0.041    0.563
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.042    0.005    9.055    0.000    0.042    0.448
##    .t3_nf_sh_bh_04        0.031    0.004    7.313    0.000    0.031    0.353
##  .t2_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.055    0.005   10.882    0.000    0.055    0.519
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.016    0.004    3.615    0.000    0.016    0.290
##    .t3_nf_sh_bh_05        0.020    0.004    4.946    0.000    0.020    0.404
##  .t2_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.012    0.004    2.647    0.008    0.012    0.209
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.078    0.006   12.532    0.000    0.078    0.462
##    .t3_nf_sh_bh_06        0.064    0.006   10.977    0.000    0.064    0.393
##  .t2_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.073    0.006   12.172    0.000    0.073    0.448
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.143    0.012   12.309    0.000    0.143    0.490
##    .t3_nf_sh_bh_07        0.119    0.012   10.131    0.000    0.119    0.392
##  .t2_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.119    0.012    9.873    0.000    0.119    0.395
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.200    0.015   13.020    0.000    0.200    0.412
##    .t3_nf_sh_bh_08        0.170    0.015   11.732    0.000    0.170    0.370
##  .t2_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.204    0.015   13.564    0.000    0.204    0.437
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.020    0.009    2.185    0.029    0.020    0.214
##    .t3_nf_sh_bh_10        0.033    0.009    3.712    0.000    0.033    0.364
##  .t2_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.058    0.009    6.777    0.000    0.058    0.692
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.071    0.009    8.116    0.000    0.071    0.325
##    .t3_nf_sh_bh_11        0.044    0.008    5.438    0.000    0.044    0.227
##  .t2_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.035    0.008    4.432    0.000    0.035    0.184
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    1.712    0.029   59.200    0.000    1.712    1.582
##    .t1_nf_sh_bh_02    1.244    0.016   79.843    0.000    1.244    2.134
##    .t1_nf_sh_bh_03    2.672    0.028   94.456    0.000    2.672    2.522
##    .t1_nf_sh_bh_04    2.725    0.028   96.494    0.000    2.725    2.576
##    .t1_nf_sh_bh_05    2.545    0.026   96.751    0.000    2.545    2.584
##    .t1_nf_sh_bh_06    2.431    0.026   93.828    0.000    2.431    2.506
##    .t1_nf_sh_bh_07    2.878    0.028  101.995    0.000    2.878    2.723
##    .t1_nf_sh_bh_08    2.194    0.026   85.417    0.000    2.194    2.283
##    .t1_nf_sh_bh_10    1.794    0.024   75.745    0.000    1.794    2.024
##    .t1_nf_sh_bh_11    1.739    0.022   78.360    0.000    1.739    2.094
##    .t2_nf_sh_bh_01    1.713    0.028   60.347    0.000    1.713    1.614
##    .t2_nf_sh_bh_02    1.214    0.013   93.495    0.000    1.214    2.498
##    .t2_nf_sh_bh_03    2.682    0.028   97.502    0.000    2.682    2.605
##    .t2_nf_sh_bh_04    2.764    0.028   99.447    0.000    2.764    2.656
##    .t2_nf_sh_bh_05    2.558    0.026   97.716    0.000    2.558    2.610
##    .t2_nf_sh_bh_06    2.434    0.026   94.906    0.000    2.434    2.536
##    .t2_nf_sh_bh_07    2.923    0.028  105.038    0.000    2.923    2.805
##    .t2_nf_sh_bh_08    2.239    0.026   87.237    0.000    2.239    2.331
##    .t2_nf_sh_bh_10    1.805    0.023   79.573    0.000    1.805    2.127
##    .t2_nf_sh_bh_11    1.735    0.021   80.683    0.000    1.735    2.156
##    .t3_nf_sh_bh_01    1.702    0.028   60.409    0.000    1.702    1.613
##    .t3_nf_sh_bh_02    1.227    0.014   90.119    0.000    1.227    2.408
##    .t3_nf_sh_bh_03    2.627    0.026   99.497    0.000    2.627    2.656
##    .t3_nf_sh_bh_04    2.692    0.027  100.168    0.000    2.692    2.674
##    .t3_nf_sh_bh_05    2.509    0.025  101.544    0.000    2.509    2.712
##    .t3_nf_sh_bh_06    2.395    0.024   98.240    0.000    2.395    2.623
##    .t3_nf_sh_bh_07    2.864    0.028  103.672    0.000    2.864    2.768
##    .t3_nf_sh_bh_08    2.178    0.025   88.164    0.000    2.178    2.357
##    .t3_nf_sh_bh_10    1.776    0.023   77.831    0.000    1.776    2.079
##    .t3_nf_sh_bh_11    1.715    0.021   81.806    0.000    1.715    2.186
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t2_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_nf_sh_bh_01    0.610    0.068    8.905    0.000    0.610    0.520
##    .t1_nf_sh_bh_02    0.287    0.012   23.112    0.000    0.287    0.844
##    .t1_nf_sh_bh_03    0.079    0.006   13.880    0.000    0.079    0.070
##    .t1_nf_sh_bh_04    0.078    0.006   13.799    0.000    0.078    0.070
##    .t1_nf_sh_bh_05    0.049    0.006    7.703    0.000    0.049    0.050
##    .t1_nf_sh_bh_06    0.169    0.008   20.948    0.000    0.169    0.179
##    .t1_nf_sh_bh_07    0.293    0.019   15.634    0.000    0.293    0.262
##    .t1_nf_sh_bh_08    0.478    0.020   23.725    0.000    0.478    0.517
##    .t1_nf_sh_bh_10    0.105    0.019    5.520    0.000    0.105    0.133
##    .t1_nf_sh_bh_11    0.224    0.015   14.581    0.000    0.224    0.325
##    .t2_nf_sh_bh_01    0.782    0.055   14.339    0.000    0.782    0.694
##    .t2_nf_sh_bh_02    0.204    0.009   23.425    0.000    0.204    0.863
##    .t2_nf_sh_bh_03    0.086    0.006   13.249    0.000    0.086    0.081
##    .t2_nf_sh_bh_04    0.111    0.007   15.662    0.000    0.111    0.102
##    .t2_nf_sh_bh_05    0.062    0.007    8.728    0.000    0.062    0.065
##    .t2_nf_sh_bh_06    0.169    0.009   19.784    0.000    0.169    0.183
##    .t2_nf_sh_bh_07    0.289    0.019   14.967    0.000    0.289    0.266
##    .t2_nf_sh_bh_08    0.492    0.021   23.740    0.000    0.492    0.533
##    .t2_nf_sh_bh_10    0.087    0.018    4.933    0.000    0.087    0.121
##    .t2_nf_sh_bh_11    0.214    0.014   15.355    0.000    0.214    0.331
##    .t3_nf_sh_bh_01    0.645    0.060   10.816    0.000    0.645    0.580
##    .t3_nf_sh_bh_02    0.215    0.010   22.592    0.000    0.215    0.830
##    .t3_nf_sh_bh_03    0.063    0.005   11.587    0.000    0.063    0.064
##    .t3_nf_sh_bh_04    0.100    0.006   16.362    0.000    0.100    0.099
##    .t3_nf_sh_bh_05    0.051    0.006    8.155    0.000    0.051    0.059
##    .t3_nf_sh_bh_06    0.159    0.008   20.879    0.000    0.159    0.190
##    .t3_nf_sh_bh_07    0.313    0.020   15.774    0.000    0.313    0.292
##    .t3_nf_sh_bh_08    0.444    0.019   23.161    0.000    0.444    0.520
##    .t3_nf_sh_bh_10    0.081    0.018    4.577    0.000    0.081    0.110
##    .t3_nf_sh_bh_11    0.172    0.013   13.322    0.000    0.172    0.279
##     t1_inf_sh_bh_f    0.114    0.013    8.535    0.000    1.000    1.000
##     t2_inf_sh_bh_f    0.106    0.012    8.530    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.099    0.012    8.528    0.000    1.000    1.000
##    .t1_nf_sh_bh_f1    0.449    0.064    6.976    0.000    0.798    0.798
##    .t1_nf_sh_bh_f2    0.080    0.009    9.386    0.000    0.077    0.077
##    .t1_nf_sh_bh_f3    0.106    0.009   11.509    0.000    0.115    0.115
##    .t1_nf_sh_bh_f4    0.067    0.015    4.436    0.000    0.081    0.081
##    .t1_nf_sh_bh_f5    0.491    0.027   18.022    0.000    0.721    0.721
##    .t2_nf_sh_bh_f1    0.238    0.043    5.486    0.000    0.691    0.691
##    .t2_nf_sh_bh_f2    0.071    0.009    8.074    0.000    0.073    0.073
##    .t2_nf_sh_bh_f3    0.133    0.010   12.994    0.000    0.148    0.148
##    .t2_nf_sh_bh_f4    0.087    0.016    5.533    0.000    0.109    0.109
##    .t2_nf_sh_bh_f5    0.455    0.025   18.012    0.000    0.719    0.719
##    .t3_nf_sh_bh_f1    0.370    0.053    6.967    0.000    0.789    0.789
##    .t3_nf_sh_bh_f2    0.078    0.008    9.489    0.000    0.086    0.086
##    .t3_nf_sh_bh_f3    0.097    0.009   11.039    0.000    0.120    0.120
##    .t3_nf_sh_bh_f4    0.100    0.016    6.221    0.000    0.132    0.132
##    .t3_nf_sh_bh_f5    0.485    0.026   18.702    0.000    0.746    0.746

1.3.3 Reliability

reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t1", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.879          0.913          0.946
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t2", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.877          0.922          0.940
reliabilityL2(get(paste("fit", name, no, sep = "_")), paste("t3", name, "f", sep = "_"))
##        omegaL1        omegaL2 partialOmegaL1 
##          0.868          0.905          0.941

1.3.4 Longitudinal Invariance

(anova(get(paste("fit", name, no - 1, sep = "_")), get(paste("fit", name, no, sep = "_"))))

1.4 Baseline Model

1.4.1 Second Order

name <- "all_vars"
no <- 0
model <- '
# Privacy Concerns
# create factors
t1_pri_con_f =~ 1*t1_pri_con_f1 + a2*t1_pri_con_f2
t2_pri_con_f =~ 1*t2_pri_con_f1 + a2*t2_pri_con_f2
t3_pri_con_f =~ 1*t3_pri_con_f1 + a2*t3_pri_con_f2
t1_pri_con_f1 =~ 1*t1_pri_con_04 + b2*t1_pri_con_05 + b3*t1_pri_con_06
t1_pri_con_f2 =~ 1*t1_pri_con_07 + c2*t1_pri_con_08 + c3*t1_pri_con_09
t2_pri_con_f1 =~ 1*t2_pri_con_04 + b2*t2_pri_con_05 + b3*t2_pri_con_06
t2_pri_con_f2 =~ 1*t2_pri_con_07 + c2*t2_pri_con_08 + c3*t2_pri_con_09
t3_pri_con_f1 =~ 1*t3_pri_con_04 + b2*t3_pri_con_05 + b3*t3_pri_con_06
t3_pri_con_f2 =~ 1*t3_pri_con_07 + c2*t3_pri_con_08 + c3*t3_pri_con_09

# error covariances
t3_pri_con_04 ~~ t2_pri_con_04 + t1_pri_con_04
t3_pri_con_05 ~~ t2_pri_con_05 + t1_pri_con_05
t3_pri_con_06 ~~ t2_pri_con_06 + t1_pri_con_06
t3_pri_con_07 ~~ t2_pri_con_07 + t1_pri_con_07
t3_pri_con_08 ~~ t2_pri_con_08 + t1_pri_con_08
t3_pri_con_09 ~~ t2_pri_con_09 + t1_pri_con_09
t2_pri_con_04 ~~ t1_pri_con_04
t2_pri_con_05 ~~ t1_pri_con_05 
t2_pri_con_06 ~~ t1_pri_con_06
t2_pri_con_07 ~~ t1_pri_con_07
t2_pri_con_08 ~~ t1_pri_con_08
t2_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t1_pri_con_f ~~ t2_pri_con_f + t3_pri_con_f
t2_pri_con_f ~~ t3_pri_con_f

# Information Sharing Attitude
# create factors
t1_inf_sha_att_f =~ 1*t1_inf_sha_att_f1 + d2*t1_inf_sha_att_f2 + d3*t1_inf_sha_att_f3 + d4*t1_inf_sha_att_f4 + d5*t1_inf_sha_att_f5
t2_inf_sha_att_f =~ 1*t2_inf_sha_att_f1 + d2*t2_inf_sha_att_f2 + d3*t2_inf_sha_att_f3 + d4*t2_inf_sha_att_f4 + d5*t2_inf_sha_att_f5
t3_inf_sha_att_f =~ 1*t3_inf_sha_att_f1 + d2*t3_inf_sha_att_f2 + d3*t3_inf_sha_att_f3 + d4*t3_inf_sha_att_f4 + d5*t3_inf_sha_att_f5
t1_inf_sha_att_f1 =~ 1*t1_inf_sha_att_01 + e*t1_inf_sha_att_02
t1_inf_sha_att_f2 =~ 1*t1_inf_sha_att_03 + f*t1_inf_sha_att_04
t1_inf_sha_att_f3 =~ 1*t1_inf_sha_att_05 + g*t1_inf_sha_att_06
t1_inf_sha_att_f4 =~ 1*t1_inf_sha_att_07 + h*t1_inf_sha_att_08
t1_inf_sha_att_f5 =~ 1*t1_inf_sha_att_10 + i*t1_inf_sha_att_11
t2_inf_sha_att_f1 =~ 1*t2_inf_sha_att_01 + e*t2_inf_sha_att_02
t2_inf_sha_att_f2 =~ 1*t2_inf_sha_att_03 + f*t2_inf_sha_att_04
t2_inf_sha_att_f3 =~ 1*t2_inf_sha_att_05 + g*t2_inf_sha_att_06
t2_inf_sha_att_f4 =~ 1*t2_inf_sha_att_07 + h*t2_inf_sha_att_08
t2_inf_sha_att_f5 =~ 1*t2_inf_sha_att_10 + i*t2_inf_sha_att_11
t3_inf_sha_att_f1 =~ 1*t3_inf_sha_att_01 + e*t3_inf_sha_att_02
t3_inf_sha_att_f2 =~ 1*t3_inf_sha_att_03 + f*t3_inf_sha_att_04
t3_inf_sha_att_f3 =~ 1*t3_inf_sha_att_05 + g*t3_inf_sha_att_06
t3_inf_sha_att_f4 =~ 1*t3_inf_sha_att_07 + h*t3_inf_sha_att_08
t3_inf_sha_att_f5 =~ 1*t3_inf_sha_att_10 + i*t3_inf_sha_att_11

# factor covariance
t1_inf_sha_att_f ~~ t2_inf_sha_att_f + t3_inf_sha_att_f
t2_inf_sha_att_f ~~ t3_inf_sha_att_f

# item error covariance
t1_inf_sha_att_01 ~~ t2_inf_sha_att_01 + t3_inf_sha_att_01
t2_inf_sha_att_01 ~~ t3_inf_sha_att_01
t1_inf_sha_att_02 ~~ t2_inf_sha_att_02 + t3_inf_sha_att_02
t2_inf_sha_att_02 ~~ t3_inf_sha_att_02
t1_inf_sha_att_03 ~~ t2_inf_sha_att_03 + t3_inf_sha_att_03
t2_inf_sha_att_03 ~~ t3_inf_sha_att_03
t1_inf_sha_att_04 ~~ t2_inf_sha_att_04 + t3_inf_sha_att_04
t2_inf_sha_att_04 ~~ t3_inf_sha_att_04
t1_inf_sha_att_05 ~~ t2_inf_sha_att_05 + t3_inf_sha_att_05
t2_inf_sha_att_05 ~~ t3_inf_sha_att_05
t1_inf_sha_att_06 ~~ t2_inf_sha_att_06 + t3_inf_sha_att_06
t2_inf_sha_att_06 ~~ t3_inf_sha_att_06
t1_inf_sha_att_07 ~~ t2_inf_sha_att_07 + t3_inf_sha_att_07
t2_inf_sha_att_07 ~~ t3_inf_sha_att_07
t1_inf_sha_att_08 ~~ t2_inf_sha_att_08 + t3_inf_sha_att_08
t2_inf_sha_att_08 ~~ t3_inf_sha_att_08
t1_inf_sha_att_10 ~~ t2_inf_sha_att_10 + t3_inf_sha_att_10
t2_inf_sha_att_10 ~~ t3_inf_sha_att_10
t1_inf_sha_att_11 ~~ t2_inf_sha_att_11 + t3_inf_sha_att_11
t2_inf_sha_att_11 ~~ t3_inf_sha_att_11

# information sharing behavior
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_f1 + o2*t1_inf_sha_beh_f2 + o3*t1_inf_sha_beh_f3 + o4*t1_inf_sha_beh_f4 + o5*t1_inf_sha_beh_f5
t2_inf_sha_beh_f =~ 1*t2_inf_sha_beh_f1 + o2*t2_inf_sha_beh_f2 + o3*t2_inf_sha_beh_f3 + o4*t2_inf_sha_beh_f4 + o5*t2_inf_sha_beh_f5
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_f1 + o2*t3_inf_sha_beh_f2 + o3*t3_inf_sha_beh_f3 + o4*t3_inf_sha_beh_f4 + o5*t3_inf_sha_beh_f5
t1_inf_sha_beh_f1 =~ 1*t1_inf_sha_beh_01 + j2*t1_inf_sha_beh_02
t1_inf_sha_beh_f2 =~ 1*t1_inf_sha_beh_03 + k2*t1_inf_sha_beh_04
t1_inf_sha_beh_f3 =~ 1*t1_inf_sha_beh_05 + l2*t1_inf_sha_beh_06
t1_inf_sha_beh_f4 =~ 1*t1_inf_sha_beh_07 + m2*t1_inf_sha_beh_08
t1_inf_sha_beh_f5 =~ 1*t1_inf_sha_beh_10 + n2*t1_inf_sha_beh_11
t2_inf_sha_beh_f1 =~ 1*t2_inf_sha_beh_01 + j2*t2_inf_sha_beh_02
t2_inf_sha_beh_f2 =~ 1*t2_inf_sha_beh_03 + k2*t2_inf_sha_beh_04
t2_inf_sha_beh_f3 =~ 1*t2_inf_sha_beh_05 + l2*t2_inf_sha_beh_06
t2_inf_sha_beh_f4 =~ 1*t2_inf_sha_beh_07 + m2*t2_inf_sha_beh_08
t2_inf_sha_beh_f5 =~ 1*t2_inf_sha_beh_10 + n2*t2_inf_sha_beh_11
t3_inf_sha_beh_f1 =~ 1*t3_inf_sha_beh_01 + j2*t3_inf_sha_beh_02
t3_inf_sha_beh_f2 =~ 1*t3_inf_sha_beh_03 + k2*t3_inf_sha_beh_04
t3_inf_sha_beh_f3 =~ 1*t3_inf_sha_beh_05 + l2*t3_inf_sha_beh_06
t3_inf_sha_beh_f4 =~ 1*t3_inf_sha_beh_07 + m2*t3_inf_sha_beh_08
t3_inf_sha_beh_f5 =~ 1*t3_inf_sha_beh_10 + n2*t3_inf_sha_beh_11

# factor covariance
t1_inf_sha_beh_f ~~ t2_inf_sha_beh_f + t3_inf_sha_beh_f
t2_inf_sha_beh_f ~~ t3_inf_sha_beh_f

# item error covariance
t1_inf_sha_beh_01 ~~ t2_inf_sha_beh_01 + t3_inf_sha_beh_01
t2_inf_sha_beh_01 ~~ t3_inf_sha_beh_01
t1_inf_sha_beh_02 ~~ t2_inf_sha_beh_02 + t3_inf_sha_beh_02
t2_inf_sha_beh_02 ~~ t3_inf_sha_beh_02
t1_inf_sha_beh_03 ~~ t2_inf_sha_beh_03 + t3_inf_sha_beh_03
t2_inf_sha_beh_03 ~~ t3_inf_sha_beh_03
t1_inf_sha_beh_04 ~~ t2_inf_sha_beh_04 + t3_inf_sha_beh_04
t2_inf_sha_beh_04 ~~ t3_inf_sha_beh_04
t1_inf_sha_beh_05 ~~ t2_inf_sha_beh_05 + t3_inf_sha_beh_05
t2_inf_sha_beh_05 ~~ t3_inf_sha_beh_05
t1_inf_sha_beh_06 ~~ t2_inf_sha_beh_06 + t3_inf_sha_beh_06
t2_inf_sha_beh_06 ~~ t3_inf_sha_beh_06
t1_inf_sha_beh_07 ~~ t2_inf_sha_beh_07 + t3_inf_sha_beh_07
t2_inf_sha_beh_07 ~~ t3_inf_sha_beh_07
t1_inf_sha_beh_08 ~~ t2_inf_sha_beh_08 + t3_inf_sha_beh_08
t2_inf_sha_beh_08 ~~ t3_inf_sha_beh_08
t1_inf_sha_beh_10 ~~ t2_inf_sha_beh_10 + t3_inf_sha_beh_10
t2_inf_sha_beh_10 ~~ t3_inf_sha_beh_10
t1_inf_sha_beh_11 ~~ t2_inf_sha_beh_11 + t3_inf_sha_beh_11
t2_inf_sha_beh_11 ~~ t3_inf_sha_beh_11

## Correlations Attitude and Behavior-Items
t1_inf_sha_beh_01 ~~ t1_inf_sha_att_01
t1_inf_sha_beh_02 ~~ t1_inf_sha_att_02
t1_inf_sha_beh_03 ~~ t1_inf_sha_att_03
t1_inf_sha_beh_04 ~~ t1_inf_sha_att_04
t1_inf_sha_beh_05 ~~ t1_inf_sha_att_05
t1_inf_sha_beh_06 ~~ t1_inf_sha_att_06
t1_inf_sha_beh_07 ~~ t1_inf_sha_att_07
t1_inf_sha_beh_08 ~~ t1_inf_sha_att_08
t1_inf_sha_beh_10 ~~ t1_inf_sha_att_10
t1_inf_sha_beh_11 ~~ t1_inf_sha_att_11
t2_inf_sha_beh_01 ~~ t2_inf_sha_att_01
t2_inf_sha_beh_02 ~~ t2_inf_sha_att_02
t2_inf_sha_beh_03 ~~ t2_inf_sha_att_03
t2_inf_sha_beh_04 ~~ t2_inf_sha_att_04
t2_inf_sha_beh_05 ~~ t2_inf_sha_att_05
t2_inf_sha_beh_06 ~~ t2_inf_sha_att_06
t2_inf_sha_beh_07 ~~ t2_inf_sha_att_07
t2_inf_sha_beh_08 ~~ t2_inf_sha_att_08
t2_inf_sha_beh_10 ~~ t2_inf_sha_att_10
t2_inf_sha_beh_11 ~~ t2_inf_sha_att_11
t3_inf_sha_beh_01 ~~ t3_inf_sha_att_01
t3_inf_sha_beh_02 ~~ t3_inf_sha_att_02
t3_inf_sha_beh_03 ~~ t3_inf_sha_att_03
t3_inf_sha_beh_04 ~~ t3_inf_sha_att_04
t3_inf_sha_beh_05 ~~ t3_inf_sha_att_05
t3_inf_sha_beh_06 ~~ t3_inf_sha_att_06
t3_inf_sha_beh_07 ~~ t3_inf_sha_att_07
t3_inf_sha_beh_08 ~~ t3_inf_sha_att_08
t3_inf_sha_beh_10 ~~ t3_inf_sha_att_10
t3_inf_sha_beh_11 ~~ t3_inf_sha_att_11
'
no <- no + 1
assign(paste("fit", name, no, sep = "_"), cfa(model, d_wide, missing = "ML"))
summary(get(paste("fit", name, no, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 339 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        414
##   Number of equality constraints                    46
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                       109
##                                                       
## Model Test User Model:
##                                                        
##   Test statistic                              11028.436
##   Degrees of freedom                               2791
##   P-value (Chi-square)                            0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             99651.877
##   Degrees of freedom                              3003
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.915
##   Tucker-Lewis Index (TLI)                       0.908
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)            -113455.861
##   Loglikelihood unrestricted model (H1)    -107941.643
##                                                       
##   Akaike (AIC)                              227647.721
##   Bayesian (BIC)                            229578.385
##   Sample-size adjusted Bayesian (BIC)       228409.385
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.046
##   90 Percent confidence interval - lower         0.045
##   90 Percent confidence interval - upper         0.047
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.066
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                           
##     t1_pr_c_1             1.000                               0.943    0.943
##     t1_pr_c_2 (a2)        1.207    0.031   38.919    0.000    0.950    0.950
##   t2_pri_con_f =~                                                           
##     t2_pr_c_1             1.000                               0.966    0.966
##     t2_pr_c_2 (a2)        1.207    0.031   38.919    0.000    0.952    0.952
##   t3_pri_con_f =~                                                           
##     t3_pr_c_1             1.000                               0.986    0.986
##     t3_pr_c_2 (a2)        1.207    0.031   38.919    0.000    0.954    0.954
##   t1_pri_con_f1 =~                                                          
##     t1_pr__04             1.000                               0.846    0.790
##     t1_pr__05 (b2)        1.024    0.028   37.035    0.000    0.866    0.674
##     t1_pr__06 (b3)        1.086    0.024   44.576    0.000    0.919    0.779
##   t1_pri_con_f2 =~                                                          
##     t1_pr__07             1.000                               1.013    0.816
##     t1_pr__08 (c2)        0.972    0.018   55.068    0.000    0.984    0.841
##     t1_pr__09 (c3)        0.859    0.016   52.493    0.000    0.871    0.827
##   t2_pri_con_f1 =~                                                          
##     t2_pr__04             1.000                               0.847    0.798
##     t2_pr__05 (b2)        1.024    0.028   37.035    0.000    0.868    0.672
##     t2_pr__06 (b3)        1.086    0.024   44.576    0.000    0.921    0.791
##   t2_pri_con_f2 =~                                                          
##     t2_pr__07             1.000                               1.039    0.839
##     t2_pr__08 (c2)        0.972    0.018   55.068    0.000    1.009    0.855
##     t2_pr__09 (c3)        0.859    0.016   52.493    0.000    0.892    0.834
##   t3_pri_con_f1 =~                                                          
##     t3_pr__04             1.000                               0.835    0.791
##     t3_pr__05 (b2)        1.024    0.028   37.035    0.000    0.855    0.658
##     t3_pr__06 (b3)        1.086    0.024   44.576    0.000    0.907    0.791
##   t3_pri_con_f2 =~                                                          
##     t3_pr__07             1.000                               1.042    0.843
##     t3_pr__08 (c2)        0.972    0.018   55.068    0.000    1.012    0.869
##     t3_pr__09 (c3)        0.859    0.016   52.493    0.000    0.895    0.831
##   t1_inf_sha_att_f =~                                                       
##     t1_nf___1             1.000                               0.427    0.427
##     t1_nf___2 (d2)        2.922    0.169   17.338    0.000    0.957    0.957
##     t1_nf___3 (d3)        2.849    0.164   17.339    0.000    0.929    0.929
##     t1_nf___4 (d4)        2.196    0.131   16.707    0.000    0.883    0.883
##     t1_nf___5 (d5)        1.474    0.096   15.365    0.000    0.489    0.489
##   t2_inf_sha_att_f =~                                                       
##     t2_nf___1             1.000                               0.450    0.450
##     t2_nf___2 (d2)        2.922    0.169   17.338    0.000    0.962    0.962
##     t2_nf___3 (d3)        2.849    0.164   17.339    0.000    0.942    0.942
##     t2_nf___4 (d4)        2.196    0.131   16.707    0.000    0.917    0.917
##     t2_nf___5 (d5)        1.474    0.096   15.365    0.000    0.492    0.492
##   t3_inf_sha_att_f =~                                                       
##     t3_nf___1             1.000                               0.443    0.443
##     t3_nf___2 (d2)        2.922    0.169   17.338    0.000    0.935    0.935
##     t3_nf___3 (d3)        2.849    0.164   17.339    0.000    0.923    0.923
##     t3_nf___4 (d4)        2.196    0.131   16.707    0.000    0.901    0.901
##     t3_nf___5 (d5)        1.474    0.096   15.365    0.000    0.485    0.485
##   t1_inf_sha_att_f1 =~                                                      
##     t1_n___01             1.000                               0.771    0.698
##     t1_n___02  (e)        0.870    0.059   14.673    0.000    0.671    0.615
##   t1_inf_sha_att_f2 =~                                                      
##     t1_n___03             1.000                               1.006    0.920
##     t1_n___04  (f)        0.953    0.012   81.166    0.000    0.959    0.901
##   t1_inf_sha_att_f3 =~                                                      
##     t1_n___05             1.000                               1.010    0.944
##     t1_n___06  (g)        0.942    0.012   77.141    0.000    0.952    0.881
##   t1_inf_sha_att_f4 =~                                                      
##     t1_n___07             1.000                               0.819    0.751
##     t1_n___08  (h)        0.883    0.024   36.334    0.000    0.724    0.687
##   t1_inf_sha_att_f5 =~                                                      
##     t1_n___10             1.000                               0.993    0.930
##     t1_n___11  (i)        0.976    0.020   49.884    0.000    0.969    0.920
##   t2_inf_sha_att_f1 =~                                                      
##     t2_n___01             1.000                               0.734    0.656
##     t2_n___02  (e)        0.870    0.059   14.673    0.000    0.639    0.594
##   t2_inf_sha_att_f2 =~                                                      
##     t2_n___03             1.000                               1.003    0.920
##     t2_n___04  (f)        0.953    0.012   81.166    0.000    0.956    0.893
##   t2_inf_sha_att_f3 =~                                                      
##     t2_n___05             1.000                               0.999    0.946
##     t2_n___06  (g)        0.942    0.012   77.141    0.000    0.941    0.867
##   t2_inf_sha_att_f4 =~                                                      
##     t2_n___07             1.000                               0.792    0.731
##     t2_n___08  (h)        0.883    0.024   36.334    0.000    0.699    0.664
##   t2_inf_sha_att_f5 =~                                                      
##     t2_n___10             1.000                               0.990    0.948
##     t2_n___11  (i)        0.976    0.020   49.884    0.000    0.967    0.921
##   t3_inf_sha_att_f1 =~                                                      
##     t3_n___01             1.000                               0.718    0.647
##     t3_n___02  (e)        0.870    0.059   14.673    0.000    0.625    0.598
##   t3_inf_sha_att_f2 =~                                                      
##     t3_n___03             1.000                               0.996    0.933
##     t3_n___04  (f)        0.953    0.012   81.166    0.000    0.949    0.895
##   t3_inf_sha_att_f3 =~                                                      
##     t3_n___05             1.000                               0.984    0.936
##     t3_n___06  (g)        0.942    0.012   77.141    0.000    0.927    0.872
##   t3_inf_sha_att_f4 =~                                                      
##     t3_n___07             1.000                               0.777    0.753
##     t3_n___08  (h)        0.883    0.024   36.334    0.000    0.686    0.675
##   t3_inf_sha_att_f5 =~                                                      
##     t3_n___10             1.000                               0.967    0.944
##     t3_n___11  (i)        0.976    0.020   49.884    0.000    0.944    0.917
##   t1_inf_sha_beh_f =~                                                       
##     t1_nf___1             1.000                               0.476    0.476
##     t1_nf___2 (o2)        2.866    0.153   18.734    0.000    0.961    0.961
##     t1_nf___3 (o3)        2.651    0.141   18.753    0.000    0.943    0.943
##     t1_nf___4 (o4)        2.555    0.138   18.482    0.000    0.969    0.969
##     t1_nf___5 (o5)        1.280    0.077   16.568    0.000    0.532    0.532
##   t2_inf_sha_beh_f =~                                                       
##     t2_nf___1             1.000                               0.586    0.586
##     t2_nf___2 (o2)        2.866    0.153   18.734    0.000    0.961    0.961
##     t2_nf___3 (o3)        2.651    0.141   18.753    0.000    0.925    0.925
##     t2_nf___4 (o4)        2.555    0.138   18.482    0.000    0.956    0.956
##     t2_nf___5 (o5)        1.280    0.077   16.568    0.000    0.533    0.533
##   t3_inf_sha_beh_f =~                                                       
##     t3_nf___1             1.000                               0.498    0.498
##     t3_nf___2 (o2)        2.866    0.153   18.734    0.000    0.954    0.954
##     t3_nf___3 (o3)        2.651    0.141   18.753    0.000    0.942    0.942
##     t3_nf___4 (o4)        2.555    0.138   18.482    0.000    0.944    0.944
##     t3_nf___5 (o5)        1.280    0.077   16.568    0.000    0.507    0.507
##   t1_inf_sha_beh_f1 =~                                                      
##     t1_n___01             1.000                               0.718    0.673
##     t1_n___02 (j2)        0.305    0.028   10.729    0.000    0.219    0.378
##   t1_inf_sha_beh_f2 =~                                                      
##     t1_n___03             1.000                               1.019    0.964
##     t1_n___04 (k2)        0.999    0.008  129.856    0.000    1.017    0.965
##   t1_inf_sha_beh_f3 =~                                                      
##     t1_n___05             1.000                               0.960    0.974
##     t1_n___06 (l2)        0.919    0.009   98.441    0.000    0.883    0.910
##   t1_inf_sha_beh_f4 =~                                                      
##     t1_n___07             1.000                               0.901    0.854
##     t1_n___08 (m2)        0.738    0.016   44.897    0.000    0.664    0.697
##   t1_inf_sha_beh_f5 =~                                                      
##     t1_n___10             1.000                               0.822    0.926
##     t1_n___11 (n2)        0.828    0.021   38.714    0.000    0.680    0.825
##   t2_inf_sha_beh_f1 =~                                                      
##     t2_n___01             1.000                               0.564    0.539
##     t2_n___02 (j2)        0.305    0.028   10.729    0.000    0.172    0.358
##   t2_inf_sha_beh_f2 =~                                                      
##     t2_n___03             1.000                               0.986    0.961
##     t2_n___04 (k2)        0.999    0.008  129.856    0.000    0.985    0.949
##   t2_inf_sha_beh_f3 =~                                                      
##     t2_n___05             1.000                               0.947    0.966
##     t2_n___06 (l2)        0.919    0.009   98.441    0.000    0.871    0.908
##   t2_inf_sha_beh_f4 =~                                                      
##     t2_n___07             1.000                               0.884    0.849
##     t2_n___08 (m2)        0.738    0.016   44.897    0.000    0.652    0.689
##   t2_inf_sha_beh_f5 =~                                                      
##     t2_n___10             1.000                               0.794    0.938
##     t2_n___11 (n2)        0.828    0.021   38.714    0.000    0.657    0.817
##   t3_inf_sha_beh_f1 =~                                                      
##     t3_n___01             1.000                               0.638    0.615
##     t3_n___02 (j2)        0.305    0.028   10.729    0.000    0.195    0.387
##   t3_inf_sha_beh_f2 =~                                                      
##     t3_n___03             1.000                               0.956    0.968
##     t3_n___04 (k2)        0.999    0.008  129.856    0.000    0.955    0.951
##   t3_inf_sha_beh_f3 =~                                                      
##     t3_n___05             1.000                               0.895    0.969
##     t3_n___06 (l2)        0.919    0.009   98.441    0.000    0.823    0.903
##   t3_inf_sha_beh_f4 =~                                                      
##     t3_n___07             1.000                               0.861    0.836
##     t3_n___08 (m2)        0.738    0.016   44.897    0.000    0.635    0.697
##   t3_inf_sha_beh_f5 =~                                                      
##     t3_n___10             1.000                               0.803    0.946
##     t3_n___11 (n2)        0.828    0.021   38.714    0.000    0.665    0.846
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t2_pri_con_04 ~~                                                          
##    .t3_pri_con_04         0.071    0.014    4.983    0.000    0.071    0.172
##  .t1_pri_con_04 ~~                                                          
##    .t3_pri_con_04         0.093    0.015    6.240    0.000    0.093    0.220
##  .t2_pri_con_05 ~~                                                          
##    .t3_pri_con_05         0.433    0.031   14.121    0.000    0.433    0.464
##  .t1_pri_con_05 ~~                                                          
##    .t3_pri_con_05         0.454    0.031   14.638    0.000    0.454    0.490
##  .t2_pri_con_06 ~~                                                          
##    .t3_pri_con_06         0.166    0.018    9.427    0.000    0.166    0.332
##  .t1_pri_con_06 ~~                                                          
##    .t3_pri_con_06         0.160    0.018    8.820    0.000    0.160    0.308
##  .t2_pri_con_07 ~~                                                          
##    .t3_pri_con_07         0.157    0.017    9.461    0.000    0.157    0.349
##  .t1_pri_con_07 ~~                                                          
##    .t3_pri_con_07         0.171    0.018    9.754    0.000    0.171    0.359
##  .t2_pri_con_08 ~~                                                          
##    .t3_pri_con_08         0.109    0.014    8.049    0.000    0.109    0.310
##  .t1_pri_con_08 ~~                                                          
##    .t3_pri_con_08         0.099    0.014    7.174    0.000    0.099    0.272
##  .t2_pri_con_09 ~~                                                          
##    .t3_pri_con_09         0.109    0.013    8.564    0.000    0.109    0.307
##  .t1_pri_con_09 ~~                                                          
##    .t3_pri_con_09         0.070    0.012    5.586    0.000    0.070    0.197
##  .t1_pri_con_04 ~~                                                          
##    .t2_pri_con_04         0.087    0.015    5.844    0.000    0.087    0.208
##  .t1_pri_con_05 ~~                                                          
##    .t2_pri_con_05         0.401    0.030   13.351    0.000    0.401    0.442
##  .t1_pri_con_06 ~~                                                          
##    .t2_pri_con_06         0.157    0.019    8.492    0.000    0.157    0.299
##  .t1_pri_con_07 ~~                                                          
##    .t2_pri_con_07         0.158    0.018    8.984    0.000    0.158    0.326
##  .t1_pri_con_08 ~~                                                          
##    .t2_pri_con_08         0.092    0.014    6.441    0.000    0.092    0.239
##  .t1_pri_con_09 ~~                                                          
##    .t2_pri_con_09         0.075    0.012    6.055    0.000    0.075    0.215
##   t1_pri_con_f ~~                                                           
##     t2_pri_con_f          0.514    0.030   17.198    0.000    0.787    0.787
##     t3_pri_con_f          0.507    0.029   17.201    0.000    0.772    0.772
##   t2_pri_con_f ~~                                                           
##     t3_pri_con_f          0.530    0.030   17.387    0.000    0.786    0.786
##   t1_inf_sha_att_f ~~                                                       
##     t2_inf_sh_tt_f        0.063    0.008    7.861    0.000    0.577    0.577
##     t3_inf_sh_tt_f        0.059    0.008    7.841    0.000    0.563    0.563
##   t2_inf_sha_att_f ~~                                                       
##     t3_inf_sh_tt_f        0.067    0.008    7.984    0.000    0.636    0.636
##  .t1_inf_sha_att_01 ~~                                                      
##    .t2_nf_sh_tt_01        0.240    0.028    8.508    0.000    0.240    0.359
##    .t3_nf_sh_tt_01        0.259    0.028    9.248    0.000    0.259    0.387
##  .t2_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_tt_01        0.279    0.030    9.411    0.000    0.279    0.390
##  .t1_inf_sha_att_02 ~~                                                      
##    .t2_nf_sh_tt_02        0.311    0.028   11.136    0.000    0.311    0.419
##    .t3_nf_sh_tt_02        0.292    0.027   10.816    0.000    0.292    0.406
##  .t2_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_tt_02        0.348    0.028   12.567    0.000    0.348    0.481
##  .t1_inf_sha_att_03 ~~                                                      
##    .t2_nf_sh_tt_03        0.057    0.008    6.793    0.000    0.057    0.313
##    .t3_nf_sh_tt_03        0.055    0.008    6.778    0.000    0.055    0.336
##  .t2_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_tt_03        0.057    0.008    7.047    0.000    0.057    0.347
##  .t1_inf_sha_att_04 ~~                                                      
##    .t2_nf_sh_tt_04        0.070    0.009    7.824    0.000    0.070    0.315
##    .t3_nf_sh_tt_04        0.053    0.009    6.106    0.000    0.053    0.243
##  .t2_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_tt_04        0.075    0.009    8.011    0.000    0.075    0.327
##  .t1_inf_sha_att_05 ~~                                                      
##    .t2_nf_sh_tt_05        0.026    0.007    3.493    0.000    0.026    0.213
##    .t3_nf_sh_tt_05        0.031    0.008    4.025    0.000    0.031    0.234
##  .t2_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_tt_05        0.024    0.007    3.319    0.001    0.024    0.191
##  .t1_inf_sha_att_06 ~~                                                      
##    .t2_nf_sh_tt_06        0.136    0.011   12.653    0.000    0.136    0.493
##    .t3_nf_sh_tt_06        0.116    0.010   11.249    0.000    0.116    0.434
##  .t2_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_tt_06        0.122    0.011   11.493    0.000    0.122    0.432
##  .t1_inf_sha_att_07 ~~                                                      
##    .t2_nf_sh_tt_07        0.238    0.019   12.350    0.000    0.238    0.449
##    .t3_nf_sh_tt_07        0.198    0.018   11.046    0.000    0.198    0.406
##  .t2_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_tt_07        0.232    0.018   12.645    0.000    0.232    0.464
##  .t1_inf_sha_att_08 ~~                                                      
##    .t2_nf_sh_tt_08        0.216    0.020   10.682    0.000    0.216    0.358
##    .t3_nf_sh_tt_08        0.227    0.019   11.705    0.000    0.227    0.396
##  .t2_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_tt_08        0.208    0.020   10.514    0.000    0.208    0.353
##  .t1_inf_sha_att_10 ~~                                                      
##    .t2_nf_sh_tt_10        0.032    0.011    2.975    0.003    0.032    0.247
##    .t3_nf_sh_tt_10        0.006    0.011    0.577    0.564    0.006    0.048
##  .t2_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_tt_10        0.001    0.011    0.126    0.899    0.001    0.012
##  .t1_inf_sha_att_11 ~~                                                      
##    .t2_nf_sh_tt_11        0.034    0.011    3.117    0.002    0.034    0.199
##    .t3_nf_sh_tt_11        0.049    0.011    4.519    0.000    0.049    0.286
##  .t2_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_tt_11        0.045    0.011    4.218    0.000    0.045    0.266
##   t1_inf_sha_beh_f ~~                                                       
##     t2_inf_sh_bh_f        0.072    0.008    8.496    0.000    0.635    0.635
##     t3_inf_sh_bh_f        0.068    0.008    8.474    0.000    0.625    0.625
##   t2_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.068    0.008    8.501    0.000    0.645    0.645
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.335    0.028   12.002    0.000    0.335    0.482
##    .t3_nf_sh_bh_01        0.301    0.027   11.039    0.000    0.301    0.465
##  .t2_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.362    0.028   12.926    0.000    0.362    0.503
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.052    0.007    7.332    0.000    0.052    0.217
##    .t3_nf_sh_bh_02        0.049    0.007    6.703    0.000    0.049    0.198
##  .t2_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.056    0.006    8.944    0.000    0.056    0.269
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.022    0.004    5.260    0.000    0.022    0.276
##    .t3_nf_sh_bh_03        0.028    0.004    7.164    0.000    0.028    0.404
##  .t2_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.036    0.004    8.666    0.000    0.036    0.521
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.035    0.004    7.812    0.000    0.035    0.386
##    .t3_nf_sh_bh_04        0.025    0.004    6.033    0.000    0.025    0.290
##  .t2_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.047    0.005    9.691    0.000    0.047    0.462
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.013    0.004    2.898    0.004    0.013    0.224
##    .t3_nf_sh_bh_05        0.018    0.004    4.567    0.000    0.018    0.353
##  .t2_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.010    0.004    2.446    0.014    0.010    0.180
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.068    0.006   11.042    0.000    0.068    0.417
##    .t3_nf_sh_bh_06        0.053    0.006    9.326    0.000    0.053    0.338
##  .t2_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.064    0.006   10.982    0.000    0.064    0.406
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.130    0.011   11.534    0.000    0.130    0.432
##    .t3_nf_sh_bh_07        0.095    0.011    8.326    0.000    0.095    0.305
##  .t2_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.097    0.012    8.235    0.000    0.097    0.312
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.165    0.015   11.268    0.000    0.165    0.351
##    .t3_nf_sh_bh_08        0.129    0.014    9.277    0.000    0.129    0.290
##  .t2_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.151    0.014   10.575    0.000    0.151    0.338
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.019    0.009    2.001    0.045    0.019    0.192
##    .t3_nf_sh_bh_10        0.030    0.009    3.350    0.001    0.030    0.329
##  .t2_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.053    0.009    6.220    0.000    0.053    0.662
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.066    0.009    7.546    0.000    0.066    0.306
##    .t3_nf_sh_bh_11        0.041    0.008    4.985    0.000    0.041    0.210
##  .t2_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.034    0.008    4.131    0.000    0.034    0.174
##  .t1_inf_sha_att_01 ~~                                                      
##    .t1_nf_sh_bh_01        0.163    0.024    6.782    0.000    0.163    0.262
##  .t1_inf_sha_att_02 ~~                                                      
##    .t1_nf_sh_bh_02        0.062    0.014    4.593    0.000    0.062    0.135
##  .t1_inf_sha_att_03 ~~                                                      
##    .t1_nf_sh_bh_03        0.018    0.005    3.431    0.001    0.018    0.153
##  .t1_inf_sha_att_04 ~~                                                      
##    .t1_nf_sh_bh_04        0.027    0.005    5.004    0.000    0.027    0.213
##  .t1_inf_sha_att_05 ~~                                                      
##    .t1_nf_sh_bh_05        0.008    0.005    1.557    0.119    0.008    0.102
##  .t1_inf_sha_att_06 ~~                                                      
##    .t1_nf_sh_bh_06        0.033    0.006    5.065    0.000    0.033    0.160
##  .t1_inf_sha_att_07 ~~                                                      
##    .t1_nf_sh_bh_07        0.071    0.012    5.790    0.000    0.071    0.180
##  .t1_inf_sha_att_08 ~~                                                      
##    .t1_nf_sh_bh_08        0.109    0.015    7.318    0.000    0.109    0.209
##  .t1_inf_sha_att_10 ~~                                                      
##    .t1_nf_sh_bh_10        0.003    0.010    0.267    0.789    0.003    0.021
##  .t1_inf_sha_att_11 ~~                                                      
##    .t1_nf_sh_bh_11        0.040    0.009    4.197    0.000    0.040    0.207
##  .t2_inf_sha_att_01 ~~                                                      
##    .t2_nf_sh_bh_01        0.163    0.024    6.708    0.000    0.163    0.219
##  .t2_inf_sha_att_02 ~~                                                      
##    .t2_nf_sh_bh_02        0.063    0.011    5.644    0.000    0.063    0.163
##  .t2_inf_sha_att_03 ~~                                                      
##    .t2_nf_sh_bh_03        0.032    0.005    6.112    0.000    0.032    0.264
##  .t2_inf_sha_att_04 ~~                                                      
##    .t2_nf_sh_bh_04        0.026    0.006    4.403    0.000    0.026    0.162
##  .t2_inf_sha_att_05 ~~                                                      
##    .t2_nf_sh_bh_05        0.020    0.005    3.643    0.000    0.020    0.225
##  .t2_inf_sha_att_06 ~~                                                      
##    .t2_nf_sh_bh_06        0.031    0.007    4.667    0.000    0.031    0.143
##  .t2_inf_sha_att_07 ~~                                                      
##    .t2_nf_sh_bh_07        0.076    0.012    6.141    0.000    0.076    0.187
##  .t2_inf_sha_att_08 ~~                                                      
##    .t2_nf_sh_bh_08        0.117    0.015    7.573    0.000    0.117    0.217
##  .t2_inf_sha_att_10 ~~                                                      
##    .t2_nf_sh_bh_10        0.020    0.009    2.188    0.029    0.020    0.205
##  .t2_inf_sha_att_11 ~~                                                      
##    .t2_nf_sh_bh_11        0.011    0.009    1.163    0.245    0.011    0.056
##  .t3_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.168    0.024    6.949    0.000    0.168    0.242
##  .t3_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.068    0.011    5.940    0.000    0.068    0.174
##  .t3_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.020    0.005    4.326    0.000    0.020    0.214
##  .t3_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.032    0.006    5.720    0.000    0.032    0.215
##  .t3_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.024    0.005    4.627    0.000    0.024    0.282
##  .t3_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.035    0.006    5.457    0.000    0.035    0.173
##  .t3_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.090    0.013    7.108    0.000    0.090    0.235
##  .t3_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.115    0.015    7.931    0.000    0.115    0.236
##  .t3_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.026    0.009    2.870    0.004    0.026    0.277
##  .t3_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_bh_11       -0.003    0.009   -0.299    0.765   -0.003   -0.015
##   t1_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.051    0.009   -5.953    0.000   -0.196   -0.196
##     t2_inf_sh_tt_f       -0.056    0.009   -6.342    0.000   -0.211   -0.211
##     t3_inf_sh_tt_f       -0.044    0.008   -5.376    0.000   -0.175   -0.175
##     t1_inf_sh_bh_f       -0.031    0.008   -3.728    0.000   -0.114   -0.114
##     t2_inf_sh_bh_f       -0.021    0.008   -2.682    0.007   -0.081   -0.081
##     t3_inf_sh_bh_f       -0.017    0.008   -2.241    0.025   -0.068   -0.068
##   t2_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.049    0.009   -5.616    0.000   -0.181   -0.181
##     t2_inf_sh_tt_f       -0.058    0.009   -6.464    0.000   -0.213   -0.213
##     t3_inf_sh_tt_f       -0.046    0.008   -5.447    0.000   -0.175   -0.175
##     t1_inf_sh_bh_f       -0.029    0.008   -3.407    0.001   -0.102   -0.102
##     t2_inf_sh_bh_f       -0.022    0.008   -2.680    0.007   -0.080   -0.080
##     t3_inf_sh_bh_f       -0.019    0.008   -2.379    0.017   -0.071   -0.071
##   t3_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.046    0.009   -5.347    0.000   -0.170   -0.170
##     t2_inf_sh_tt_f       -0.055    0.009   -6.172    0.000   -0.201   -0.201
##     t3_inf_sh_tt_f       -0.045    0.008   -5.419    0.000   -0.173   -0.173
##     t1_inf_sh_bh_f       -0.028    0.008   -3.354    0.001   -0.100   -0.100
##     t2_inf_sh_bh_f       -0.026    0.008   -3.177    0.001   -0.095   -0.095
##     t3_inf_sh_bh_f       -0.018    0.008   -2.365    0.018   -0.070   -0.070
##   t1_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.048    0.005    9.308    0.000    0.430    0.430
##     t2_inf_sh_bh_f        0.037    0.004    8.408    0.000    0.342    0.342
##     t3_inf_sh_bh_f        0.041    0.005    8.923    0.000    0.389    0.389
##   t2_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.043    0.005    8.870    0.000    0.383    0.383
##     t2_inf_sh_bh_f        0.047    0.005    9.319    0.000    0.432    0.432
##     t3_inf_sh_bh_f        0.044    0.005    9.198    0.000    0.418    0.418
##   t3_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.042    0.005    8.878    0.000    0.386    0.386
##     t2_inf_sh_bh_f        0.046    0.005    9.329    0.000    0.434    0.434
##     t3_inf_sh_bh_f        0.053    0.005    9.945    0.000    0.524    0.524
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     3.745    0.029  130.880    0.000    3.745    3.499
##    .t1_pri_con_05     3.842    0.034  111.483    0.000    3.842    2.990
##    .t1_pri_con_06     3.314    0.032  105.108    0.000    3.314    2.810
##    .t1_pri_con_07     3.623    0.033  109.196    0.000    3.623    2.919
##    .t1_pri_con_08     3.624    0.031  115.840    0.000    3.624    3.097
##    .t1_pri_con_09     4.095    0.028  145.553    0.000    4.095    3.892
##    .t2_pri_con_04     3.675    0.028  129.336    0.000    3.675    3.458
##    .t2_pri_con_05     3.784    0.035  109.357    0.000    3.784    2.931
##    .t2_pri_con_06     3.258    0.031  104.665    0.000    3.258    2.799
##    .t2_pri_con_07     3.556    0.033  107.462    0.000    3.556    2.873
##    .t2_pri_con_08     3.551    0.032  112.597    0.000    3.551    3.010
##    .t2_pri_con_09     3.994    0.029  139.686    0.000    3.994    3.733
##    .t3_pri_con_04     3.664    0.028  129.793    0.000    3.664    3.471
##    .t3_pri_con_05     3.709    0.035  106.540    0.000    3.709    2.857
##    .t3_pri_con_06     3.256    0.031  106.187    0.000    3.256    2.839
##    .t3_pri_con_07     3.492    0.033  105.643    0.000    3.492    2.825
##    .t3_pri_con_08     3.560    0.031  114.265    0.000    3.560    3.056
##    .t3_pri_con_09     3.959    0.029  137.482    0.000    3.959    3.677
##    .t1_nf_sh_tt_01    1.704    0.029   57.766    0.000    1.704    1.543
##    .t1_nf_sh_tt_02    1.900    0.029   65.212    0.000    1.900    1.744
##    .t1_nf_sh_tt_03    2.788    0.029   95.482    0.000    2.788    2.551
##    .t1_nf_sh_tt_04    2.940    0.028  103.429    0.000    2.940    2.763
##    .t1_nf_sh_tt_05    2.626    0.029   91.849    0.000    2.626    2.454
##    .t1_nf_sh_tt_06    2.373    0.029   82.165    0.000    2.373    2.196
##    .t1_nf_sh_tt_07    3.011    0.029  103.365    0.000    3.011    2.762
##    .t1_nf_sh_tt_08    2.293    0.028   81.475    0.000    2.293    2.177
##    .t1_nf_sh_tt_10    2.249    0.029   78.845    0.000    2.249    2.108
##    .t1_nf_sh_tt_11    2.295    0.028   81.531    0.000    2.295    2.179
##    .t2_nf_sh_tt_01    1.764    0.030   58.870    0.000    1.764    1.576
##    .t2_nf_sh_tt_02    1.932    0.029   67.096    0.000    1.932    1.797
##    .t2_nf_sh_tt_03    2.903    0.029   99.573    0.000    2.903    2.664
##    .t2_nf_sh_tt_04    2.998    0.029  104.623    0.000    2.998    2.800
##    .t2_nf_sh_tt_05    2.710    0.028   95.895    0.000    2.710    2.566
##    .t2_nf_sh_tt_06    2.428    0.029   83.576    0.000    2.428    2.237
##    .t2_nf_sh_tt_07    3.119    0.029  107.636    0.000    3.119    2.882
##    .t2_nf_sh_tt_08    2.332    0.028   82.737    0.000    2.332    2.215
##    .t2_nf_sh_tt_10    2.271    0.028   81.149    0.000    2.271    2.175
##    .t2_nf_sh_tt_11    2.363    0.028   83.963    0.000    2.363    2.251
##    .t3_nf_sh_tt_01    1.777    0.030   59.910    0.000    1.777    1.600
##    .t3_nf_sh_tt_02    1.887    0.028   67.626    0.000    1.887    1.806
##    .t3_nf_sh_tt_03    2.951    0.028  103.577    0.000    2.951    2.765
##    .t3_nf_sh_tt_04    3.057    0.028  107.956    0.000    3.057    2.882
##    .t3_nf_sh_tt_05    2.737    0.028   97.466    0.000    2.737    2.603
##    .t3_nf_sh_tt_06    2.473    0.028   87.188    0.000    2.473    2.328
##    .t3_nf_sh_tt_07    3.103    0.028  112.660    0.000    3.103    3.010
##    .t3_nf_sh_tt_08    2.368    0.027   87.262    0.000    2.368    2.331
##    .t3_nf_sh_tt_10    2.297    0.027   83.925    0.000    2.297    2.242
##    .t3_nf_sh_tt_11    2.366    0.028   85.992    0.000    2.366    2.296
##    .t1_nf_sh_bh_01    1.713    0.029   60.081    0.000    1.713    1.605
##    .t1_nf_sh_bh_02    1.244    0.015   80.287    0.000    1.244    2.145
##    .t1_nf_sh_bh_03    2.672    0.028   94.720    0.000    2.672    2.529
##    .t1_nf_sh_bh_04    2.725    0.028   96.795    0.000    2.725    2.584
##    .t1_nf_sh_bh_05    2.545    0.026   96.688    0.000    2.545    2.582
##    .t1_nf_sh_bh_06    2.431    0.026   93.869    0.000    2.431    2.507
##    .t1_nf_sh_bh_07    2.878    0.028  102.195    0.000    2.878    2.729
##    .t1_nf_sh_bh_08    2.194    0.025   86.140    0.000    2.194    2.302
##    .t1_nf_sh_bh_10    1.793    0.024   75.653    0.000    1.793    2.022
##    .t1_nf_sh_bh_11    1.739    0.022   78.954    0.000    1.739    2.110
##    .t2_nf_sh_bh_01    1.713    0.028   61.277    0.000    1.713    1.639
##    .t2_nf_sh_bh_02    1.214    0.013   94.409    0.000    1.214    2.522
##    .t2_nf_sh_bh_03    2.681    0.027   97.837    0.000    2.681    2.613
##    .t2_nf_sh_bh_04    2.764    0.028   99.692    0.000    2.764    2.663
##    .t2_nf_sh_bh_05    2.558    0.026   97.672    0.000    2.558    2.609
##    .t2_nf_sh_bh_06    2.434    0.026   94.964    0.000    2.434    2.537
##    .t2_nf_sh_bh_07    2.923    0.028  105.145    0.000    2.923    2.808
##    .t2_nf_sh_bh_08    2.239    0.025   88.523    0.000    2.239    2.365
##    .t2_nf_sh_bh_10    1.805    0.023   79.856    0.000    1.805    2.134
##    .t2_nf_sh_bh_11    1.734    0.021   80.702    0.000    1.734    2.156
##    .t3_nf_sh_bh_01    1.702    0.028   61.391    0.000    1.702    1.639
##    .t3_nf_sh_bh_02    1.226    0.013   91.181    0.000    1.226    2.436
##    .t3_nf_sh_bh_03    2.627    0.026   99.684    0.000    2.627    2.661
##    .t3_nf_sh_bh_04    2.692    0.027  100.443    0.000    2.692    2.682
##    .t3_nf_sh_bh_05    2.509    0.025  101.643    0.000    2.509    2.714
##    .t3_nf_sh_bh_06    2.395    0.024   98.409    0.000    2.395    2.628
##    .t3_nf_sh_bh_07    2.865    0.027  104.202    0.000    2.865    2.783
##    .t3_nf_sh_bh_08    2.178    0.024   89.471    0.000    2.178    2.392
##    .t3_nf_sh_bh_10    1.776    0.023   78.319    0.000    1.776    2.092
##    .t3_nf_sh_bh_11    1.715    0.021   81.704    0.000    1.715    2.183
##     t1_pri_con_f      0.000                               0.000    0.000
##     t2_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
##    .t1_pri_con_f1     0.000                               0.000    0.000
##    .t1_pri_con_f2     0.000                               0.000    0.000
##    .t2_pri_con_f1     0.000                               0.000    0.000
##    .t2_pri_con_f2     0.000                               0.000    0.000
##    .t3_pri_con_f1     0.000                               0.000    0.000
##    .t3_pri_con_f2     0.000                               0.000    0.000
##     t1_inf_sh_tt_f    0.000                               0.000    0.000
##     t2_inf_sh_tt_f    0.000                               0.000    0.000
##     t3_inf_sh_tt_f    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t2_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f5    0.000                               0.000    0.000
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t2_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t2_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     0.430    0.022   19.770    0.000    0.430    0.375
##    .t1_pri_con_05     0.901    0.040   22.795    0.000    0.901    0.545
##    .t1_pri_con_06     0.546    0.027   20.394    0.000    0.546    0.393
##    .t1_pri_con_07     0.514    0.025   20.296    0.000    0.514    0.334
##    .t1_pri_con_08     0.400    0.021   19.068    0.000    0.400    0.292
##    .t1_pri_con_09     0.350    0.018   19.974    0.000    0.350    0.316
##    .t2_pri_con_04     0.411    0.020   20.148    0.000    0.411    0.364
##    .t2_pri_con_05     0.913    0.039   23.245    0.000    0.913    0.548
##    .t2_pri_con_06     0.507    0.025   20.546    0.000    0.507    0.374
##    .t2_pri_con_07     0.454    0.023   19.893    0.000    0.454    0.296
##    .t2_pri_con_08     0.373    0.020   18.952    0.000    0.373    0.268
##    .t2_pri_con_09     0.349    0.017   19.964    0.000    0.349    0.304
##    .t3_pri_con_04     0.418    0.020   20.636    0.000    0.418    0.375
##    .t3_pri_con_05     0.955    0.040   23.584    0.000    0.955    0.566
##    .t3_pri_con_06     0.493    0.024   20.725    0.000    0.493    0.375
##    .t3_pri_con_07     0.443    0.022   20.068    0.000    0.443    0.290
##    .t3_pri_con_08     0.333    0.018   18.495    0.000    0.333    0.245
##    .t3_pri_con_09     0.358    0.017   20.651    0.000    0.358    0.309
##    .t1_nf_sh_tt_01    0.624    0.051   12.213    0.000    0.624    0.512
##    .t1_nf_sh_tt_02    0.738    0.044   16.630    0.000    0.738    0.621
##    .t1_nf_sh_tt_03    0.182    0.012   15.173    0.000    0.182    0.153
##    .t1_nf_sh_tt_04    0.213    0.012   17.894    0.000    0.213    0.188
##    .t1_nf_sh_tt_05    0.125    0.011   11.317    0.000    0.125    0.109
##    .t1_nf_sh_tt_06    0.262    0.013   19.759    0.000    0.262    0.225
##    .t1_nf_sh_tt_07    0.517    0.028   18.710    0.000    0.517    0.435
##    .t1_nf_sh_tt_08    0.586    0.027   21.919    0.000    0.586    0.528
##    .t1_nf_sh_tt_10    0.153    0.021    7.153    0.000    0.153    0.135
##    .t1_nf_sh_tt_11    0.170    0.020    8.287    0.000    0.170    0.153
##    .t2_nf_sh_tt_01    0.714    0.050   14.152    0.000    0.714    0.570
##    .t2_nf_sh_tt_02    0.747    0.043   17.371    0.000    0.747    0.647
##    .t2_nf_sh_tt_03    0.182    0.012   15.418    0.000    0.182    0.153
##    .t2_nf_sh_tt_04    0.233    0.012   18.968    0.000    0.233    0.203
##    .t2_nf_sh_tt_05    0.118    0.011   11.088    0.000    0.118    0.105
##    .t2_nf_sh_tt_06    0.293    0.014   21.050    0.000    0.293    0.249
##    .t2_nf_sh_tt_07    0.545    0.028   19.475    0.000    0.545    0.465
##    .t2_nf_sh_tt_08    0.620    0.027   22.644    0.000    0.620    0.559
##    .t2_nf_sh_tt_10    0.110    0.020    5.380    0.000    0.110    0.101
##    .t2_nf_sh_tt_11    0.168    0.020    8.371    0.000    0.168    0.152
##    .t3_nf_sh_tt_01    0.718    0.050   14.480    0.000    0.718    0.582
##    .t3_nf_sh_tt_02    0.701    0.041   16.920    0.000    0.701    0.642
##    .t3_nf_sh_tt_03    0.147    0.011   13.033    0.000    0.147    0.129
##    .t3_nf_sh_tt_04    0.224    0.012   18.648    0.000    0.224    0.199
##    .t3_nf_sh_tt_05    0.138    0.012   11.909    0.000    0.138    0.125
##    .t3_nf_sh_tt_06    0.270    0.014   19.992    0.000    0.270    0.239
##    .t3_nf_sh_tt_07    0.460    0.025   18.526    0.000    0.460    0.433
##    .t3_nf_sh_tt_08    0.561    0.025   22.763    0.000    0.561    0.544
##    .t3_nf_sh_tt_10    0.114    0.021    5.561    0.000    0.114    0.109
##    .t3_nf_sh_tt_11    0.170    0.020    8.523    0.000    0.170    0.160
##    .t1_nf_sh_bh_01    0.624    0.065    9.627    0.000    0.624    0.548
##    .t1_nf_sh_bh_02    0.288    0.012   23.729    0.000    0.288    0.857
##    .t1_nf_sh_bh_03    0.078    0.005   14.195    0.000    0.078    0.070
##    .t1_nf_sh_bh_04    0.077    0.005   14.119    0.000    0.077    0.069
##    .t1_nf_sh_bh_05    0.050    0.006    8.109    0.000    0.050    0.051
##    .t1_nf_sh_bh_06    0.161    0.008   21.073    0.000    0.161    0.172
##    .t1_nf_sh_bh_07    0.301    0.018   16.441    0.000    0.301    0.271
##    .t1_nf_sh_bh_08    0.467    0.019   24.317    0.000    0.467    0.514
##    .t1_nf_sh_bh_10    0.111    0.019    5.983    0.000    0.111    0.142
##    .t1_nf_sh_bh_11    0.217    0.015   14.462    0.000    0.217    0.319
##    .t2_nf_sh_bh_01    0.775    0.052   14.926    0.000    0.775    0.709
##    .t2_nf_sh_bh_02    0.202    0.008   23.892    0.000    0.202    0.872
##    .t2_nf_sh_bh_03    0.081    0.006   13.342    0.000    0.081    0.077
##    .t2_nf_sh_bh_04    0.108    0.007   16.252    0.000    0.108    0.100
##    .t2_nf_sh_bh_05    0.064    0.007    9.284    0.000    0.064    0.067
##    .t2_nf_sh_bh_06    0.162    0.008   19.952    0.000    0.162    0.176
##    .t2_nf_sh_bh_07    0.302    0.019   15.925    0.000    0.302    0.279
##    .t2_nf_sh_bh_08    0.471    0.019   24.494    0.000    0.471    0.525
##    .t2_nf_sh_bh_10    0.085    0.017    4.887    0.000    0.085    0.119
##    .t2_nf_sh_bh_11    0.216    0.014   15.481    0.000    0.216    0.333
##    .t3_nf_sh_bh_01    0.670    0.056   12.049    0.000    0.670    0.622
##    .t3_nf_sh_bh_02    0.215    0.009   23.437    0.000    0.215    0.850
##    .t3_nf_sh_bh_03    0.061    0.005   11.810    0.000    0.061    0.062
##    .t3_nf_sh_bh_04    0.097    0.006   16.841    0.000    0.097    0.096
##    .t3_nf_sh_bh_05    0.053    0.006    8.761    0.000    0.053    0.062
##    .t3_nf_sh_bh_06    0.153    0.007   21.252    0.000    0.153    0.185
##    .t3_nf_sh_bh_07    0.319    0.019   16.608    0.000    0.319    0.301
##    .t3_nf_sh_bh_08    0.425    0.018   23.964    0.000    0.425    0.513
##    .t3_nf_sh_bh_10    0.075    0.017    4.351    0.000    0.075    0.105
##    .t3_nf_sh_bh_11    0.175    0.013   13.533    0.000    0.175    0.284
##     t1_pri_con_f      0.636    0.035   18.264    0.000    1.000    1.000
##     t2_pri_con_f      0.671    0.036   18.623    0.000    1.000    1.000
##     t3_pri_con_f      0.678    0.036   18.806    0.000    1.000    1.000
##    .t1_pri_con_f1     0.079    0.014    5.532    0.000    0.111    0.111
##    .t1_pri_con_f2     0.100    0.019    5.355    0.000    0.097    0.097
##    .t2_pri_con_f1     0.048    0.013    3.673    0.000    0.066    0.066
##    .t2_pri_con_f2     0.102    0.018    5.772    0.000    0.094    0.094
##    .t3_pri_con_f1     0.019    0.012    1.535    0.125    0.027    0.027
##    .t3_pri_con_f2     0.097    0.017    5.697    0.000    0.090    0.090
##     t1_inf_sh_tt_f    0.109    0.013    8.314    0.000    1.000    1.000
##     t2_inf_sh_tt_f    0.109    0.013    8.312    0.000    1.000    1.000
##     t3_inf_sh_tt_f    0.101    0.012    8.299    0.000    1.000    1.000
##    .t1_nf_sh_tt_f1    0.486    0.048   10.048    0.000    0.817    0.817
##    .t1_nf_sh_tt_f2    0.085    0.013    6.479    0.000    0.084    0.084
##    .t1_nf_sh_tt_f3    0.139    0.014    9.844    0.000    0.136    0.136
##    .t1_nf_sh_tt_f4    0.147    0.020    7.480    0.000    0.219    0.219
##    .t1_nf_sh_tt_f5    0.749    0.036   20.686    0.000    0.760    0.760
##    .t2_nf_sh_tt_f1    0.430    0.045    9.571    0.000    0.797    0.797
##    .t2_nf_sh_tt_f2    0.074    0.012    6.068    0.000    0.074    0.074
##    .t2_nf_sh_tt_f3    0.112    0.013    8.607    0.000    0.112    0.112
##    .t2_nf_sh_tt_f4    0.100    0.018    5.476    0.000    0.160    0.160
##    .t2_nf_sh_tt_f5    0.743    0.036   20.918    0.000    0.758    0.758
##    .t3_nf_sh_tt_f1    0.415    0.043    9.535    0.000    0.803    0.803
##    .t3_nf_sh_tt_f2    0.125    0.014    9.091    0.000    0.126    0.126
##    .t3_nf_sh_tt_f3    0.144    0.015    9.899    0.000    0.149    0.149
##    .t3_nf_sh_tt_f4    0.114    0.017    6.556    0.000    0.189    0.189
##    .t3_nf_sh_tt_f5    0.715    0.034   20.767    0.000    0.764    0.764
##     t1_inf_sh_bh_f    0.117    0.013    8.887    0.000    1.000    1.000
##     t2_inf_sh_bh_f    0.109    0.012    8.884    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.101    0.011    8.882    0.000    1.000    1.000
##    .t1_nf_sh_bh_f1    0.398    0.060    6.594    0.000    0.774    0.774
##    .t1_nf_sh_bh_f2    0.080    0.008    9.594    0.000    0.077    0.077
##    .t1_nf_sh_bh_f3    0.103    0.009   11.475    0.000    0.111    0.111
##    .t1_nf_sh_bh_f4    0.050    0.015    3.403    0.001    0.061    0.061
##    .t1_nf_sh_bh_f5    0.484    0.027   18.081    0.000    0.717    0.717
##    .t2_nf_sh_bh_f1    0.209    0.042    5.013    0.000    0.656    0.656
##    .t2_nf_sh_bh_f2    0.074    0.009    8.583    0.000    0.076    0.076
##    .t2_nf_sh_bh_f3    0.129    0.010   12.935    0.000    0.144    0.144
##    .t2_nf_sh_bh_f4    0.068    0.015    4.534    0.000    0.087    0.087
##    .t2_nf_sh_bh_f5    0.451    0.025   18.029    0.000    0.716    0.716
##    .t3_nf_sh_bh_f1    0.306    0.049    6.278    0.000    0.752    0.752
##    .t3_nf_sh_bh_f2    0.082    0.008   10.243    0.000    0.090    0.090
##    .t3_nf_sh_bh_f3    0.091    0.008   10.813    0.000    0.113    0.113
##    .t3_nf_sh_bh_f4    0.080    0.015    5.223    0.000    0.108    0.108
##    .t3_nf_sh_bh_f5    0.480    0.026   18.753    0.000    0.743    0.743

2 Results

In what follows, we report additional models, which are also related to our research question.

2.1 RI-CLPM

2.1.1 Two Variables

Here, we look at the bivariate relations of privacy concerns and information sharing. This is interesting, because in the paper we also address privacy attitudes, thereby potentially attenuating the effect of privacy concerns. However, when analyzing only these two variables we do not find larger effects sizes.

2.1.1.1 Model 1

Here, we use regular observed means.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_m + 1*t2_pri_con_m + 1*t3_pri_con_m
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t2_inf_sha_beh_m + 1*t3_inf_sha_beh_m

# intercepts
t1_pri_con_m ~ mu1*1
t2_pri_con_m ~ mu2*1
t3_pri_con_m ~ mu3*1
t1_inf_sha_beh_m ~ pi1*1
t2_inf_sha_beh_m ~ pi2*1
t3_inf_sha_beh_m ~ pi3*1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_m
t2_pri_con_w =~ 1*t2_pri_con_m
t3_pri_con_w =~ 1*t3_pri_con_m
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w
'

fit <- lavaan(model, data = d_wide, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 42 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         26
##   Number of equality constraints                     5
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         4
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 3.780
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.706
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4114.935
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.001
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7478.685
##   Loglikelihood unrestricted model (H1)      -7476.795
##                                                       
##   Akaike (AIC)                               14999.371
##   Bayesian (BIC)                             15109.545
##   Sample-size adjusted Bayesian (BIC)        15042.835
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.026
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.010
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_m         1.000                               0.758    0.856
##     t2_pri_con_m         1.000                               0.758    0.850
##     t3_pri_con_m         1.000                               0.758    0.850
##   inf_sha_beh_b =~                                                         
##     t1_inf_sh_bh_m       1.000                               0.495    0.757
##     t2_inf_sh_bh_m       1.000                               0.495    0.771
##     t3_inf_sh_bh_m       1.000                               0.495    0.803
##   t1_pri_con_w =~                                                          
##     t1_pri_con_m         1.000                               0.458    0.517
##   t2_pri_con_w =~                                                          
##     t2_pri_con_m         1.000                               0.471    0.527
##   t3_pri_con_w =~                                                          
##     t3_pri_con_m         1.000                               0.469    0.526
##   t1_inf_sha_beh_w =~                                                      
##     t1_inf_sh_bh_m       1.000                               0.428    0.654
##   t2_inf_sha_beh_w =~                                                      
##     t2_inf_sh_bh_m       1.000                               0.408    0.636
##   t3_inf_sha_beh_w =~                                                      
##     t3_inf_sh_bh_m       1.000                               0.367    0.596
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t2_pri_con_w ~                                                          
##     t1_pr_cn_ (a1)      0.087    0.071    1.225    0.220    0.084    0.084
##     t1_nf_s__ (a2)      0.013    0.038    0.333    0.739    0.011    0.011
##   t2_inf_sha_beh_w ~                                                      
##     t1_pr_cn_ (b1)      0.035    0.029    1.196    0.232    0.039    0.039
##     t1_nf_s__ (b2)      0.042    0.046    0.903    0.367    0.044    0.044
##   t3_pri_con_w ~                                                          
##     t2_pr_cn_ (a1)      0.087    0.071    1.225    0.220    0.087    0.087
##     t2_nf_s__ (a2)      0.013    0.038    0.333    0.739    0.011    0.011
##   t3_inf_sha_beh_w ~                                                      
##     t2_pr_cn_ (b1)      0.035    0.029    1.196    0.232    0.045    0.045
##     t2_nf_s__ (b2)      0.042    0.046    0.903    0.367    0.046    0.046
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.068    0.013   -5.346    0.000   -0.182   -0.182
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__       -0.011    0.008   -1.457    0.145   -0.058   -0.058
##  .t2_pri_con_w ~~                                                       
##    .t2_nf_sh__ (a)    0.006    0.007    0.963    0.336    0.033    0.033
##  .t3_pri_con_w ~~                                                       
##    .t3_nf_sh__ (a)    0.006    0.007    0.963    0.336    0.037    0.037
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pr_c_ (mu1)    3.671    0.024  155.157    0.000    3.671    4.146
##    .t2_pr_c_ (mu2)    3.617    0.024  151.750    0.000    3.617    4.053
##    .t3_pr_c_ (mu3)    3.589    0.024  150.625    0.000    3.589    4.026
##    .t1_nf___ (pi1)    2.122    0.017  121.474    0.000    2.122    3.243
##    .t2_nf___ (pi2)    2.135    0.017  124.561    0.000    2.135    3.325
##    .t3_nf___ (pi3)    2.101    0.016  127.588    0.000    2.101    3.406
##     pri_cn_b          0.000                               0.000    0.000
##     inf_sh__          0.000                               0.000    0.000
##     t1_pr_c_          0.000                               0.000    0.000
##    .t2_pr_c_          0.000                               0.000    0.000
##    .t3_pr_c_          0.000                               0.000    0.000
##     t1_nf___          0.000                               0.000    0.000
##    .t2_nf___          0.000                               0.000    0.000
##    .t3_nf___          0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.575    0.027   21.060    0.000    1.000    1.000
##     inf_sha_beh_b     0.245    0.013   19.278    0.000    1.000    1.000
##     t1_pri_con_w      0.209    0.013   16.655    0.000    1.000    1.000
##    .t2_pri_con_w      0.220    0.026    8.386    0.000    0.993    0.993
##    .t3_pri_con_w      0.218    0.013   17.469    0.000    0.992    0.992
##     t1_inf_sh_bh_w    0.183    0.010   18.744    0.000    1.000    1.000
##    .t2_inf_sh_bh_w    0.166    0.014   11.927    0.000    0.997    0.997
##    .t3_inf_sh_bh_w    0.134    0.008   17.035    0.000    0.996    0.996
##    .t1_pri_con_m      0.000                               0.000    0.000
##    .t2_pri_con_m      0.000                               0.000    0.000
##    .t3_pri_con_m      0.000                               0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000
##    .t2_inf_sh_bh_m    0.000                               0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000

2.1.1.2 Model 2

Model with a (broad) single item measure of privacy concerns (β€œIn general, how concerned are you about your privacy while using the Internet?”).

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_01 + 1*t2_pri_con_01 + 1*t3_pri_con_01
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t2_inf_sha_beh_m + 1*t3_inf_sha_beh_m

# intercepts
t1_pri_con_01 ~ mu1*1
t2_pri_con_01 ~ mu2*1
t3_pri_con_01 ~ mu3*1
t1_inf_sha_beh_m ~ pi1*1
t2_inf_sha_beh_m ~ pi2*1
t3_inf_sha_beh_m ~ pi3*1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_01
t2_pri_con_w =~ 1*t2_pri_con_01
t3_pri_con_w =~ 1*t3_pri_con_01
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w
'

fit <- lavaan(model, data = d_wide, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 42 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         26
##   Number of equality constraints                     5
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         4
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 1.834
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.934
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2962.543
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.004
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -8913.859
##   Loglikelihood unrestricted model (H1)      -8912.942
##                                                       
##   Akaike (AIC)                               17869.717
##   Bayesian (BIC)                             17979.891
##   Sample-size adjusted Bayesian (BIC)        17913.182
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.009
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.007
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_01        1.000                               0.841    0.766
##     t2_pri_con_01        1.000                               0.841    0.784
##     t3_pri_con_01        1.000                               0.841    0.759
##   inf_sha_beh_b =~                                                         
##     t1_inf_sh_bh_m       1.000                               0.495    0.756
##     t2_inf_sh_bh_m       1.000                               0.495    0.772
##     t3_inf_sh_bh_m       1.000                               0.495    0.804
##   t1_pri_con_w =~                                                          
##     t1_pri_con_01        1.000                               0.706    0.643
##   t2_pri_con_w =~                                                          
##     t2_pri_con_01        1.000                               0.666    0.621
##   t3_pri_con_w =~                                                          
##     t3_pri_con_01        1.000                               0.721    0.651
##   t1_inf_sha_beh_w =~                                                      
##     t1_inf_sh_bh_m       1.000                               0.429    0.654
##   t2_inf_sha_beh_w =~                                                      
##     t2_inf_sh_bh_m       1.000                               0.408    0.636
##   t3_inf_sha_beh_w =~                                                      
##     t3_inf_sh_bh_m       1.000                               0.366    0.595
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t2_pri_con_w ~                                                          
##     t1_pr_cn_ (a1)     -0.027    0.051   -0.530    0.596   -0.029   -0.029
##     t1_nf_s__ (a2)     -0.048    0.055   -0.881    0.378   -0.031   -0.031
##   t2_inf_sha_beh_w ~                                                      
##     t1_pr_cn_ (b1)      0.010    0.018    0.528    0.598    0.017    0.017
##     t1_nf_s__ (b2)      0.041    0.047    0.880    0.379    0.043    0.043
##   t3_pri_con_w ~                                                          
##     t2_pr_cn_ (a1)     -0.027    0.051   -0.530    0.596   -0.025   -0.025
##     t2_nf_s__ (a2)     -0.048    0.055   -0.881    0.378   -0.027   -0.027
##   t3_inf_sha_beh_w ~                                                      
##     t2_pr_cn_ (b1)      0.010    0.018    0.528    0.598    0.017    0.017
##     t2_nf_s__ (b2)      0.041    0.047    0.880    0.379    0.046    0.046
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.046    0.015   -3.102    0.002   -0.110   -0.110
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__       -0.024    0.011   -2.128    0.033   -0.080   -0.080
##  .t2_pri_con_w ~~                                                       
##    .t2_nf_sh__ (a)   -0.008    0.009   -0.889    0.374   -0.030   -0.030
##  .t3_pri_con_w ~~                                                       
##    .t3_nf_sh__ (a)   -0.008    0.009   -0.889    0.374   -0.031   -0.031
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_p__01 (mu1)    3.335    0.029  113.605    0.000    3.335    3.037
##    .t2_p__01 (mu2)    3.334    0.029  116.365    0.000    3.334    3.109
##    .t3_p__01 (mu3)    3.337    0.030  112.652    0.000    3.337    3.012
##    .t1_nf___ (pi1)    2.122    0.017  121.362    0.000    2.122    3.240
##    .t2_nf___ (pi2)    2.135    0.017  124.611    0.000    2.135    3.327
##    .t3_nf___ (pi3)    2.101    0.016  127.702    0.000    2.101    3.409
##     pri_cn_b          0.000                               0.000    0.000
##     inf_sh__          0.000                               0.000    0.000
##     t1_pr_c_          0.000                               0.000    0.000
##    .t2_pr_c_          0.000                               0.000    0.000
##    .t3_pr_c_          0.000                               0.000    0.000
##     t1_nf___          0.000                               0.000    0.000
##    .t2_nf___          0.000                               0.000    0.000
##    .t3_nf___          0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.707    0.037   19.173    0.000    1.000    1.000
##     inf_sha_beh_b     0.245    0.013   19.261    0.000    1.000    1.000
##     t1_pri_con_w      0.498    0.027   18.186    0.000    1.000    1.000
##    .t2_pri_con_w      0.442    0.043   10.295    0.000    0.998    0.998
##    .t3_pri_con_w      0.519    0.027   18.911    0.000    0.999    0.999
##     t1_inf_sh_bh_w    0.184    0.010   18.734    0.000    1.000    1.000
##    .t2_inf_sh_bh_w    0.166    0.014   11.855    0.000    0.998    0.998
##    .t3_inf_sh_bh_w    0.134    0.008   16.993    0.000    0.998    0.998
##    .t1_pri_con_01     0.000                               0.000    0.000
##    .t2_pri_con_01     0.000                               0.000    0.000
##    .t3_pri_con_01     0.000                               0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000
##    .t2_inf_sh_bh_m    0.000                               0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000

2.1.1.3 Model 3

With Factor Scores.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs

# intercepts
t1_pri_con_fs ~ 1
t2_pri_con_fs ~ 1
t3_pri_con_fs ~ 1
t1_inf_sha_beh_fs ~ 1
t2_inf_sha_beh_fs ~ 1
t3_inf_sha_beh_fs ~ 1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w
'
fit <- lavaan(model, data = d_wide)
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 48 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         26
##   Number of equality constraints                     5
##                                                       
##   Number of observations                          1403
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 4.872
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.560
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4626.337
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.001
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7132.491
##   Loglikelihood unrestricted model (H1)      -7130.055
##                                                       
##   Akaike (AIC)                               14306.982
##   Bayesian (BIC)                             14417.156
##   Sample-size adjusted Bayesian (BIC)        14350.446
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.031
##   P-value RMSEA <= 0.05                          0.999
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.011
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_fs        1.000                               0.755    0.882
##     t2_pri_con_fs        1.000                               0.755    0.861
##     t3_pri_con_fs        1.000                               0.755    0.872
##   inf_sha_beh_b =~                                                         
##     t1_nf_sh_bh_fs       1.000                               0.500    0.766
##     t2_nf_sh_bh_fs       1.000                               0.500    0.785
##     t3_nf_sh_bh_fs       1.000                               0.500    0.807
##   t1_pri_con_w =~                                                          
##     t1_pri_con_fs        1.000                               0.403    0.471
##   t2_pri_con_w =~                                                          
##     t2_pri_con_fs        1.000                               0.446    0.509
##   t3_pri_con_w =~                                                          
##     t3_pri_con_fs        1.000                               0.424    0.490
##   t1_inf_sha_beh_w =~                                                      
##     t1_nf_sh_bh_fs       1.000                               0.420    0.643
##   t2_inf_sha_beh_w =~                                                      
##     t2_nf_sh_bh_fs       1.000                               0.395    0.620
##   t3_inf_sha_beh_w =~                                                      
##     t3_nf_sh_bh_fs       1.000                               0.366    0.591
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t2_pri_con_w ~                                                          
##     t1_pr_cn_ (a1)      0.136    0.064    2.108    0.035    0.122    0.122
##     t1_nf_s__ (a2)     -0.022    0.035   -0.615    0.539   -0.020   -0.020
##   t2_inf_sha_beh_w ~                                                      
##     t1_pr_cn_ (b1)      0.013    0.033    0.390    0.696    0.013    0.013
##     t1_nf_s__ (b2)      0.028    0.050    0.564    0.573    0.030    0.030
##   t3_pri_con_w ~                                                          
##     t2_pr_cn_ (a1)      0.136    0.064    2.108    0.035    0.143    0.143
##     t2_nf_s__ (a2)     -0.022    0.035   -0.615    0.539   -0.020   -0.020
##   t3_inf_sha_beh_w ~                                                      
##     t2_pr_cn_ (b1)      0.013    0.033    0.390    0.696    0.015    0.015
##     t2_nf_s__ (b2)      0.028    0.050    0.564    0.573    0.030    0.030
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.054    0.012   -4.330    0.000   -0.143   -0.143
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__       -0.016    0.007   -2.279    0.023   -0.094   -0.094
##  .t2_pri_con_w ~~                                                       
##    .t2_nf_sh__ (a)    0.007    0.006    1.100    0.271    0.037    0.037
##  .t3_pri_con_w ~~                                                       
##    .t3_nf_sh__ (a)    0.007    0.006    1.100    0.271    0.043    0.043
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_fs     3.707    0.023  162.274    0.000    3.707    4.332
##    .t2_pri_con_fs     3.636    0.023  155.317    0.000    3.636    4.147
##    .t3_pri_con_fs     3.607    0.023  156.023    0.000    3.607    4.165
##    .t1_nf_sh_bh_fs    2.193    0.017  125.833    0.000    2.193    3.359
##    .t2_nf_sh_bh_fs    2.206    0.017  129.597    0.000    2.206    3.460
##    .t3_nf_sh_bh_fs    2.168    0.017  131.009    0.000    2.168    3.498
##     pri_con_b         0.000                               0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.570    0.026   22.266    0.000    1.000    1.000
##     inf_sha_beh_b     0.250    0.013   19.509    0.000    1.000    1.000
##     t1_pri_con_w      0.162    0.010   15.544    0.000    1.000    1.000
##    .t2_pri_con_w      0.196    0.020   10.020    0.000    0.984    0.984
##    .t3_pri_con_w      0.176    0.010   16.999    0.000    0.979    0.979
##     t1_inf_sh_bh_w    0.176    0.009   18.803    0.000    1.000    1.000
##    .t2_inf_sh_bh_w    0.156    0.014   10.841    0.000    0.999    0.999
##    .t3_inf_sh_bh_w    0.134    0.008   17.221    0.000    0.999    0.999
##    .t1_pri_con_fs     0.000                               0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000

2.1.1.4 Model 4

With Factor Scores and Control Variables.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs

# intercepts
t1_pri_con_fs ~ 1
t2_pri_con_fs ~ 1
t3_pri_con_fs ~ 1
t1_inf_sha_beh_fs ~ 1
t2_inf_sha_beh_fs ~ 1
t3_inf_sha_beh_fs ~ 1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w

# control variables
t1_pri_con_fs ~ age + edu_num + male
t2_pri_con_fs ~ age + edu_num + male
t3_pri_con_fs ~ age + edu_num + male
t1_inf_sha_beh_fs ~ age + edu_num + male
t2_inf_sha_beh_fs ~ age + edu_num + male
t3_inf_sha_beh_fs ~ age + edu_num + male
'

fit <- lavaan(model, data = d_wide, missing = "ml")
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 113 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         44
##   Number of equality constraints                     5
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         1
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 6.268
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.394
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4835.945
##   Degrees of freedom                                33
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7028.385
##   Loglikelihood unrestricted model (H1)      -7025.251
##                                                       
##   Akaike (AIC)                               14134.770
##   Bayesian (BIC)                             14339.379
##   Sample-size adjusted Bayesian (BIC)        14215.490
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.006
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.036
##   P-value RMSEA <= 0.05                          0.998
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.008
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_fs        1.000                               0.737    0.862
##     t2_pri_con_fs        1.000                               0.737    0.840
##     t3_pri_con_fs        1.000                               0.737    0.849
##   inf_sha_beh_b =~                                                         
##     t1_nf_sh_bh_fs       1.000                               0.468    0.718
##     t2_nf_sh_bh_fs       1.000                               0.468    0.734
##     t3_nf_sh_bh_fs       1.000                               0.468    0.754
##   t1_pri_con_w =~                                                          
##     t1_pri_con_fs        1.000                               0.403    0.472
##   t2_pri_con_w =~                                                          
##     t2_pri_con_fs        1.000                               0.450    0.513
##   t3_pri_con_w =~                                                          
##     t3_pri_con_fs        1.000                               0.425    0.489
##   t1_inf_sha_beh_w =~                                                      
##     t1_nf_sh_bh_fs       1.000                               0.421    0.646
##   t2_inf_sha_beh_w =~                                                      
##     t2_nf_sh_bh_fs       1.000                               0.394    0.618
##   t3_inf_sha_beh_w =~                                                      
##     t3_nf_sh_bh_fs       1.000                               0.364    0.586
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t2_pri_con_w ~                                                           
##     t1_pr_cn_ (a1)       0.145    0.067    2.163    0.031    0.130    0.130
##     t1_nf_s__ (a2)      -0.021    0.035   -0.609    0.542   -0.020   -0.020
##   t2_inf_sha_beh_w ~                                                       
##     t1_pr_cn_ (b1)       0.013    0.031    0.412    0.680    0.013    0.013
##     t1_nf_s__ (b2)       0.027    0.044    0.621    0.534    0.029    0.029
##   t3_pri_con_w ~                                                           
##     t2_pr_cn_ (a1)       0.145    0.067    2.163    0.031    0.154    0.154
##     t2_nf_s__ (a2)      -0.021    0.035   -0.609    0.542   -0.020   -0.020
##   t3_inf_sha_beh_w ~                                                       
##     t2_pr_cn_ (b1)       0.013    0.031    0.412    0.680    0.016    0.016
##     t2_nf_s__ (b2)       0.027    0.044    0.621    0.534    0.030    0.030
##   t1_pri_con_fs ~                                                          
##     age                  0.010    0.001    6.844    0.000    0.010    0.184
##     edu_num             -0.023    0.013   -1.759    0.079   -0.023   -0.047
##     male                -0.002    0.046   -0.043    0.966   -0.002   -0.001
##   t2_pri_con_fs ~                                                          
##     age                  0.010    0.002    6.509    0.000    0.010    0.175
##     edu_num             -0.023    0.013   -1.676    0.094   -0.023   -0.045
##     male                 0.012    0.047    0.251    0.802    0.012    0.007
##   t3_pri_con_fs ~                                                          
##     age                  0.011    0.002    7.473    0.000    0.011    0.200
##     edu_num             -0.017    0.013   -1.310    0.190   -0.017   -0.035
##     male                 0.010    0.047    0.220    0.825    0.010    0.006
##   t1_inf_sha_beh_fs ~                                                      
##     age                 -0.009    0.001   -7.936    0.000   -0.009   -0.210
##     edu_num              0.057    0.010    5.848    0.000    0.057    0.153
##     male                -0.132    0.035   -3.830    0.000   -0.132   -0.102
##   t2_inf_sha_beh_fs ~                                                      
##     age                 -0.010    0.001   -9.072    0.000   -0.010   -0.238
##     edu_num              0.065    0.010    6.769    0.000    0.065    0.176
##     male                -0.083    0.034   -2.467    0.014   -0.083   -0.065
##   t3_inf_sha_beh_fs ~                                                      
##     age                 -0.009    0.001   -8.798    0.000   -0.009   -0.230
##     edu_num              0.070    0.009    7.607    0.000    0.070    0.196
##     male                -0.121    0.033   -3.734    0.000   -0.121   -0.098
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.030    0.012   -2.614    0.009   -0.088   -0.088
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__       -0.017    0.007   -2.348    0.019   -0.098   -0.098
##  .t2_pri_con_w ~~                                                       
##    .t2_nf_sh__ (a)    0.007    0.006    1.138    0.255    0.037    0.037
##  .t3_pri_con_w ~~                                                       
##    .t3_nf_sh__ (a)    0.007    0.006    1.138    0.255    0.043    0.043
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_fs     3.270    0.136   24.029    0.000    3.270    3.827
##    .t2_pri_con_fs     3.189    0.140   22.794    0.000    3.189    3.637
##    .t3_pri_con_fs     3.064    0.138   22.237    0.000    3.064    3.532
##    .t1_nf_sh_bh_fs    2.583    0.102   25.304    0.000    2.583    3.963
##    .t2_nf_sh_bh_fs    2.539    0.099   25.598    0.000    2.539    3.980
##    .t3_nf_sh_bh_fs    2.497    0.096   25.988    0.000    2.497    4.024
##     pri_con_b         0.000                               0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.542    0.025   21.867    0.000    1.000    1.000
##     inf_sha_beh_b     0.219    0.011   19.078    0.000    1.000    1.000
##     t1_pri_con_w      0.163    0.010   15.492    0.000    1.000    1.000
##    .t2_pri_con_w      0.199    0.021    9.694    0.000    0.982    0.982
##    .t3_pri_con_w      0.176    0.011   16.699    0.000    0.976    0.976
##     t1_inf_sh_bh_w    0.177    0.010   18.671    0.000    1.000    1.000
##    .t2_inf_sh_bh_w    0.155    0.013   12.395    0.000    0.999    0.999
##    .t3_inf_sh_bh_w    0.132    0.008   17.350    0.000    0.999    0.999
##    .t1_pri_con_fs     0.000                               0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000

2.1.1.5 Model 5

In this model, we omit all longitudinal paths in order to better estimate the concurrent relations of the variables for all waves (in the regular RI-CLPM, only the relations at wave 1 can be interpreted meaningfully).

model <- "
# between relations
pri_con_b =~ 1*t1_pri_con_m + 1*t2_pri_con_m + 1*t3_pri_con_m
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t2_inf_sha_beh_m + 1*t3_inf_sha_beh_m

# intercepts
t1_pri_con_m ~ mu1*1
t2_pri_con_m ~ mu2*1
t3_pri_con_m ~ mu3*1
t1_inf_sha_beh_m ~ pi1*1
t2_inf_sha_beh_m ~ pi2*1
t3_inf_sha_beh_m ~ pi3*1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_m
t2_pri_con_w =~ 1*t2_pri_con_m
t3_pri_con_w =~ 1*t3_pri_con_m
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ a*t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w
"

fit <- lavaan(model, data = d_wide, missing = "ml")
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 43 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         18
##   Number of equality constraints                     2
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         4
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 9.758
##   Degrees of freedom                                11
##   P-value (Chi-square)                           0.552
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4114.935
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.000
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7481.675
##   Loglikelihood unrestricted model (H1)      -7476.795
##                                                       
##   Akaike (AIC)                               14995.349
##   Bayesian (BIC)                             15079.291
##   Sample-size adjusted Bayesian (BIC)        15028.465
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.026
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.014
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_m         1.000                               0.768    0.861
##     t2_pri_con_m         1.000                               0.768    0.869
##     t3_pri_con_m         1.000                               0.768    0.856
##   inf_sha_beh_b =~                                                         
##     t1_inf_sh_bh_m       1.000                               0.500    0.762
##     t2_inf_sh_bh_m       1.000                               0.500    0.784
##     t3_inf_sh_bh_m       1.000                               0.500    0.808
##   t1_pri_con_w =~                                                          
##     t1_pri_con_m         1.000                               0.454    0.509
##   t2_pri_con_w =~                                                          
##     t2_pri_con_m         1.000                               0.437    0.495
##   t3_pri_con_w =~                                                          
##     t3_pri_con_m         1.000                               0.463    0.517
##   t1_inf_sha_beh_w =~                                                      
##     t1_inf_sh_bh_m       1.000                               0.425    0.647
##   t2_inf_sha_beh_w =~                                                      
##     t2_inf_sh_bh_m       1.000                               0.396    0.621
##   t3_inf_sha_beh_w =~                                                      
##     t3_inf_sh_bh_m       1.000                               0.365    0.589
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.065    0.012   -5.365    0.000   -0.169   -0.169
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__ (a)   -0.002    0.003   -0.596    0.551   -0.010   -0.010
##   t2_pri_con_w ~~                                                       
##     t2_nf_sh__ (a)   -0.002    0.003   -0.596    0.551   -0.012   -0.012
##   t3_pri_con_w ~~                                                       
##     t3_nf_sh__ (a)   -0.002    0.003   -0.596    0.551   -0.012   -0.012
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pr_c_ (mu1)    3.671    0.024  154.082    0.000    3.671    4.117
##    .t2_pr_c_ (mu2)    3.617    0.024  153.306    0.000    3.617    4.095
##    .t3_pr_c_ (mu3)    3.589    0.024  149.810    0.000    3.589    4.004
##    .t1_nf___ (pi1)    2.122    0.018  121.158    0.000    2.122    3.235
##    .t2_nf___ (pi2)    2.135    0.017  125.399    0.000    2.135    3.348
##    .t3_nf___ (pi3)    2.101    0.017  127.142    0.000    2.101    3.394
##     pri_cn_b          0.000                               0.000    0.000
##     inf_sh__          0.000                               0.000    0.000
##     t1_pr_c_          0.000                               0.000    0.000
##     t2_pr_c_          0.000                               0.000    0.000
##     t3_pr_c_          0.000                               0.000    0.000
##     t1_nf___          0.000                               0.000    0.000
##     t2_nf___          0.000                               0.000    0.000
##     t3_nf___          0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.589    0.025   23.655    0.000    1.000    1.000
##     inf_sha_beh_b     0.250    0.011   21.807    0.000    1.000    1.000
##     t1_pri_con_w      0.206    0.011   18.002    0.000    1.000    1.000
##     t2_pri_con_w      0.191    0.011   17.470    0.000    1.000    1.000
##     t3_pri_con_w      0.214    0.012   18.435    0.000    1.000    1.000
##     t1_inf_sh_bh_w    0.180    0.009   19.921    0.000    1.000    1.000
##     t2_inf_sh_bh_w    0.157    0.008   18.899    0.000    1.000    1.000
##     t3_inf_sh_bh_w    0.133    0.008   17.519    0.000    1.000    1.000
##    .t1_pri_con_m      0.000                               0.000    0.000
##    .t2_pri_con_m      0.000                               0.000    0.000
##    .t3_pri_con_m      0.000                               0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000
##    .t2_inf_sh_bh_m    0.000                               0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000

2.1.1.6 Model 6

The same like above, using Factor Scores and control variables.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs

# intercepts
t1_pri_con_fs ~ 1
t2_pri_con_fs ~ 1
t3_pri_con_fs ~ 1
t1_inf_sha_beh_fs ~ 1
t2_inf_sha_beh_fs ~ 1
t3_inf_sha_beh_fs ~ 1

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs

# estimate variances
pri_con_b ~~ pri_con_b
inf_sha_beh_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_pri_con_w
t2_pri_con_w ~~ t2_pri_con_w
t3_pri_con_w ~~ t3_pri_con_w
t1_inf_sha_beh_w ~~ t1_inf_sha_beh_w
t2_inf_sha_beh_w ~~ t2_inf_sha_beh_w
t3_inf_sha_beh_w ~~ t3_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ a*t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_beh_w

# control variables
t1_pri_con_fs ~ age + edu_num + male
t2_pri_con_fs ~ age + edu_num + male
t3_pri_con_fs ~ age + edu_num + male
t1_inf_sha_beh_fs ~ age + edu_num + male
t2_inf_sha_beh_fs ~ age + edu_num + male
t3_inf_sha_beh_fs ~ age + edu_num + male
'

fit <- lavaan(model, data = d_wide, missing = "ml")
summary(fit, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 112 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         36
##   Number of equality constraints                     2
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         1
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                18.421
##   Degrees of freedom                                11
##   P-value (Chi-square)                           0.072
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4835.945
##   Degrees of freedom                                33
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.998
##   Tucker-Lewis Index (TLI)                       0.995
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -7034.461
##   Loglikelihood unrestricted model (H1)      -7025.251
##                                                       
##   Akaike (AIC)                               14136.923
##   Bayesian (BIC)                             14315.299
##   Sample-size adjusted Bayesian (BIC)        14207.294
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.022
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.039
##   P-value RMSEA <= 0.05                          0.998
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.013
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b =~                                                             
##     t1_pri_con_fs        1.000                               0.750    0.867
##     t2_pri_con_fs        1.000                               0.750    0.869
##     t3_pri_con_fs        1.000                               0.750    0.860
##   inf_sha_beh_b =~                                                         
##     t1_nf_sh_bh_fs       1.000                               0.471    0.722
##     t2_nf_sh_bh_fs       1.000                               0.471    0.741
##     t3_nf_sh_bh_fs       1.000                               0.471    0.757
##   t1_pri_con_w =~                                                          
##     t1_pri_con_fs        1.000                               0.400    0.463
##   t2_pri_con_w =~                                                          
##     t2_pri_con_fs        1.000                               0.399    0.462
##   t3_pri_con_w =~                                                          
##     t3_pri_con_fs        1.000                               0.411    0.471
##   t1_inf_sha_beh_w =~                                                      
##     t1_nf_sh_bh_fs       1.000                               0.419    0.642
##   t2_inf_sha_beh_w =~                                                      
##     t2_nf_sh_bh_fs       1.000                               0.387    0.608
##   t3_inf_sha_beh_w =~                                                      
##     t3_nf_sh_bh_fs       1.000                               0.363    0.583
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_fs ~                                                          
##     age                  0.010    0.002    6.759    0.000    0.010    0.182
##     edu_num             -0.023    0.013   -1.737    0.082   -0.023   -0.046
##     male                -0.002    0.047   -0.042    0.966   -0.002   -0.001
##   t2_pri_con_fs ~                                                          
##     age                  0.010    0.002    6.614    0.000    0.010    0.178
##     edu_num             -0.023    0.013   -1.703    0.089   -0.023   -0.045
##     male                 0.012    0.047    0.255    0.799    0.012    0.007
##   t3_pri_con_fs ~                                                          
##     age                  0.011    0.002    7.429    0.000    0.011    0.199
##     edu_num             -0.017    0.013   -1.303    0.193   -0.017   -0.035
##     male                 0.010    0.047    0.219    0.826    0.010    0.006
##   t1_inf_sha_beh_fs ~                                                      
##     age                 -0.009    0.001   -7.927    0.000   -0.009   -0.209
##     edu_num              0.057    0.010    5.841    0.000    0.057    0.153
##     male                -0.132    0.035   -3.825    0.000   -0.132   -0.101
##   t2_inf_sha_beh_fs ~                                                      
##     age                 -0.010    0.001   -9.112    0.000   -0.010   -0.239
##     edu_num              0.065    0.009    6.799    0.000    0.065    0.176
##     male                -0.083    0.033   -2.478    0.013   -0.083   -0.065
##   t3_inf_sha_beh_fs ~                                                      
##     age                 -0.009    0.001   -8.776    0.000   -0.009   -0.229
##     edu_num              0.070    0.009    7.588    0.000    0.070    0.196
##     male                -0.121    0.033   -3.724    0.000   -0.121   -0.098
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   pri_con_b ~~                                                          
##     inf_sh_bh_       -0.031    0.011   -2.851    0.004   -0.089   -0.089
##   t1_pri_con_w ~~                                                       
##     t1_nf_sh__ (a)    0.000    0.003    0.142    0.887    0.003    0.003
##   t2_pri_con_w ~~                                                       
##     t2_nf_sh__ (a)    0.000    0.003    0.142    0.887    0.003    0.003
##   t3_pri_con_w ~~                                                       
##     t3_nf_sh__ (a)    0.000    0.003    0.142    0.887    0.003    0.003
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_fs     3.270    0.138   23.732    0.000    3.270    3.781
##    .t2_pri_con_fs     3.189    0.138   23.164    0.000    3.189    3.694
##    .t3_pri_con_fs     3.064    0.139   22.107    0.000    3.064    3.512
##    .t1_nf_sh_bh_fs    2.583    0.102   25.274    0.000    2.583    3.959
##    .t2_nf_sh_bh_fs    2.539    0.099   25.712    0.000    2.539    3.997
##    .t3_nf_sh_bh_fs    2.497    0.096   25.922    0.000    2.497    4.014
##     pri_con_b         0.000                               0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000
##     t2_pri_con_w      0.000                               0.000    0.000
##     t3_pri_con_w      0.000                               0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000
##     t2_inf_sh_bh_w    0.000                               0.000    0.000
##     t3_inf_sh_bh_w    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     pri_con_b         0.562    0.023   24.101    0.000    1.000    1.000
##     inf_sha_beh_b     0.222    0.010   21.431    0.000    1.000    1.000
##     t1_pri_con_w      0.160    0.009   17.623    0.000    1.000    1.000
##     t2_pri_con_w      0.159    0.009   17.698    0.000    1.000    1.000
##     t3_pri_con_w      0.169    0.009   18.168    0.000    1.000    1.000
##     t1_inf_sh_bh_w    0.176    0.009   20.015    0.000    1.000    1.000
##     t2_inf_sh_bh_w    0.149    0.008   18.825    0.000    1.000    1.000
##     t3_inf_sh_bh_w    0.131    0.007   17.765    0.000    1.000    1.000
##    .t1_pri_con_fs     0.000                               0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000

2.1.2 Three Variables

2.1.2.1 Model 1

With observed means.

model <- '
# random intercepts (between person)
pri_con_b =~ 1*t1_pri_con_m + 1*t2_pri_con_m + 1*t3_pri_con_m
inf_sha_att_b =~ 1*t1_inf_sha_att_m + 1*t2_inf_sha_att_m + 1*t3_inf_sha_att_m
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t2_inf_sha_beh_m + 1*t3_inf_sha_beh_m

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_m
t2_pri_con_w =~ 1*t2_pri_con_m
t3_pri_con_w =~ 1*t3_pri_con_m
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_m
t2_inf_sha_att_w =~ 1*t2_inf_sha_att_m
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_m
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t2_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_att_w + a3*t2_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_att_w + b3*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t2_pri_con_w + c2*t2_inf_sha_att_w + c3*t2_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_m ~~ 0*t1_pri_con_m
t2_pri_con_m ~~ 0*t2_pri_con_m
t3_pri_con_m ~~ 0*t3_pri_con_m
t1_inf_sha_att_m ~~ 0*t1_inf_sha_att_m
t2_inf_sha_att_m ~~ 0*t2_inf_sha_att_m
t3_inf_sha_att_m ~~ 0*t3_inf_sha_att_m
t1_inf_sha_beh_m ~~ 0*t1_inf_sha_beh_m
t2_inf_sha_beh_m ~~ 0*t2_inf_sha_beh_m
t3_inf_sha_beh_m ~~ 0*t3_inf_sha_beh_m

# allow covariances RIs & variables measured at the same time
pri_con_b ~~ inf_sha_att_b + inf_sha_beh_b
inf_sha_att_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_att_w + t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_att_w + b*t2_inf_sha_beh_w
t2_inf_sha_att_w ~~ c*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w
'
fit <- sem(model, estimator = "ML", data = d_wide, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 76 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         51
##   Number of equality constraints                    12
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         7
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                16.409
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.355
## 
## Model Test Baseline Model:
## 
##   Test statistic                              6284.683
##   Degrees of freedom                                36
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       0.999
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10864.395
##   Loglikelihood unrestricted model (H1)     -10856.190
##                                                       
##   Akaike (AIC)                               21806.789
##   Bayesian (BIC)                             22011.398
##   Sample-size adjusted Bayesian (BIC)        21887.509
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.008
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.027
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.013
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_m         1.000                               1.000    1.000    0.758    0.856
##     t2_pri_con_m         1.000                               1.000    1.000    0.758    0.851
##     t3_pri_con_m         1.000                               1.000    1.000    0.758    0.850
##   inf_sha_att_b =~                                                                           
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.525    0.741
##     t2_inf_sh_tt_m       1.000                               1.000    1.000    0.525    0.744
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.525    0.761
##   inf_sha_beh_b =~                                                                           
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.492    0.752
##     t2_inf_sh_bh_m       1.000                               1.000    1.000    0.492    0.761
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.492    0.804
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_m         1.000                               1.000    1.000    0.457    0.516
##   t2_pri_con_w =~                                                                            
##     t2_pri_con_m         1.000                               1.000    1.000    0.468    0.525
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_m         1.000                               1.000    1.000    0.470    0.527
##   t1_inf_sha_att_w =~                                                                        
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.475    0.671
##   t2_inf_sha_att_w =~                                                                        
##     t2_inf_sh_tt_m       1.000                               1.000    1.000    0.471    0.668
##   t3_inf_sha_att_w =~                                                                        
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.447    0.649
##   t1_inf_sha_beh_w =~                                                                        
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.432    0.660
##   t2_inf_sha_beh_w =~                                                                        
##     t2_inf_sh_bh_m       1.000                               1.000    1.000    0.420    0.649
##   t3_inf_sha_beh_w =~                                                                        
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.364    0.595
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t2_pri_con_w ~                                                                            
##     t1_pr_cn_ (a1)      0.082    0.072    1.139    0.255   -0.059    0.222    0.080    0.080
##     t1_nf_s__ (a2)     -0.032    0.035   -0.932    0.351   -0.101    0.036   -0.033   -0.033
##     t1_nf_s__ (a3)      0.008    0.037    0.223    0.824   -0.065    0.081    0.008    0.008
##   t2_inf_sha_att_w ~                                                                        
##     t1_pr_cn_ (b1)     -0.018    0.035   -0.507    0.612   -0.087    0.051   -0.017   -0.017
##     t1_nf_s__ (b2)      0.111    0.046    2.415    0.016    0.021    0.202    0.112    0.112
##     t1_nf_s__ (b3)      0.038    0.036    1.038    0.299   -0.033    0.109    0.035    0.035
##   t2_inf_sha_beh_w ~                                                                        
##     t1_pr_cn_ (c1)      0.032    0.029    1.107    0.268   -0.025    0.090    0.035    0.035
##     t1_nf_s__ (c2)     -0.006    0.029   -0.195    0.846   -0.062    0.051   -0.006   -0.006
##     t1_nf_s__ (c3)      0.066    0.041    1.605    0.108   -0.015    0.147    0.068    0.068
##   t3_pri_con_w ~                                                                            
##     t2_pr_cn_ (a1)      0.082    0.072    1.139    0.255   -0.059    0.222    0.081    0.081
##     t2_nf_s__ (a2)     -0.032    0.035   -0.932    0.351   -0.101    0.036   -0.032   -0.032
##     t2_nf_s__ (a3)      0.008    0.037    0.223    0.824   -0.065    0.081    0.007    0.007
##   t3_inf_sha_att_w ~                                                                        
##     t2_pr_cn_ (b1)     -0.018    0.035   -0.507    0.612   -0.087    0.051   -0.019   -0.019
##     t2_nf_s__ (b2)      0.111    0.046    2.415    0.016    0.021    0.202    0.117    0.117
##     t2_nf_s__ (b3)      0.038    0.036    1.038    0.299   -0.033    0.109    0.035    0.035
##   t3_inf_sha_beh_w ~                                                                        
##     t2_pr_cn_ (c1)      0.032    0.029    1.107    0.268   -0.025    0.090    0.042    0.042
##     t2_nf_s__ (c2)     -0.006    0.029   -0.195    0.846   -0.062    0.051   -0.007   -0.007
##     t2_nf_s__ (c3)      0.066    0.041    1.605    0.108   -0.015    0.147    0.077    0.077
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     inf_sh_tt_          -0.128    0.015   -8.769    0.000   -0.156   -0.099   -0.321   -0.321
##     inf_sh_bh_          -0.067    0.013   -5.248    0.000   -0.092   -0.042   -0.180   -0.180
##   inf_sha_att_b ~~                                                                           
##     inf_sh_bh_           0.174    0.011   15.664    0.000    0.152    0.196    0.675    0.675
##   t1_pri_con_w ~~                                                                            
##     t1_nf_sh__          -0.002    0.009   -0.209    0.834   -0.019    0.016   -0.009   -0.009
##     t1_nf_sh__          -0.011    0.008   -1.416    0.157   -0.027    0.004   -0.057   -0.057
##   t1_inf_sha_att_w ~~                                                                        
##     t1_nf_sh__           0.028    0.008    3.510    0.000    0.012    0.043    0.136    0.136
##  .t2_pri_con_w ~~                                                                            
##    .t2_nf_sh__ (a)      -0.007    0.008   -0.896    0.370   -0.023    0.008   -0.032   -0.032
##    .t2_nf_sh__ (b)       0.005    0.007    0.736    0.462   -0.008    0.018    0.025    0.025
##  .t2_inf_sha_att_w ~~                                                                        
##    .t2_nf_sh__ (c)       0.032    0.006    4.947    0.000    0.019    0.045    0.164    0.164
##  .t3_pri_con_w ~~                                                                            
##    .t3_nf_sh__ (a)      -0.007    0.008   -0.896    0.370   -0.023    0.008   -0.034   -0.034
##    .t3_nf_sh__ (b)       0.005    0.007    0.736    0.462   -0.008    0.018    0.028    0.028
##  .t3_inf_sha_att_w ~~                                                                        
##    .t3_nf_sh__ (c)       0.032    0.006    4.947    0.000    0.019    0.045    0.200    0.200
##   pri_con_b ~~                                                                               
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      3.671    0.024  155.214    0.000    3.625    3.717    3.671    4.147
##    .t2_pri_con_m      3.617    0.024  151.977    0.000    3.570    3.664    3.617    4.059
##    .t3_pri_con_m      3.589    0.024  150.526    0.000    3.543    3.636    3.589    4.023
##    .t1_inf_sh_tt_m    2.342    0.019  123.900    0.000    2.305    2.379    2.342    3.308
##    .t2_inf_sh_tt_m    2.402    0.019  127.433    0.000    2.365    2.438    2.402    3.407
##    .t3_inf_sh_tt_m    2.421    0.018  131.570    0.000    2.385    2.457    2.421    3.513
##    .t1_inf_sh_bh_m    2.122    0.017  121.415    0.000    2.088    2.157    2.122    3.241
##    .t2_inf_sh_bh_m    2.135    0.017  123.635    0.000    2.101    2.169    2.135    3.301
##    .t3_inf_sh_bh_m    2.101    0.016  128.586    0.000    2.069    2.133    2.101    3.433
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.575    0.027   20.987    0.000    0.521    0.629    1.000    1.000
##     inf_sha_att_b     0.275    0.016   17.149    0.000    0.244    0.307    1.000    1.000
##     inf_sha_beh_b     0.242    0.013   19.290    0.000    0.217    0.267    1.000    1.000
##     t1_pri_con_w      0.209    0.013   16.673    0.000    0.184    0.233    1.000    1.000
##    .t2_pri_con_w      0.217    0.026    8.271    0.000    0.166    0.269    0.993    0.993
##    .t3_pri_con_w      0.219    0.013   17.466    0.000    0.195    0.244    0.992    0.992
##     t1_inf_sh_tt_w    0.226    0.013   17.958    0.000    0.201    0.250    1.000    1.000
##    .t2_inf_sh_tt_w    0.218    0.016   13.910    0.000    0.187    0.249    0.985    0.985
##    .t3_inf_sh_tt_w    0.196    0.011   18.271    0.000    0.175    0.218    0.983    0.983
##     t1_inf_sh_bh_w    0.187    0.010   18.785    0.000    0.167    0.206    1.000    1.000
##    .t2_inf_sh_bh_w    0.175    0.012   14.279    0.000    0.151    0.199    0.994    0.994
##    .t3_inf_sh_bh_w    0.131    0.008   16.945    0.000    0.116    0.147    0.992    0.992

2.1.2.2 Model 2

With observed means and control variables.

model <- '
# random intercepts (between person)
pri_con_b =~ 1*t1_pri_con_m + 1*t2_pri_con_m + 1*t3_pri_con_m
inf_sha_att_b =~ 1*t1_inf_sha_att_m + 1*t2_inf_sha_att_m + 1*t3_inf_sha_att_m
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t2_inf_sha_beh_m + 1*t3_inf_sha_beh_m

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_m
t2_pri_con_w =~ 1*t2_pri_con_m
t3_pri_con_w =~ 1*t3_pri_con_m
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_m
t2_inf_sha_att_w =~ 1*t2_inf_sha_att_m
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_m
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t2_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_att_w + a3*t2_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_att_w + b3*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t2_pri_con_w + c2*t2_inf_sha_att_w + c3*t2_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_m ~~ 0*t1_pri_con_m
t2_pri_con_m ~~ 0*t2_pri_con_m
t3_pri_con_m ~~ 0*t3_pri_con_m
t1_inf_sha_att_m ~~ 0*t1_inf_sha_att_m
t2_inf_sha_att_m ~~ 0*t2_inf_sha_att_m
t3_inf_sha_att_m ~~ 0*t3_inf_sha_att_m
t1_inf_sha_beh_m ~~ 0*t1_inf_sha_beh_m
t2_inf_sha_beh_m ~~ 0*t2_inf_sha_beh_m
t3_inf_sha_beh_m ~~ 0*t3_inf_sha_beh_m

# allow covariances RIs & variables measured at the same time
pri_con_b ~~ inf_sha_att_b + inf_sha_beh_b
inf_sha_att_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_att_w + t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_att_w + b*t2_inf_sha_beh_w
t2_inf_sha_att_w ~~ c*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w

# control variables
t1_pri_con_m ~ age + edu_num + male
t2_pri_con_m ~ age + edu_num + male
t3_pri_con_m ~ age + edu_num + male
t1_inf_sha_beh_m ~ age + edu_num + male
t2_inf_sha_beh_m ~ age + edu_num + male
t3_inf_sha_beh_m ~ age + edu_num + male
t1_inf_sha_att_m ~ age + edu_num + male
t2_inf_sha_att_m ~ age + edu_num + male
t3_inf_sha_att_m ~ age + edu_num + male
'
fit <- sem(model, estimator = "ML", data = d_wide, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 172 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         78
##   Number of equality constraints                    12
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         7
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                16.098
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.376
## 
## Model Test Baseline Model:
## 
##   Test statistic                              6592.769
##   Degrees of freedom                                63
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       0.999
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10710.196
##   Loglikelihood unrestricted model (H1)     -10702.147
##                                                       
##   Akaike (AIC)                               21552.392
##   Bayesian (BIC)                             21898.652
##   Sample-size adjusted Bayesian (BIC)        21688.995
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.007
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.027
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.008
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_m         1.000                               1.000    1.000    0.734    0.831
##     t2_pri_con_m         1.000                               1.000    1.000    0.734    0.824
##     t3_pri_con_m         1.000                               1.000    1.000    0.734    0.822
##   inf_sha_att_b =~                                                                           
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.499    0.709
##     t2_inf_sh_tt_m       1.000                               1.000    1.000    0.499    0.707
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.499    0.720
##   inf_sha_beh_b =~                                                                           
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.461    0.705
##     t2_inf_sh_bh_m       1.000                               1.000    1.000    0.461    0.715
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.461    0.751
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_m         1.000                               1.000    1.000    0.457    0.518
##   t2_pri_con_w =~                                                                            
##     t2_pri_con_m         1.000                               1.000    1.000    0.471    0.528
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_m         1.000                               1.000    1.000    0.470    0.526
##   t1_inf_sha_att_w =~                                                                        
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.472    0.671
##   t2_inf_sha_att_w =~                                                                        
##     t2_inf_sh_tt_m       1.000                               1.000    1.000    0.465    0.660
##   t3_inf_sha_att_w =~                                                                        
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.445    0.643
##   t1_inf_sha_beh_w =~                                                                        
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.433    0.662
##   t2_inf_sha_beh_w =~                                                                        
##     t2_inf_sh_bh_m       1.000                               1.000    1.000    0.414    0.642
##   t3_inf_sha_beh_w =~                                                                        
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.361    0.588
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t2_pri_con_w ~                                                                            
##     t1_pr_cn_ (a1)      0.088    0.069    1.283    0.200   -0.046    0.223    0.086    0.086
##     t1_nf_s__ (a2)     -0.028    0.035   -0.802    0.422   -0.096    0.040   -0.028   -0.028
##     t1_nf_s__ (a3)      0.012    0.037    0.337    0.736   -0.060    0.085    0.011    0.011
##   t2_inf_sha_att_w ~                                                                        
##     t1_pr_cn_ (b1)     -0.010    0.035   -0.296    0.767   -0.079    0.058   -0.010   -0.010
##     t1_nf_s__ (b2)      0.101    0.046    2.210    0.027    0.011    0.191    0.103    0.103
##     t1_nf_s__ (b3)      0.029    0.036    0.814    0.416   -0.041    0.098    0.027    0.027
##   t2_inf_sha_beh_w ~                                                                        
##     t1_pr_cn_ (c1)      0.038    0.028    1.329    0.184   -0.018    0.094    0.042    0.042
##     t1_nf_s__ (c2)     -0.007    0.028   -0.239    0.811   -0.062    0.048   -0.008   -0.008
##     t1_nf_s__ (c3)      0.055    0.039    1.398    0.162   -0.022    0.132    0.058    0.058
##   t3_pri_con_w ~                                                                            
##     t2_pr_cn_ (a1)      0.088    0.069    1.283    0.200   -0.046    0.223    0.088    0.088
##     t2_nf_s__ (a2)     -0.028    0.035   -0.802    0.422   -0.096    0.040   -0.028   -0.028
##     t2_nf_s__ (a3)      0.012    0.037    0.337    0.736   -0.060    0.085    0.011    0.011
##   t3_inf_sha_att_w ~                                                                        
##     t2_pr_cn_ (b1)     -0.010    0.035   -0.296    0.767   -0.079    0.058   -0.011   -0.011
##     t2_nf_s__ (b2)      0.101    0.046    2.210    0.027    0.011    0.191    0.106    0.106
##     t2_nf_s__ (b3)      0.029    0.036    0.814    0.416   -0.041    0.098    0.027    0.027
##   t3_inf_sha_beh_w ~                                                                        
##     t2_pr_cn_ (c1)      0.038    0.028    1.329    0.184   -0.018    0.094    0.049    0.049
##     t2_nf_s__ (c2)     -0.007    0.028   -0.239    0.811   -0.062    0.048   -0.009   -0.009
##     t2_nf_s__ (c3)      0.055    0.039    1.398    0.162   -0.022    0.132    0.063    0.063
##   t1_pri_con_m ~                                                                            
##     age                 0.011    0.002    7.417    0.000    0.008    0.014    0.011    0.199
##     edu_num            -0.032    0.013   -2.356    0.018   -0.058   -0.005   -0.032   -0.062
##     male               -0.007    0.048   -0.149    0.881   -0.100    0.086   -0.007   -0.004
##   t2_pri_con_m ~                                                                            
##     age                 0.012    0.002    7.623    0.000    0.009    0.015    0.012    0.204
##     edu_num            -0.034    0.014   -2.474    0.013   -0.060   -0.007   -0.034   -0.065
##     male                0.021    0.048    0.449    0.654   -0.072    0.115    0.021    0.012
##   t3_pri_con_m ~                                                                            
##     age                 0.013    0.002    8.215    0.000    0.010    0.016    0.013    0.220
##     edu_num            -0.025    0.014   -1.871    0.061   -0.052    0.001   -0.025   -0.049
##     male                0.032    0.048    0.672    0.501   -0.062    0.126    0.032    0.018
##   t1_inf_sha_beh_m ~                                                                        
##     age                -0.009    0.001   -7.725    0.000   -0.011   -0.006   -0.009   -0.204
##     edu_num             0.056    0.010    5.650    0.000    0.036    0.075    0.056    0.148
##     male               -0.145    0.035   -4.176    0.000   -0.213   -0.077   -0.145   -0.111
##   t2_inf_sha_beh_m ~                                                                        
##     age                -0.010    0.001   -8.911    0.000   -0.012   -0.008   -0.010   -0.234
##     edu_num             0.064    0.010    6.661    0.000    0.045    0.083    0.064    0.173
##     male               -0.084    0.034   -2.464    0.014   -0.150   -0.017   -0.084   -0.065
##   t3_inf_sha_beh_m ~                                                                        
##     age                -0.010    0.001   -9.234    0.000   -0.012   -0.008   -0.010   -0.241
##     edu_num             0.068    0.009    7.450    0.000    0.050    0.086    0.068    0.192
##     male               -0.129    0.032   -4.021    0.000   -0.192   -0.066   -0.129   -0.105
##   t1_inf_sha_att_m ~                                                                        
##     age                -0.004    0.001   -3.327    0.001   -0.006   -0.002   -0.004   -0.089
##     edu_num             0.027    0.011    2.529    0.011    0.006    0.048    0.027    0.067
##     male               -0.284    0.038   -7.519    0.000   -0.357   -0.210   -0.284   -0.201
##   t2_inf_sha_att_m ~                                                                        
##     age                -0.006    0.001   -5.182    0.000   -0.009   -0.004   -0.006   -0.137
##     edu_num             0.045    0.011    4.240    0.000    0.024    0.066    0.045    0.111
##     male               -0.291    0.037   -7.763    0.000   -0.365   -0.218   -0.291   -0.206
##   t3_inf_sha_att_m ~                                                                        
##     age                -0.007    0.001   -6.146    0.000   -0.010   -0.005   -0.007   -0.162
##     edu_num             0.047    0.010    4.524    0.000    0.027    0.068    0.047    0.118
##     male               -0.268    0.037   -7.309    0.000   -0.340   -0.196   -0.268   -0.194
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     inf_sh_tt_          -0.114    0.014   -8.348    0.000   -0.141   -0.087   -0.311   -0.311
##     inf_sh_bh_          -0.040    0.012   -3.393    0.001   -0.063   -0.017   -0.118   -0.118
##   inf_sha_att_b ~~                                                                           
##     inf_sh_bh_           0.151    0.010   14.987    0.000    0.131    0.171    0.656    0.656
##   t1_pri_con_w ~~                                                                            
##     t1_nf_sh__          -0.004    0.009   -0.405    0.685   -0.021    0.014   -0.016   -0.016
##     t1_nf_sh__          -0.013    0.008   -1.583    0.113   -0.028    0.003   -0.063   -0.063
##   t1_inf_sha_att_w ~~                                                                        
##     t1_nf_sh__           0.028    0.008    3.575    0.000    0.013    0.043    0.136    0.136
##  .t2_pri_con_w ~~                                                                            
##    .t2_nf_sh__ (a)      -0.005    0.008   -0.590    0.555   -0.020    0.011   -0.021   -0.021
##    .t2_nf_sh__ (b)       0.006    0.006    0.986    0.324   -0.006    0.019    0.032    0.032
##  .t2_inf_sha_att_w ~~                                                                        
##    .t2_nf_sh__ (c)       0.030    0.006    4.887    0.000    0.018    0.042    0.158    0.158
##  .t3_pri_con_w ~~                                                                            
##    .t3_nf_sh__ (a)      -0.005    0.008   -0.590    0.555   -0.020    0.011   -0.022   -0.022
##    .t3_nf_sh__ (b)       0.006    0.006    0.986    0.324   -0.006    0.019    0.037    0.037
##  .t3_inf_sha_att_w ~~                                                                        
##    .t3_nf_sh__ (c)       0.030    0.006    4.887    0.000    0.018    0.042    0.190    0.190
##   pri_con_b ~~                                                                               
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      3.221    0.140   22.959    0.000    2.946    3.496    3.221    3.646
##    .t2_pri_con_m      3.111    0.141   22.000    0.000    2.834    3.389    3.111    3.490
##    .t3_pri_con_m      2.975    0.142   20.974    0.000    2.697    3.253    2.975    3.330
##    .t1_inf_sh_tt_m    2.847    0.111   25.548    0.000    2.629    3.066    2.847    4.045
##    .t2_inf_sh_tt_m    2.947    0.111   26.617    0.000    2.730    3.165    2.947    4.178
##    .t3_inf_sh_tt_m    2.978    0.108   27.480    0.000    2.766    3.191    2.978    4.302
##    .t1_inf_sh_bh_m    2.528    0.103   24.659    0.000    2.327    2.729    2.528    3.865
##    .t2_inf_sh_bh_m    2.468    0.100   24.566    0.000    2.271    2.664    2.468    3.825
##    .t3_inf_sh_bh_m    2.471    0.095   26.045    0.000    2.285    2.657    2.471    4.024
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.539    0.026   20.731    0.000    0.488    0.590    1.000    1.000
##     inf_sha_att_b     0.249    0.015   16.676    0.000    0.220    0.278    1.000    1.000
##     inf_sha_beh_b     0.212    0.011   18.742    0.000    0.190    0.235    1.000    1.000
##     t1_pri_con_w      0.209    0.013   16.657    0.000    0.185    0.234    1.000    1.000
##    .t2_pri_con_w      0.220    0.025    8.744    0.000    0.171    0.269    0.992    0.992
##    .t3_pri_con_w      0.219    0.013   17.514    0.000    0.194    0.243    0.991    0.991
##     t1_inf_sh_tt_w    0.223    0.012   18.207    0.000    0.199    0.247    1.000    1.000
##    .t2_inf_sh_tt_w    0.214    0.015   13.962    0.000    0.184    0.244    0.988    0.988
##    .t3_inf_sh_tt_w    0.196    0.011   18.462    0.000    0.175    0.217    0.987    0.987
##     t1_inf_sh_bh_w    0.188    0.010   18.988    0.000    0.168    0.207    1.000    1.000
##    .t2_inf_sh_bh_w    0.171    0.012   14.847    0.000    0.148    0.193    0.995    0.995
##    .t3_inf_sh_bh_w    0.129    0.008   17.175    0.000    0.115    0.144    0.993    0.993

2.1.2.3 Model 3

With Factor Scores.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs
inf_sha_att_b =~ 1*t1_inf_sha_att_fs + 1*t2_inf_sha_att_fs + 1*t3_inf_sha_att_fs

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_fs
t2_inf_sha_att_w =~ 1*t2_inf_sha_att_fs
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_fs

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t2_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_att_w + a3*t2_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_att_w + b3*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t2_pri_con_w + c2*t2_inf_sha_att_w + c3*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_att_b + inf_sha_beh_b
inf_sha_att_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_att_w + t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_att_w + b*t2_inf_sha_beh_w
t2_inf_sha_att_w ~~ c*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_fs ~~ 0*t1_pri_con_fs
t2_pri_con_fs ~~ 0*t2_pri_con_fs
t3_pri_con_fs ~~ 0*t3_pri_con_fs
t1_inf_sha_att_fs ~~ 0*t1_inf_sha_att_fs
t2_inf_sha_att_fs ~~ 0*t2_inf_sha_att_fs
t3_inf_sha_att_fs ~~ 0*t3_inf_sha_att_fs
t1_inf_sha_beh_fs ~~ 0*t1_inf_sha_beh_fs
t2_inf_sha_beh_fs ~~ 0*t2_inf_sha_beh_fs
t3_inf_sha_beh_fs ~~ 0*t3_inf_sha_beh_fs
'
fit <- sem(model, data = d_wide, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 81 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         51
##   Number of equality constraints                    12
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         1
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                26.276
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.035
## 
## Model Test Baseline Model:
## 
##   Test statistic                              6848.636
##   Degrees of freedom                                36
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.998
##   Tucker-Lewis Index (TLI)                       0.996
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10390.169
##   Loglikelihood unrestricted model (H1)     -10377.031
##                                                       
##   Akaike (AIC)                               20858.337
##   Bayesian (BIC)                             21062.945
##   Sample-size adjusted Bayesian (BIC)        20939.057
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.023
##   90 Percent confidence interval - lower         0.006
##   90 Percent confidence interval - upper         0.038
##   P-value RMSEA <= 0.05                          0.999
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.015
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_fs        1.000                               1.000    1.000    0.755    0.883
##     t2_pri_con_fs        1.000                               1.000    1.000    0.755    0.861
##     t3_pri_con_fs        1.000                               1.000    1.000    0.755    0.871
##   inf_sha_beh_b =~                                                                           
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.497    0.760
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.497    0.772
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.497    0.809
##   inf_sha_att_b =~                                                                           
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.511    0.737
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.511    0.746
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.511    0.767
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_fs        1.000                               1.000    1.000    0.402    0.470
##   t2_pri_con_w =~                                                                            
##     t2_pri_con_fs        1.000                               1.000    1.000    0.445    0.508
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_fs        1.000                               1.000    1.000    0.425    0.491
##   t1_inf_sha_beh_w =~                                                                        
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.425    0.650
##   t2_inf_sha_beh_w =~                                                                        
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.409    0.635
##   t3_inf_sha_beh_w =~                                                                        
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.361    0.588
##   t1_inf_sha_att_w =~                                                                        
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.469    0.676
##   t2_inf_sha_att_w =~                                                                        
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.456    0.666
##   t3_inf_sha_att_w =~                                                                        
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.428    0.642
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t2_pri_con_w ~                                                                            
##     t1_pr_cn_ (a1)      0.134    0.072    1.872    0.061   -0.006    0.275    0.121    0.121
##     t1_nf_s__ (a2)     -0.002    0.032   -0.058    0.954   -0.065    0.061   -0.002   -0.002
##     t1_nf_s__ (a3)     -0.029    0.035   -0.834    0.404   -0.097    0.039   -0.028   -0.028
##   t2_inf_sha_att_w ~                                                                        
##     t1_pr_cn_ (b1)     -0.024    0.038   -0.625    0.532   -0.098    0.050   -0.021   -0.021
##     t1_nf_s__ (b2)      0.112    0.047    2.408    0.016    0.021    0.203    0.115    0.115
##     t1_nf_s__ (b3)      0.049    0.036    1.354    0.176   -0.022    0.119    0.045    0.045
##   t2_inf_sha_beh_w ~                                                                        
##     t1_pr_cn_ (c1)      0.011    0.032    0.333    0.739   -0.052    0.073    0.011    0.011
##     t1_nf_s__ (c2)     -0.001    0.029   -0.021    0.983   -0.057    0.056   -0.001   -0.001
##     t1_nf_s__ (c3)      0.056    0.041    1.353    0.176   -0.025    0.136    0.058    0.058
##   t3_pri_con_w ~                                                                            
##     t2_pr_cn_ (a1)      0.134    0.072    1.872    0.061   -0.006    0.275    0.141    0.141
##     t2_nf_s__ (a2)     -0.002    0.032   -0.058    0.954   -0.065    0.061   -0.002   -0.002
##     t2_nf_s__ (a3)     -0.029    0.035   -0.834    0.404   -0.097    0.039   -0.028   -0.028
##   t3_inf_sha_att_w ~                                                                        
##     t2_pr_cn_ (b1)     -0.024    0.038   -0.625    0.532   -0.098    0.050   -0.025   -0.025
##     t2_nf_s__ (b2)      0.112    0.047    2.408    0.016    0.021    0.203    0.119    0.119
##     t2_nf_s__ (b3)      0.049    0.036    1.354    0.176   -0.022    0.119    0.046    0.046
##   t3_inf_sha_beh_w ~                                                                        
##     t2_pr_cn_ (c1)      0.011    0.032    0.333    0.739   -0.052    0.073    0.013    0.013
##     t2_nf_s__ (c2)     -0.001    0.029   -0.021    0.983   -0.057    0.056   -0.001   -0.001
##     t2_nf_s__ (c3)      0.056    0.041    1.353    0.176   -0.025    0.136    0.063    0.063
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     inf_sh_tt_          -0.123    0.014   -8.823    0.000   -0.150   -0.095   -0.317   -0.317
##     inf_sh_bh_          -0.053    0.013   -4.243    0.000   -0.078   -0.029   -0.142   -0.142
##   inf_sha_beh_b ~~                                                                           
##     inf_sh_tt_           0.172    0.011   15.824    0.000    0.151    0.194    0.679    0.679
##   t1_pri_con_w ~~                                                                            
##     t1_nf_sh__          -0.010    0.008   -1.240    0.215   -0.025    0.006   -0.052   -0.052
##     t1_nf_sh__          -0.016    0.007   -2.253    0.024   -0.030   -0.002   -0.094   -0.094
##   t1_inf_sha_beh_w ~~                                                                        
##     t1_nf_sh__           0.030    0.008    3.902    0.000    0.015    0.045    0.151    0.151
##  .t2_pri_con_w ~~                                                                            
##    .t2_nf_sh__ (a)      -0.005    0.007   -0.703    0.482   -0.018    0.009   -0.024   -0.024
##    .t2_nf_sh__ (b)       0.006    0.006    0.943    0.346   -0.006    0.017    0.031    0.031
##  .t2_inf_sha_beh_w ~~                                                                        
##    .t2_nf_sh__ (c)       0.029    0.006    4.609    0.000    0.016    0.041    0.155    0.155
##  .t3_pri_con_w ~~                                                                            
##    .t3_nf_sh__ (a)      -0.005    0.007   -0.703    0.482   -0.018    0.009   -0.027   -0.027
##    .t3_nf_sh__ (b)       0.006    0.006    0.943    0.346   -0.006    0.017    0.037    0.037
##  .t3_inf_sha_beh_w ~~                                                                        
##    .t3_nf_sh__ (c)       0.029    0.006    4.609    0.000    0.016    0.041    0.187    0.187
##   pri_con_b ~~                                                                               
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     3.707    0.023  162.325    0.000    3.663    3.752    3.707    4.334
##    .t2_pri_con_fs     3.636    0.023  155.386    0.000    3.590    3.682    3.636    4.148
##    .t3_pri_con_fs     3.607    0.023  155.930    0.000    3.561    3.652    3.607    4.163
##    .t1_nf_sh_bh_fs    2.193    0.017  125.641    0.000    2.159    2.228    2.193    3.354
##    .t2_nf_sh_bh_fs    2.206    0.017  128.511    0.000    2.173    2.240    2.206    3.431
##    .t3_nf_sh_bh_fs    2.168    0.016  132.315    0.000    2.136    2.201    2.168    3.532
##    .t1_nf_sh_tt_fs    2.418    0.019  130.551    0.000    2.382    2.454    2.418    3.485
##    .t2_nf_sh_tt_fs    2.482    0.018  135.718    0.000    2.446    2.518    2.482    3.623
##    .t3_nf_sh_tt_fs    2.502    0.018  140.473    0.000    2.467    2.537    2.502    3.750
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.570    0.026   22.006    0.000    0.519    0.621    1.000    1.000
##     inf_sha_beh_b     0.247    0.013   19.718    0.000    0.222    0.271    1.000    1.000
##     inf_sha_att_b     0.261    0.015   16.978    0.000    0.231    0.292    1.000    1.000
##     t1_pri_con_w      0.162    0.010   15.582    0.000    0.141    0.182    1.000    1.000
##    .t2_pri_con_w      0.195    0.022    8.984    0.000    0.153    0.238    0.984    0.984
##    .t3_pri_con_w      0.177    0.011   16.554    0.000    0.156    0.198    0.980    0.980
##     t1_inf_sh_bh_w    0.181    0.010   18.562    0.000    0.162    0.200    1.000    1.000
##    .t2_inf_sh_bh_w    0.166    0.012   14.182    0.000    0.143    0.189    0.997    0.997
##    .t3_inf_sh_bh_w    0.130    0.008   17.086    0.000    0.115    0.144    0.996    0.996
##     t1_inf_sh_tt_w    0.220    0.012   18.228    0.000    0.196    0.244    1.000    1.000
##    .t2_inf_sh_tt_w    0.204    0.015   13.557    0.000    0.175    0.234    0.982    0.982
##    .t3_inf_sh_tt_w    0.180    0.010   17.990    0.000    0.160    0.200    0.981    0.981

2.1.2.4 Model 4 (final)

With Factor Scores and control variables. This is the final model we report in the paper.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs
inf_sha_att_b =~ 1*t1_inf_sha_att_fs + 1*t2_inf_sha_att_fs + 1*t3_inf_sha_att_fs

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_fs
t2_inf_sha_att_w =~ 1*t2_inf_sha_att_fs
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_fs

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t2_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + a2*t2_inf_sha_att_w + a3*t2_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t2_pri_con_w + b2*t2_inf_sha_att_w + b3*t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t2_pri_con_w + c2*t2_inf_sha_att_w + c3*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ cor_b_1*inf_sha_att_b + cor_b_2*inf_sha_beh_b
inf_sha_att_b ~~ cor_b_3*inf_sha_beh_b
t1_pri_con_w ~~ cor_w_1*t1_inf_sha_att_w + cor_w_2*t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ cor_w_3*t1_inf_sha_beh_w
t2_pri_con_w ~~ a*t2_inf_sha_att_w + b*t2_inf_sha_beh_w
t2_inf_sha_att_w ~~ c*t2_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_fs ~~ 0*t1_pri_con_fs
t2_pri_con_fs ~~ 0*t2_pri_con_fs
t3_pri_con_fs ~~ 0*t3_pri_con_fs
t1_inf_sha_att_fs ~~ 0*t1_inf_sha_att_fs
t2_inf_sha_att_fs ~~ 0*t2_inf_sha_att_fs
t3_inf_sha_att_fs ~~ 0*t3_inf_sha_att_fs
t1_inf_sha_beh_fs ~~ 0*t1_inf_sha_beh_fs
t2_inf_sha_beh_fs ~~ 0*t2_inf_sha_beh_fs
t3_inf_sha_beh_fs ~~ 0*t3_inf_sha_beh_fs

# control variables
t1_pri_con_fs ~ age + edu_num + male
t2_pri_con_fs ~ age + edu_num + male
t3_pri_con_fs ~ age + edu_num + male
t1_inf_sha_beh_fs ~ age + edu_num + male
t2_inf_sha_beh_fs ~ age + edu_num + male
t3_inf_sha_beh_fs ~ age + edu_num + male
t1_inf_sha_att_fs ~ age + edu_num + male
t2_inf_sha_att_fs ~ age + edu_num + male
t3_inf_sha_att_fs ~ age + edu_num + male
'
fit <- sem(model, data = d_wide, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 162 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         78
##   Number of equality constraints                    12
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         1
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                25.184
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.048
## 
## Model Test Baseline Model:
## 
##   Test statistic                              7133.872
##   Degrees of freedom                                63
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.999
##   Tucker-Lewis Index (TLI)                       0.994
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10247.004
##   Loglikelihood unrestricted model (H1)     -10234.413
##                                                       
##   Akaike (AIC)                               20626.009
##   Bayesian (BIC)                             20972.269
##   Sample-size adjusted Bayesian (BIC)        20762.612
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.022
##   90 Percent confidence interval - lower         0.002
##   90 Percent confidence interval - upper         0.037
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.010
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_fs        1.000                               1.000    1.000    0.737    0.862
##     t2_pri_con_fs        1.000                               1.000    1.000    0.737    0.840
##     t3_pri_con_fs        1.000                               1.000    1.000    0.737    0.849
##   inf_sha_beh_b =~                                                                           
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.466    0.713
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.466    0.726
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.466    0.757
##   inf_sha_att_b =~                                                                           
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.486    0.705
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.486    0.709
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.486    0.725
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_fs        1.000                               1.000    1.000    0.402    0.471
##   t2_pri_con_w =~                                                                            
##     t2_pri_con_fs        1.000                               1.000    1.000    0.450    0.513
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_fs        1.000                               1.000    1.000    0.426    0.490
##   t1_inf_sha_beh_w =~                                                                        
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.427    0.653
##   t2_inf_sha_beh_w =~                                                                        
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.403    0.628
##   t3_inf_sha_beh_w =~                                                                        
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.358    0.582
##   t1_inf_sha_att_w =~                                                                        
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.466    0.676
##   t2_inf_sha_att_w =~                                                                        
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.451    0.658
##   t3_inf_sha_att_w =~                                                                        
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.427    0.637
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t2_pri_con_w ~                                                                             
##     t1_pr_cn_ (a1)       0.145    0.068    2.151    0.031    0.013    0.278    0.130    0.130
##     t1_nf_s__ (a2)       0.002    0.032    0.062    0.951   -0.060    0.064    0.002    0.002
##     t1_nf_s__ (a3)      -0.028    0.034   -0.802    0.422   -0.095    0.040   -0.026   -0.026
##   t2_inf_sha_att_w ~                                                                         
##     t1_pr_cn_ (b1)      -0.017    0.037   -0.466    0.641   -0.090    0.055   -0.015   -0.015
##     t1_nf_s__ (b2)       0.103    0.046    2.243    0.025    0.013    0.193    0.106    0.106
##     t1_nf_s__ (b3)       0.040    0.035    1.152    0.249   -0.028    0.109    0.038    0.038
##   t2_inf_sha_beh_w ~                                                                         
##     t1_pr_cn_ (c1)       0.013    0.031    0.409    0.683   -0.048    0.074    0.013    0.013
##     t1_nf_s__ (c2)      -0.002    0.028   -0.067    0.947   -0.057    0.053   -0.002   -0.002
##     t1_nf_s__ (c3)       0.045    0.039    1.144    0.253   -0.032    0.122    0.048    0.048
##   t3_pri_con_w ~                                                                             
##     t2_pr_cn_ (a1)       0.145    0.068    2.151    0.031    0.013    0.278    0.154    0.154
##     t2_nf_s__ (a2)       0.002    0.032    0.062    0.951   -0.060    0.064    0.002    0.002
##     t2_nf_s__ (a3)      -0.028    0.034   -0.802    0.422   -0.095    0.040   -0.026   -0.026
##   t3_inf_sha_att_w ~                                                                         
##     t2_pr_cn_ (b1)      -0.017    0.037   -0.466    0.641   -0.090    0.055   -0.018   -0.018
##     t2_nf_s__ (b2)       0.103    0.046    2.243    0.025    0.013    0.193    0.109    0.109
##     t2_nf_s__ (b3)       0.040    0.035    1.152    0.249   -0.028    0.109    0.038    0.038
##   t3_inf_sha_beh_w ~                                                                         
##     t2_pr_cn_ (c1)       0.013    0.031    0.409    0.683   -0.048    0.074    0.016    0.016
##     t2_nf_s__ (c2)      -0.002    0.028   -0.067    0.947   -0.057    0.053   -0.002   -0.002
##     t2_nf_s__ (c3)       0.045    0.039    1.144    0.253   -0.032    0.122    0.051    0.051
##   t1_pri_con_fs ~                                                                            
##     age                  0.010    0.001    6.847    0.000    0.007    0.013    0.010    0.184
##     edu_num             -0.023    0.013   -1.759    0.079   -0.049    0.003   -0.023   -0.047
##     male                -0.002    0.046   -0.043    0.966   -0.092    0.088   -0.002   -0.001
##   t2_pri_con_fs ~                                                                            
##     age                  0.010    0.002    6.510    0.000    0.007    0.013    0.010    0.175
##     edu_num             -0.023    0.013   -1.676    0.094   -0.049    0.004   -0.023   -0.045
##     male                 0.012    0.047    0.251    0.802   -0.081    0.105    0.012    0.007
##   t3_pri_con_fs ~                                                                            
##     age                  0.011    0.002    7.468    0.000    0.008    0.014    0.011    0.200
##     edu_num             -0.017    0.013   -1.310    0.190   -0.043    0.009   -0.017   -0.035
##     male                 0.010    0.047    0.220    0.826   -0.081    0.102    0.010    0.006
##   t1_inf_sha_beh_fs ~                                                                        
##     age                 -0.009    0.001   -7.913    0.000   -0.011   -0.007   -0.009   -0.209
##     edu_num              0.057    0.010    5.831    0.000    0.038    0.077    0.057    0.152
##     male                -0.132    0.035   -3.819    0.000   -0.200   -0.064   -0.132   -0.101
##   t2_inf_sha_beh_fs ~                                                                        
##     age                 -0.010    0.001   -9.013    0.000   -0.012   -0.008   -0.010   -0.237
##     edu_num              0.065    0.010    6.725    0.000    0.046    0.083    0.065    0.174
##     male                -0.083    0.034   -2.451    0.014   -0.149   -0.017   -0.083   -0.065
##   t3_inf_sha_beh_fs ~                                                                        
##     age                 -0.009    0.001   -8.878    0.000   -0.011   -0.007   -0.009   -0.232
##     edu_num              0.070    0.009    7.677    0.000    0.052    0.088    0.070    0.198
##     male                -0.121    0.032   -3.768    0.000   -0.185   -0.058   -0.121   -0.099
##   t1_inf_sha_att_fs ~                                                                        
##     age                 -0.004    0.001   -3.599    0.000   -0.007   -0.002   -0.004   -0.096
##     edu_num              0.031    0.011    2.989    0.003    0.011    0.052    0.031    0.079
##     male                -0.262    0.037   -7.083    0.000   -0.334   -0.189   -0.262   -0.190
##   t2_inf_sha_att_fs ~                                                                        
##     age                 -0.006    0.001   -5.372    0.000   -0.009   -0.004   -0.006   -0.142
##     edu_num              0.050    0.010    4.834    0.000    0.030    0.070    0.050    0.126
##     male                -0.263    0.036   -7.231    0.000   -0.334   -0.192   -0.263   -0.192
##   t3_inf_sha_att_fs ~                                                                        
##     age                 -0.007    0.001   -6.188    0.000   -0.009   -0.005   -0.007   -0.163
##     edu_num              0.051    0.010    5.100    0.000    0.032    0.071    0.051    0.133
##     male                -0.248    0.035   -6.984    0.000   -0.317   -0.178   -0.248   -0.185
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     in___ (cr_b_1)      -0.111    0.013   -8.462    0.000   -0.136   -0.085   -0.309   -0.309
##     in___ (cr_b_2)      -0.030    0.012   -2.573    0.010   -0.053   -0.007   -0.087   -0.087
##   inf_sha_beh_b ~~                                                                           
##     in___ (cr_b_3)       0.149    0.010   15.116    0.000    0.130    0.168    0.657    0.657
##   t1_pri_con_w ~~                                                                            
##     t1___ (cr_w_1)      -0.011    0.008   -1.376    0.169   -0.026    0.005   -0.057   -0.057
##     t1___ (cr_w_2)      -0.017    0.007   -2.375    0.018   -0.031   -0.003   -0.100   -0.100
##   t1_inf_sha_beh_w ~~                                                                        
##     t1___ (cr_w_3)       0.031    0.008    4.013    0.000    0.016    0.045    0.153    0.153
##  .t2_pri_con_w ~~                                                                            
##    .t2___      (a)      -0.003    0.007   -0.498    0.619   -0.017    0.010   -0.017   -0.017
##    .t2___      (b)       0.006    0.006    1.049    0.294   -0.005    0.017    0.033    0.033
##  .t2_inf_sha_beh_w ~~                                                                        
##    .t2___      (c)       0.027    0.006    4.542    0.000    0.015    0.039    0.149    0.149
##  .t3_pri_con_w ~~                                                                            
##    .t3___      (a)      -0.003    0.007   -0.498    0.619   -0.017    0.010   -0.019   -0.019
##    .t3___      (b)       0.006    0.006    1.049    0.294   -0.005    0.017    0.040    0.040
##  .t3_inf_sha_beh_w ~~                                                                        
##    .t3___      (c)       0.027    0.006    4.542    0.000    0.015    0.039    0.178    0.178
##   pri_con_b ~~                                                                               
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     3.270    0.136   24.039    0.000    3.003    3.537    3.270    3.829
##    .t2_pri_con_fs     3.189    0.140   22.798    0.000    2.914    3.463    3.189    3.638
##    .t3_pri_con_fs     3.064    0.138   22.220    0.000    2.793    3.334    3.064    3.530
##    .t1_nf_sh_bh_fs    2.583    0.102   25.230    0.000    2.382    2.783    2.583    3.952
##    .t2_nf_sh_bh_fs    2.539    0.100   25.431    0.000    2.344    2.735    2.539    3.957
##    .t3_nf_sh_bh_fs    2.497    0.095   26.225    0.000    2.310    2.684    2.497    4.057
##    .t1_nf_sh_tt_fs    2.883    0.109   26.403    0.000    2.669    3.097    2.883    4.179
##    .t2_nf_sh_tt_fs    2.964    0.107   27.586    0.000    2.754    3.175    2.964    4.324
##    .t3_nf_sh_tt_fs    2.996    0.105   28.588    0.000    2.791    3.202    2.996    4.472
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.542    0.025   21.853    0.000    0.494    0.591    1.000    1.000
##     inf_sha_beh_b     0.217    0.011   19.186    0.000    0.195    0.239    1.000    1.000
##     inf_sha_att_b     0.236    0.014   16.522    0.000    0.208    0.264    1.000    1.000
##     t1_pri_con_w      0.162    0.010   15.492    0.000    0.141    0.182    1.000    1.000
##    .t2_pri_con_w      0.199    0.021    9.670    0.000    0.158    0.239    0.982    0.982
##    .t3_pri_con_w      0.177    0.011   16.686    0.000    0.156    0.198    0.976    0.976
##     t1_inf_sh_bh_w    0.182    0.010   18.768    0.000    0.163    0.201    1.000    1.000
##    .t2_inf_sh_bh_w    0.162    0.011   14.695    0.000    0.141    0.184    0.998    0.998
##    .t3_inf_sh_bh_w    0.128    0.007   17.307    0.000    0.113    0.142    0.997    0.997
##     t1_inf_sh_tt_w    0.218    0.012   18.456    0.000    0.194    0.241    1.000    1.000
##    .t2_inf_sh_tt_w    0.200    0.015   13.697    0.000    0.172    0.229    0.985    0.985
##    .t3_inf_sh_tt_w    0.179    0.010   18.200    0.000    0.160    0.199    0.985    0.985
fit_riclpm <- fit
effect_std_ci <- standardizedsolution(fit) %>% 
  filter(lhs == "pri_con_b", rhs == "inf_sha_beh_b")

2.1.2.5 Model 5

Same model, but with unconstrained effects. That way, we can empirically test the assumption whether effects have changed over time. With Factor Scores, control variables, and 4 waves / 1 year intervals

model_free <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t2_pri_con_fs + 1*t3_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t2_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs
inf_sha_att_b =~ 1*t1_inf_sha_att_fs + 1*t2_inf_sha_att_fs + 1*t3_inf_sha_att_fs

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t2_pri_con_w =~ 1*t2_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t2_inf_sha_beh_w =~ 1*t2_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_fs
t2_inf_sha_att_w =~ 1*t2_inf_sha_att_fs
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_fs

# within person effects
t2_pri_con_w ~ a1*t1_pri_con_w + t1_inf_sha_att_w + t1_inf_sha_beh_w
t2_inf_sha_att_w ~ t1_pri_con_w + b2*t1_inf_sha_att_w + t1_inf_sha_beh_w
t2_inf_sha_beh_w ~ t1_pri_con_w + t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t3_pri_con_w ~ a1*t2_pri_con_w + t2_inf_sha_att_w + t2_inf_sha_beh_w
t3_inf_sha_att_w ~ t2_pri_con_w + b2*t2_inf_sha_att_w + t2_inf_sha_beh_w
t3_inf_sha_beh_w ~ t2_pri_con_w + t2_inf_sha_att_w + c3*t2_inf_sha_beh_w

# covariances
pri_con_b ~~ cor_b_1*inf_sha_att_b + cor_b_2*inf_sha_beh_b
inf_sha_att_b ~~ cor_b_3*inf_sha_beh_b
t1_pri_con_w ~~ cor_w_1*t1_inf_sha_att_w + cor_w_2*t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ cor_w_3*t1_inf_sha_beh_w
t2_pri_con_w ~~ t2_inf_sha_att_w + t2_inf_sha_beh_w
t2_inf_sha_att_w ~~ t2_inf_sha_beh_w
t3_pri_con_w ~~ t3_inf_sha_att_w + t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ t3_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_fs ~~ 0*t1_pri_con_fs
t2_pri_con_fs ~~ 0*t2_pri_con_fs
t3_pri_con_fs ~~ 0*t3_pri_con_fs
t1_inf_sha_att_fs ~~ 0*t1_inf_sha_att_fs
t2_inf_sha_att_fs ~~ 0*t2_inf_sha_att_fs
t3_inf_sha_att_fs ~~ 0*t3_inf_sha_att_fs
t1_inf_sha_beh_fs ~~ 0*t1_inf_sha_beh_fs
t2_inf_sha_beh_fs ~~ 0*t2_inf_sha_beh_fs
t3_inf_sha_beh_fs ~~ 0*t3_inf_sha_beh_fs

# control variables
t1_pri_con_fs ~ age + edu_num + male
t2_pri_con_fs ~ age + edu_num + male
t3_pri_con_fs ~ age + edu_num + male
t1_inf_sha_beh_fs ~ age + edu_num + male
t2_inf_sha_beh_fs ~ age + edu_num + male
t3_inf_sha_beh_fs ~ age + edu_num + male
t1_inf_sha_att_fs ~ age + edu_num + male
t2_inf_sha_att_fs ~ age + edu_num + male
t3_inf_sha_att_fs ~ age + edu_num + male
'
fit_free <- sem(model_free, data = d_wide, orthogonal = TRUE, missing = "ML")
summary(fit_free, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 185 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         78
##   Number of equality constraints                     3
##                                                       
##   Number of observations                          1403
##   Number of missing patterns                         1
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                10.935
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.090
## 
## Model Test Baseline Model:
## 
##   Test statistic                              7133.872
##   Degrees of freedom                                63
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.999
##   Tucker-Lewis Index (TLI)                       0.993
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -10239.880
##   Loglikelihood unrestricted model (H1)     -10234.413
##                                                       
##   Akaike (AIC)                               20629.760
##   Bayesian (BIC)                             21023.238
##   Sample-size adjusted Bayesian (BIC)        20784.990
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.024
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.047
##   P-value RMSEA <= 0.05                          0.973
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.007
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_fs        1.000                               1.000    1.000    0.734    0.860
##     t2_pri_con_fs        1.000                               1.000    1.000    0.734    0.838
##     t3_pri_con_fs        1.000                               1.000    1.000    0.734    0.846
##   inf_sha_beh_b =~                                                                           
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.469    0.719
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.469    0.734
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.469    0.756
##   inf_sha_att_b =~                                                                           
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.485    0.706
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.485    0.706
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.485    0.722
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_fs        1.000                               1.000    1.000    0.406    0.475
##   t2_pri_con_w =~                                                                            
##     t2_pri_con_fs        1.000                               1.000    1.000    0.453    0.517
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_fs        1.000                               1.000    1.000    0.429    0.495
##   t1_inf_sha_beh_w =~                                                                        
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.422    0.646
##   t2_inf_sha_beh_w =~                                                                        
##     t2_nf_sh_bh_fs       1.000                               1.000    1.000    0.394    0.617
##   t3_inf_sha_beh_w =~                                                                        
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.362    0.583
##   t1_inf_sha_att_w =~                                                                        
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.464    0.675
##   t2_inf_sha_att_w =~                                                                        
##     t2_nf_sh_tt_fs       1.000                               1.000    1.000    0.454    0.661
##   t3_inf_sha_att_w =~                                                                        
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.431    0.641
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t2_pri_con_w ~                                                                             
##     t1_pr_cn_ (a1)       0.148    0.066    2.253    0.024    0.019    0.277    0.133    0.133
##     t1_nf_s__           -0.050    0.048   -1.032    0.302   -0.144    0.045   -0.051   -0.051
##     t1_nf_s__           -0.043    0.051   -0.845    0.398   -0.144    0.057   -0.040   -0.040
##   t2_inf_sha_att_w ~                                                                         
##     t1_pr_cn_           -0.191    0.080   -2.403    0.016   -0.347   -0.035   -0.171   -0.171
##     t1_nf_s__ (b2)       0.105    0.050    2.084    0.037    0.006    0.203    0.107    0.107
##     t1_nf_s__           -0.035    0.050   -0.702    0.483   -0.133    0.063   -0.033   -0.033
##   t2_inf_sha_beh_w ~                                                                         
##     t1_pr_cn_           -0.016    0.074   -0.211    0.833   -0.160    0.129   -0.016   -0.016
##     t1_nf_s__           -0.055    0.041   -1.337    0.181   -0.135    0.026   -0.065   -0.065
##     t1_nf_s__ (c3)       0.026    0.043    0.596    0.551   -0.059    0.110    0.028    0.028
##   t3_pri_con_w ~                                                                             
##     t2_pr_cn_ (a1)       0.148    0.066    2.253    0.024    0.019    0.277    0.156    0.156
##     t2_nf_s__           -0.073    0.060   -1.219    0.223   -0.189    0.044   -0.077   -0.077
##     t2_nf_s__           -0.014    0.067   -0.216    0.829   -0.146    0.117   -0.013   -0.013
##   t3_inf_sha_att_w ~                                                                         
##     t2_pr_cn_           -0.014    0.049   -0.296    0.767   -0.110    0.081   -0.015   -0.015
##     t2_nf_s__ (b2)       0.105    0.050    2.084    0.037    0.006    0.203    0.111    0.111
##     t2_nf_s__            0.077    0.053    1.432    0.152   -0.028    0.181    0.070    0.070
##   t3_inf_sha_beh_w ~                                                                         
##     t2_pr_cn_            0.005    0.044    0.110    0.913   -0.082    0.092    0.006    0.006
##     t2_nf_s__            0.021    0.045    0.463    0.643   -0.067    0.109    0.026    0.026
##     t2_nf_s__ (c3)       0.026    0.043    0.596    0.551   -0.059    0.110    0.028    0.028
##   t1_pri_con_fs ~                                                                            
##     age                  0.010    0.001    6.850    0.000    0.007    0.013    0.010    0.184
##     edu_num             -0.023    0.013   -1.760    0.078   -0.049    0.003   -0.023   -0.047
##     male                -0.002    0.046   -0.043    0.966   -0.092    0.088   -0.002   -0.001
##   t2_pri_con_fs ~                                                                            
##     age                  0.010    0.002    6.509    0.000    0.007    0.013    0.010    0.175
##     edu_num             -0.023    0.013   -1.676    0.094   -0.049    0.004   -0.023   -0.045
##     male                 0.012    0.047    0.251    0.802   -0.081    0.105    0.012    0.007
##   t3_pri_con_fs ~                                                                            
##     age                  0.011    0.002    7.468    0.000    0.008    0.014    0.011    0.200
##     edu_num             -0.017    0.013   -1.310    0.190   -0.043    0.009   -0.017   -0.035
##     male                 0.010    0.047    0.220    0.826   -0.081    0.102    0.010    0.006
##   t1_inf_sha_beh_fs ~                                                                        
##     age                 -0.009    0.001   -7.926    0.000   -0.011   -0.007   -0.009   -0.209
##     edu_num              0.057    0.010    5.840    0.000    0.038    0.077    0.057    0.153
##     male                -0.132    0.035   -3.825    0.000   -0.200   -0.065   -0.132   -0.101
##   t2_inf_sha_beh_fs ~                                                                        
##     age                 -0.010    0.001   -9.064    0.000   -0.012   -0.008   -0.010   -0.238
##     edu_num              0.065    0.010    6.763    0.000    0.046    0.083    0.065    0.175
##     male                -0.083    0.034   -2.465    0.014   -0.149   -0.017   -0.083   -0.065
##   t3_inf_sha_beh_fs ~                                                                        
##     age                 -0.009    0.001   -8.808    0.000   -0.011   -0.007   -0.009   -0.230
##     edu_num              0.070    0.009    7.617    0.000    0.052    0.088    0.070    0.197
##     male                -0.121    0.032   -3.738    0.000   -0.185   -0.058   -0.121   -0.098
##   t1_inf_sha_att_fs ~                                                                        
##     age                 -0.004    0.001   -3.612    0.000   -0.007   -0.002   -0.004   -0.096
##     edu_num              0.031    0.010    2.999    0.003    0.011    0.052    0.031    0.079
##     male                -0.262    0.037   -7.107    0.000   -0.334   -0.190   -0.262   -0.190
##   t2_inf_sha_att_fs ~                                                                        
##     age                 -0.006    0.001   -5.361    0.000   -0.009   -0.004   -0.006   -0.142
##     edu_num              0.050    0.010    4.824    0.000    0.030    0.070    0.050    0.126
##     male                -0.263    0.036   -7.217    0.000   -0.335   -0.192   -0.263   -0.191
##   t3_inf_sha_att_fs ~                                                                        
##     age                 -0.007    0.001   -6.171    0.000   -0.009   -0.005   -0.007   -0.163
##     edu_num              0.051    0.010    5.085    0.000    0.032    0.071    0.051    0.133
##     male                -0.248    0.036   -6.963    0.000   -0.318   -0.178   -0.248   -0.184
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     in___ (cr_b_1)      -0.100    0.014   -7.257    0.000   -0.128   -0.073   -0.282   -0.282
##     in___ (cr_b_2)      -0.028    0.012   -2.322    0.020   -0.052   -0.004   -0.081   -0.081
##   inf_sha_beh_b ~~                                                                           
##     in___ (cr_b_3)       0.150    0.010   14.757    0.000    0.130    0.170    0.661    0.661
##   t1_pri_con_w ~~                                                                            
##     t1___ (cr_w_1)      -0.020    0.009   -2.106    0.035   -0.038   -0.001   -0.106   -0.106
##     t1___ (cr_w_2)      -0.020    0.009   -2.205    0.027   -0.038   -0.002   -0.117   -0.117
##   t1_inf_sha_beh_w ~~                                                                        
##     t1___ (cr_w_3)       0.023    0.008    2.769    0.006    0.007    0.038    0.115    0.115
##  .t2_pri_con_w ~~                                                                            
##    .t2___               -0.028    0.014   -2.073    0.038   -0.055   -0.002   -0.142   -0.142
##    .t2___                0.001    0.012    0.085    0.932   -0.022    0.024    0.006    0.006
##  .t2_inf_sha_beh_w ~~                                                                        
##    .t2___                0.019    0.011    1.797    0.072   -0.002    0.041    0.111    0.111
##  .t3_pri_con_w ~~                                                                            
##    .t3___                0.003    0.008    0.378    0.706   -0.013    0.018    0.017    0.017
##    .t3___                0.009    0.007    1.169    0.242   -0.006    0.023    0.057    0.057
##  .t3_inf_sha_beh_w ~~                                                                        
##    .t3___                0.036    0.007    5.168    0.000    0.022    0.050    0.235    0.235
##   pri_con_b ~~                                                                               
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     3.270    0.136   24.049    0.000    3.004    3.537    3.270    3.830
##    .t2_pri_con_fs     3.189    0.140   22.796    0.000    2.914    3.463    3.189    3.638
##    .t3_pri_con_fs     3.064    0.138   22.221    0.000    2.793    3.334    3.064    3.530
##    .t1_nf_sh_bh_fs    2.583    0.102   25.272    0.000    2.382    2.783    2.583    3.958
##    .t2_nf_sh_bh_fs    2.539    0.099   25.575    0.000    2.345    2.734    2.539    3.977
##    .t3_nf_sh_bh_fs    2.497    0.096   26.019    0.000    2.309    2.685    2.497    4.028
##    .t1_nf_sh_tt_fs    2.883    0.109   26.494    0.000    2.669    3.096    2.883    4.192
##    .t2_nf_sh_tt_fs    2.964    0.108   27.531    0.000    2.753    3.175    2.964    4.316
##    .t3_nf_sh_tt_fs    2.996    0.105   28.506    0.000    2.790    3.202    2.996    4.460
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t2_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t2_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t2_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.539    0.025   21.832    0.000    0.491    0.588    1.000    1.000
##     inf_sha_beh_b     0.220    0.011   19.154    0.000    0.197    0.242    1.000    1.000
##     inf_sha_att_b     0.235    0.015   15.941    0.000    0.206    0.264    1.000    1.000
##     t1_pri_con_w      0.164    0.011   15.252    0.000    0.143    0.186    1.000    1.000
##    .t2_pri_con_w      0.200    0.020    9.980    0.000    0.161    0.240    0.975    0.975
##    .t3_pri_con_w      0.178    0.011   16.735    0.000    0.157    0.199    0.965    0.965
##     t1_inf_sh_bh_w    0.178    0.010   18.456    0.000    0.159    0.197    1.000    1.000
##    .t2_inf_sh_bh_w    0.155    0.013   12.059    0.000    0.130    0.180    0.995    0.995
##    .t3_inf_sh_bh_w    0.131    0.008   17.383    0.000    0.116    0.145    0.998    0.998
##     t1_inf_sh_tt_w    0.215    0.012   17.811    0.000    0.192    0.239    1.000    1.000
##    .t2_inf_sh_tt_w    0.197    0.017   11.660    0.000    0.164    0.230    0.957    0.957
##    .t3_inf_sh_tt_w    0.182    0.010   18.035    0.000    0.162    0.201    0.980    0.980
effect_std_ci_free <- standardizedsolution(fit) %>% 
  filter(lhs == "pri_con_b", rhs == "inf_sha_beh_b")

# model comparison
(model_comp <- anova(fit_riclpm, fit_free))

Shows that model with freely estimated parameters does not show significantly improved fit.

2.1.2.6 Model 6

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_m + 1*t3_pri_con_m + 1*t4_pri_con_m + 1*t5_pri_con_m
inf_sha_beh_b =~ 1*t1_inf_sha_beh_m + 1*t3_inf_sha_beh_m + 1*t4_inf_sha_beh_m + 1*t5_inf_sha_beh_m
inf_sha_att_b =~ 1*t1_inf_sha_att_m + 1*t3_inf_sha_att_m + 1*t4_inf_sha_att_m + 1*t5_inf_sha_att_m

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_m
t3_pri_con_w =~ 1*t3_pri_con_m
t4_pri_con_w =~ 1*t4_pri_con_m
t5_pri_con_w =~ 1*t5_pri_con_m
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_m
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_m
t4_inf_sha_beh_w =~ 1*t4_inf_sha_beh_m
t5_inf_sha_beh_w =~ 1*t5_inf_sha_beh_m
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_m
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_m
t4_inf_sha_att_w =~ 1*t4_inf_sha_att_m
t5_inf_sha_att_w =~ 1*t5_inf_sha_att_m

# within person effects
t3_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t4_pri_con_w ~ a1*t3_pri_con_w + a2*t3_inf_sha_att_w + a3*t3_inf_sha_beh_w
t4_inf_sha_att_w ~ b1*t3_pri_con_w + b2*t3_inf_sha_att_w + b3*t3_inf_sha_beh_w
t4_inf_sha_beh_w ~ c1*t3_pri_con_w + c2*t3_inf_sha_att_w + c3*t3_inf_sha_beh_w
t5_pri_con_w ~ a1*t4_pri_con_w + a2*t4_inf_sha_att_w + a3*t4_inf_sha_beh_w
t5_inf_sha_att_w ~ b1*t4_pri_con_w + b2*t4_inf_sha_att_w + b3*t4_inf_sha_beh_w
t5_inf_sha_beh_w ~ c1*t4_pri_con_w + c2*t4_inf_sha_att_w + c3*t4_inf_sha_beh_w

# covariances
pri_con_b ~~ inf_sha_att_b + inf_sha_beh_b
inf_sha_att_b ~~ inf_sha_beh_b
t1_pri_con_w ~~ t1_inf_sha_att_w + t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ t1_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w
t4_pri_con_w ~~ a*t4_inf_sha_att_w + b*t4_inf_sha_beh_w
t4_inf_sha_att_w ~~ c*t4_inf_sha_beh_w
t5_pri_con_w ~~ a*t5_inf_sha_att_w + b*t5_inf_sha_beh_w
t5_inf_sha_att_w ~~ c*t5_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_m ~~ 0*t1_pri_con_m
t3_pri_con_m ~~ 0*t3_pri_con_m
t4_pri_con_m ~~ 0*t4_pri_con_m
t5_pri_con_m ~~ 0*t5_pri_con_m
t1_inf_sha_att_m ~~ 0*t1_inf_sha_att_m
t3_inf_sha_att_m ~~ 0*t3_inf_sha_att_m
t4_inf_sha_att_m ~~ 0*t4_inf_sha_att_m
t5_inf_sha_att_m ~~ 0*t5_inf_sha_att_m
t1_inf_sha_beh_m ~~ 0*t1_inf_sha_beh_m
t3_inf_sha_beh_m ~~ 0*t3_inf_sha_beh_m
t4_inf_sha_beh_m ~~ 0*t4_inf_sha_beh_m
t5_inf_sha_beh_m ~~ 0*t5_inf_sha_beh_m

# control variables
t1_pri_con_m ~ age + edu_num + male
t3_pri_con_m ~ age + edu_num + male
t4_pri_con_m ~ age + edu_num + male
t5_pri_con_m ~ age + edu_num + male
t1_inf_sha_beh_m ~ age + edu_num + male
t3_inf_sha_beh_m ~ age + edu_num + male
t4_inf_sha_beh_m ~ age + edu_num + male
t5_inf_sha_beh_m ~ age + edu_num + male
t1_inf_sha_att_m ~ age + edu_num + male
t3_inf_sha_att_m ~ age + edu_num + male
t4_inf_sha_att_m ~ age + edu_num + male
t5_inf_sha_att_m ~ age + edu_num + male
'
fit <- sem(model, data = d_wide_all, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 194 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        105
##   Number of equality constraints                    24
##                                                       
##                                                   Used       Total
##   Number of observations                           803         893
##   Number of missing patterns                         4            
##                                                                   
## Model Test User Model:
##                                                       
##   Test statistic                               245.361
##   Degrees of freedom                                45
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              4878.239
##   Degrees of freedom                               102
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.958
##   Tucker-Lewis Index (TLI)                       0.905
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -8739.515
##   Loglikelihood unrestricted model (H1)      -8616.835
##                                                       
##   Akaike (AIC)                               17641.030
##   Bayesian (BIC)                             18020.786
##   Sample-size adjusted Bayesian (BIC)        17763.566
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074
##   90 Percent confidence interval - lower         0.065
##   90 Percent confidence interval - upper         0.084
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.079
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_m         1.000                               1.000    1.000    0.715    0.813
##     t3_pri_con_m         1.000                               1.000    1.000    0.715    0.822
##     t4_pri_con_m         1.000                               1.000    1.000    0.715    0.799
##     t5_pri_con_m         1.000                               1.000    1.000    0.715    0.801
##   inf_sha_beh_b =~                                                                           
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.413    0.654
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.413    0.718
##     t4_inf_sh_bh_m       1.000                               1.000    1.000    0.413    0.694
##     t5_inf_sh_bh_m       1.000                               1.000    1.000    0.413    0.278
##   inf_sha_att_b =~                                                                           
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.479    0.681
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.479    0.701
##     t4_inf_sh_tt_m       1.000                               1.000    1.000    0.479    0.730
##     t5_inf_sh_tt_m       1.000                               1.000    1.000    0.479    0.702
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_m         1.000                               1.000    1.000    0.481    0.547
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_m         1.000                               1.000    1.000    0.465    0.535
##   t4_pri_con_w =~                                                                            
##     t4_pri_con_m         1.000                               1.000    1.000    0.506    0.565
##   t5_pri_con_w =~                                                                            
##     t5_pri_con_m         1.000                               1.000    1.000    0.492    0.551
##   t1_inf_sha_beh_w =~                                                                        
##     t1_inf_sh_bh_m       1.000                               1.000    1.000    0.459    0.727
##   t3_inf_sha_beh_w =~                                                                        
##     t3_inf_sh_bh_m       1.000                               1.000    1.000    0.370    0.643
##   t4_inf_sha_beh_w =~                                                                        
##     t4_inf_sh_bh_m       1.000                               1.000    1.000    0.407    0.683
##   t5_inf_sha_beh_w =~                                                                        
##     t5_inf_sh_bh_m       1.000                               1.000    1.000    1.426    0.958
##   t1_inf_sha_att_w =~                                                                        
##     t1_inf_sh_tt_m       1.000                               1.000    1.000    0.496    0.705
##   t3_inf_sha_att_w =~                                                                        
##     t3_inf_sh_tt_m       1.000                               1.000    1.000    0.467    0.683
##   t4_inf_sha_att_w =~                                                                        
##     t4_inf_sh_tt_m       1.000                               1.000    1.000    0.425    0.648
##   t5_inf_sha_att_w =~                                                                        
##     t5_inf_sh_tt_m       1.000                               1.000    1.000    0.461    0.676
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t3_pri_con_w ~                                                                            
##     t1_pr_cn_ (a1)      0.166    0.037    4.437    0.000    0.092    0.239    0.171    0.171
##     t1_nf_s__ (a2)      0.016    0.030    0.541    0.588   -0.043    0.076    0.017    0.017
##     t1_nf_s__ (a3)     -0.025    0.036   -0.691    0.490   -0.096    0.046   -0.025   -0.025
##   t3_inf_sha_att_w ~                                                                        
##     t1_pr_cn_ (b1)      0.037    0.028    1.304    0.192   -0.018    0.092    0.038    0.038
##     t1_nf_s__ (b2)      0.071    0.035    2.055    0.040    0.003    0.139    0.076    0.076
##     t1_nf_s__ (b3)      0.055    0.034    1.617    0.106   -0.012    0.122    0.054    0.054
##   t3_inf_sha_beh_w ~                                                                        
##     t1_pr_cn_ (c1)     -0.002    0.032   -0.056    0.956   -0.065    0.062   -0.002   -0.002
##     t1_nf_s__ (c2)      0.003    0.031    0.113    0.910   -0.057    0.063    0.005    0.005
##     t1_nf_s__ (c3)      0.069    0.053    1.302    0.193   -0.035    0.172    0.085    0.085
##   t4_pri_con_w ~                                                                            
##     t3_pr_cn_ (a1)      0.166    0.037    4.437    0.000    0.092    0.239    0.152    0.152
##     t3_nf_s__ (a2)      0.016    0.030    0.541    0.588   -0.043    0.076    0.015    0.015
##     t3_nf_s__ (a3)     -0.025    0.036   -0.691    0.490   -0.096    0.046   -0.018   -0.018
##   t4_inf_sha_att_w ~                                                                        
##     t3_pr_cn_ (b1)      0.037    0.028    1.304    0.192   -0.018    0.092    0.040    0.040
##     t3_nf_s__ (b2)      0.071    0.035    2.055    0.040    0.003    0.139    0.078    0.078
##     t3_nf_s__ (b3)      0.055    0.034    1.617    0.106   -0.012    0.122    0.048    0.048
##   t4_inf_sha_beh_w ~                                                                        
##     t3_pr_cn_ (c1)     -0.002    0.032   -0.056    0.956   -0.065    0.062   -0.002   -0.002
##     t3_nf_s__ (c2)      0.003    0.031    0.113    0.910   -0.057    0.063    0.004    0.004
##     t3_nf_s__ (c3)      0.069    0.053    1.302    0.193   -0.035    0.172    0.062    0.062
##   t5_pri_con_w ~                                                                            
##     t4_pr_cn_ (a1)      0.166    0.037    4.437    0.000    0.092    0.239    0.170    0.170
##     t4_nf_s__ (a2)      0.016    0.030    0.541    0.588   -0.043    0.076    0.014    0.014
##     t4_nf_s__ (a3)     -0.025    0.036   -0.691    0.490   -0.096    0.046   -0.021   -0.021
##   t5_inf_sha_att_w ~                                                                        
##     t4_pr_cn_ (b1)      0.037    0.028    1.304    0.192   -0.018    0.092    0.040    0.040
##     t4_nf_s__ (b2)      0.071    0.035    2.055    0.040    0.003    0.139    0.066    0.066
##     t4_nf_s__ (b3)      0.055    0.034    1.617    0.106   -0.012    0.122    0.049    0.049
##   t5_inf_sha_beh_w ~                                                                        
##     t4_pr_cn_ (c1)     -0.002    0.032   -0.056    0.956   -0.065    0.062   -0.001   -0.001
##     t4_nf_s__ (c2)      0.003    0.031    0.113    0.910   -0.057    0.063    0.001    0.001
##     t4_nf_s__ (c3)      0.069    0.053    1.302    0.193   -0.035    0.172    0.020    0.020
##   t1_pri_con_m ~                                                                            
##     age                 0.012    0.002    5.396    0.000    0.007    0.016    0.012    0.193
##     edu_num            -0.030    0.018   -1.726    0.084   -0.065    0.004   -0.030   -0.060
##     male               -0.028    0.063   -0.444    0.657   -0.152    0.096   -0.028   -0.016
##   t3_pri_con_m ~                                                                            
##     age                 0.011    0.002    5.280    0.000    0.007    0.016    0.011    0.189
##     edu_num            -0.040    0.017   -2.285    0.022   -0.074   -0.006   -0.040   -0.080
##     male                0.002    0.063    0.026    0.979   -0.122    0.125    0.002    0.001
##   t4_pri_con_m ~                                                                            
##     age                 0.012    0.002    5.318    0.000    0.007    0.016    0.012    0.190
##     edu_num            -0.046    0.018   -2.561    0.010   -0.081   -0.011   -0.046   -0.090
##     male               -0.027    0.065   -0.414    0.679   -0.153    0.100   -0.027   -0.015
##   t5_pri_con_m ~                                                                            
##     age                 0.014    0.002    6.353    0.000    0.010    0.018    0.014    0.225
##     edu_num            -0.043    0.018   -2.431    0.015   -0.078   -0.008   -0.043   -0.084
##     male               -0.015    0.064   -0.232    0.816   -0.140    0.110   -0.015   -0.008
##   t1_inf_sha_beh_m ~                                                                        
##     age                -0.006    0.002   -4.021    0.000   -0.009   -0.003   -0.006   -0.143
##     edu_num             0.050    0.013    3.921    0.000    0.025    0.074    0.050    0.137
##     male               -0.130    0.045   -2.859    0.004   -0.219   -0.041   -0.130   -0.102
##   t3_inf_sha_beh_m ~                                                                        
##     age                -0.007    0.001   -4.814    0.000   -0.009   -0.004   -0.007   -0.169
##     edu_num             0.066    0.011    5.801    0.000    0.044    0.088    0.066    0.200
##     male               -0.121    0.041   -2.963    0.003   -0.201   -0.041   -0.121   -0.105
##   t4_inf_sha_beh_m ~                                                                        
##     age                -0.008    0.001   -5.165    0.000   -0.010   -0.005   -0.008   -0.183
##     edu_num             0.055    0.012    4.595    0.000    0.031    0.078    0.055    0.160
##     male               -0.046    0.043   -1.087    0.277   -0.130    0.037   -0.046   -0.039
##   t5_inf_sha_beh_m ~                                                                        
##     age                 0.004    0.004    0.968    0.333   -0.004    0.011    0.004    0.035
##     edu_num            -0.050    0.030   -1.659    0.097   -0.110    0.009   -0.050   -0.059
##     male                0.069    0.109    0.628    0.530   -0.145    0.283    0.069    0.023
##   t1_inf_sha_att_m ~                                                                        
##     age                -0.003    0.002   -1.787    0.074   -0.007    0.000   -0.003   -0.064
##     edu_num             0.026    0.014    1.818    0.069   -0.002    0.053    0.026    0.064
##     male               -0.261    0.051   -5.147    0.000   -0.360   -0.162   -0.261   -0.185
##   t3_inf_sha_att_m ~                                                                        
##     age                -0.005    0.002   -2.934    0.003   -0.008   -0.002   -0.005   -0.105
##     edu_num             0.045    0.014    3.288    0.001    0.018    0.072    0.045    0.115
##     male               -0.208    0.049   -4.239    0.000   -0.305   -0.112   -0.208   -0.152
##   t4_inf_sha_att_m ~                                                                        
##     age                -0.006    0.002   -3.454    0.001   -0.009   -0.002   -0.006   -0.123
##     edu_num             0.044    0.013    3.364    0.001    0.018    0.070    0.044    0.117
##     male               -0.209    0.047   -4.435    0.000   -0.301   -0.117   -0.209   -0.158
##   t5_inf_sha_att_m ~                                                                        
##     age                -0.006    0.002   -3.860    0.000   -0.010   -0.003   -0.006   -0.137
##     edu_num             0.051    0.014    3.769    0.000    0.025    0.078    0.051    0.131
##     male               -0.200    0.049   -4.088    0.000   -0.296   -0.104   -0.200   -0.146
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     inf_sh_tt_          -0.110    0.016   -7.108    0.000   -0.141   -0.080   -0.323   -0.323
##     inf_sh_bh_          -0.042    0.014   -3.038    0.002   -0.069   -0.015   -0.142   -0.142
##   inf_sha_beh_b ~~                                                                           
##     inf_sh_tt_           0.124    0.011   11.197    0.000    0.103    0.146    0.629    0.629
##   t1_pri_con_w ~~                                                                            
##     t1_nf_sh__          -0.014    0.011   -1.217    0.224   -0.036    0.008   -0.057   -0.057
##     t1_nf_sh__          -0.020    0.011   -1.859    0.063   -0.042    0.001   -0.092   -0.092
##   t1_inf_sha_beh_w ~~                                                                        
##     t1_nf_sh__           0.046    0.011    4.227    0.000    0.025    0.067    0.201    0.201
##  .t3_pri_con_w ~~                                                                            
##    .t3_nf_sh__ (a)      -0.010    0.006   -1.620    0.105   -0.023    0.002   -0.048   -0.048
##    .t3_nf_sh__ (b)       0.001    0.007    0.164    0.870   -0.012    0.015    0.007    0.007
##  .t3_inf_sha_beh_w ~~                                                                        
##    .t3_nf_sh__ (c)       0.039    0.006    6.001    0.000    0.026    0.051    0.226    0.226
##  .t4_pri_con_w ~~                                                                            
##    .t4_nf_sh__ (a)      -0.010    0.006   -1.620    0.105   -0.023    0.002   -0.048   -0.048
##    .t4_nf_sh__ (b)       0.001    0.007    0.164    0.870   -0.012    0.015    0.006    0.006
##  .t4_inf_sha_beh_w ~~                                                                        
##    .t4_nf_sh__ (c)       0.039    0.006    6.001    0.000    0.026    0.051    0.225    0.225
##  .t5_pri_con_w ~~                                                                            
##    .t5_nf_sh__ (a)      -0.010    0.006   -1.620    0.105   -0.023    0.002   -0.046   -0.046
##    .t5_nf_sh__ (b)       0.001    0.007    0.164    0.870   -0.012    0.015    0.002    0.002
##  .t5_inf_sha_beh_w ~~                                                                        
##    .t5_nf_sh__ (c)       0.039    0.006    6.001    0.000    0.026    0.051    0.059    0.059
##   pri_con_b ~~                                                                               
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1_pr_cn_w           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
##     t1_nf_sh__           0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      3.192    0.196   16.312    0.000    2.808    3.575    3.192    3.629
##    .t3_pri_con_m      3.140    0.194   16.163    0.000    2.759    3.520    3.140    3.607
##    .t4_pri_con_m      3.131    0.199   15.723    0.000    2.741    3.521    3.131    3.500
##    .t5_pri_con_m      2.935    0.197   14.896    0.000    2.549    3.321    2.935    3.288
##    .t1_inf_sh_bh_m    2.426    0.140   17.296    0.000    2.151    2.701    2.426    3.841
##    .t3_inf_sh_bh_m    2.341    0.126   18.590    0.000    2.095    2.588    2.341    4.069
##    .t4_inf_sh_bh_m    2.382    0.132   18.095    0.000    2.124    2.640    2.382    3.997
##    .t5_inf_sh_bh_m    2.708    0.337    8.030    0.000    2.047    3.368    2.708    1.819
##    .t1_inf_sh_tt_m    2.809    0.156   17.956    0.000    2.503    3.116    2.809    3.996
##    .t3_inf_sh_tt_m    2.823    0.152   18.598    0.000    2.525    3.120    2.823    4.132
##    .t4_inf_sh_tt_m    2.769    0.145   19.044    0.000    2.484    3.054    2.769    4.220
##    .t5_inf_sh_tt_m    2.814    0.151   18.647    0.000    2.518    3.109    2.814    4.127
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t4_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t5_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t4_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t5_pri_con_m      0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_tt_m    0.000                               0.000    0.000    0.000    0.000
##    .t1_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_bh_m    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.511    0.030   17.062    0.000    0.453    0.570    1.000    1.000
##     inf_sha_beh_b     0.171    0.014   11.782    0.000    0.142    0.199    1.000    1.000
##     inf_sha_att_b     0.229    0.015   15.046    0.000    0.199    0.259    1.000    1.000
##     t1_pri_con_w      0.231    0.016   14.085    0.000    0.199    0.263    1.000    1.000
##    .t3_pri_con_w      0.210    0.015   13.819    0.000    0.180    0.240    0.970    0.970
##    .t4_pri_con_w      0.250    0.017   14.513    0.000    0.216    0.283    0.977    0.977
##    .t5_pri_con_w      0.235    0.015   15.944    0.000    0.206    0.264    0.971    0.971
##     t1_inf_sh_bh_w    0.211    0.015   13.672    0.000    0.181    0.241    1.000    1.000
##    .t3_inf_sh_bh_w    0.136    0.013   10.650    0.000    0.111    0.161    0.993    0.993
##    .t4_inf_sh_bh_w    0.165    0.011   14.906    0.000    0.143    0.186    0.996    0.996
##    .t5_inf_sh_bh_w    2.034    0.103   19.672    0.000    1.831    2.237    1.000    1.000
##     t1_inf_sh_tt_w    0.246    0.015   15.973    0.000    0.216    0.276    1.000    1.000
##    .t3_inf_sh_tt_w    0.215    0.014   15.837    0.000    0.189    0.242    0.989    0.989
##    .t4_inf_sh_tt_w    0.179    0.013   14.099    0.000    0.154    0.204    0.989    0.989
##    .t5_inf_sh_tt_w    0.210    0.013   16.322    0.000    0.185    0.236    0.990    0.990

2.1.2.7 Model 7 (longer intervals)

This is like the final model reported in the paper, but with other, that is longer, intervals. Now, waves are separated by 1 year and span until 2018.

We first need to redo the factor scores, because we now have a different sample.

Specifically, we first estimate a model containing all measures, which is then used to extract factor scores.

name <- "all_vars"
model <- '
# Privacy Concerns
# create factors
t1_pri_con_f =~ 1*t1_pri_con_f1 + a2*t1_pri_con_f2
t3_pri_con_f =~ 1*t3_pri_con_f1 + a2*t3_pri_con_f2
t4_pri_con_f =~ 1*t4_pri_con_f1 + a2*t4_pri_con_f2
t5_pri_con_f =~ 1*t5_pri_con_f1 + a2*t5_pri_con_f2
t1_pri_con_f1 =~ 1*t1_pri_con_04 + b2*t1_pri_con_05 + b3*t1_pri_con_06
t1_pri_con_f2 =~ 1*t1_pri_con_07 + c2*t1_pri_con_08 + c3*t1_pri_con_09
t3_pri_con_f1 =~ 1*t3_pri_con_04 + b2*t3_pri_con_05 + b3*t3_pri_con_06
t3_pri_con_f2 =~ 1*t3_pri_con_07 + c2*t3_pri_con_08 + c3*t3_pri_con_09
t4_pri_con_f1 =~ 1*t4_pri_con_04 + b2*t4_pri_con_05 + b3*t4_pri_con_06
t4_pri_con_f2 =~ 1*t4_pri_con_07 + c2*t4_pri_con_08 + c3*t4_pri_con_09
t5_pri_con_f1 =~ 1*t5_pri_con_04 + b2*t5_pri_con_05 + b3*t5_pri_con_06
t5_pri_con_f2 =~ 1*t5_pri_con_07 + c2*t5_pri_con_08 + c3*t5_pri_con_09

# error covariances
t5_pri_con_04 ~~ t4_pri_con_04 + t3_pri_con_04 + t1_pri_con_04
t5_pri_con_05 ~~ t4_pri_con_05 + t3_pri_con_05 + t1_pri_con_05
t5_pri_con_06 ~~ t4_pri_con_06 + t3_pri_con_06 + t1_pri_con_06
t5_pri_con_07 ~~ t4_pri_con_07 + t3_pri_con_07 + t1_pri_con_07
t5_pri_con_08 ~~ t4_pri_con_08 + t3_pri_con_08 + t1_pri_con_08
t5_pri_con_09 ~~ t4_pri_con_09 + t3_pri_con_09 + t1_pri_con_09
t4_pri_con_04 ~~ t3_pri_con_04 + t1_pri_con_04
t4_pri_con_05 ~~ t3_pri_con_05 + t1_pri_con_05
t4_pri_con_06 ~~ t3_pri_con_06 + t1_pri_con_06
t4_pri_con_07 ~~ t3_pri_con_07 + t1_pri_con_07
t4_pri_con_08 ~~ t3_pri_con_08 + t1_pri_con_08
t4_pri_con_09 ~~ t3_pri_con_09 + t1_pri_con_09
t3_pri_con_04 ~~ t1_pri_con_04
t3_pri_con_05 ~~ t1_pri_con_05 
t3_pri_con_06 ~~ t1_pri_con_06
t3_pri_con_07 ~~ t1_pri_con_07
t3_pri_con_08 ~~ t1_pri_con_08
t3_pri_con_09 ~~ t1_pri_con_09

# factor covariances
t5_pri_con_f ~~ t1_pri_con_f + t3_pri_con_f + t4_pri_con_f
t1_pri_con_f ~~ t3_pri_con_f + t4_pri_con_f
t3_pri_con_f ~~ t4_pri_con_f

# Information Sharing Attitude
# create factors
t1_inf_sha_att_f =~ 1*t1_inf_sha_att_f1 + d2*t1_inf_sha_att_f2 + d3*t1_inf_sha_att_f3 + d4*t1_inf_sha_att_f4 + d5*t1_inf_sha_att_f5
t3_inf_sha_att_f =~ 1*t3_inf_sha_att_f1 + d2*t3_inf_sha_att_f2 + d3*t3_inf_sha_att_f3 + d4*t3_inf_sha_att_f4 + d5*t3_inf_sha_att_f5
t4_inf_sha_att_f =~ 1*t4_inf_sha_att_f1 + d2*t4_inf_sha_att_f2 + d3*t4_inf_sha_att_f3 + d4*t4_inf_sha_att_f4 + d5*t4_inf_sha_att_f5
t5_inf_sha_att_f =~ 1*t5_inf_sha_att_f1 + d2*t5_inf_sha_att_f2 + d3*t5_inf_sha_att_f3 + d4*t5_inf_sha_att_f4 + d5*t5_inf_sha_att_f5

t1_inf_sha_att_f1 =~ 1*t1_inf_sha_att_01 + e*t1_inf_sha_att_02
t1_inf_sha_att_f2 =~ 1*t1_inf_sha_att_03 + f*t1_inf_sha_att_04
t1_inf_sha_att_f3 =~ 1*t1_inf_sha_att_05 + g*t1_inf_sha_att_06
t1_inf_sha_att_f4 =~ 1*t1_inf_sha_att_07 + h*t1_inf_sha_att_08
t1_inf_sha_att_f5 =~ 1*t1_inf_sha_att_10 + i*t1_inf_sha_att_11
t3_inf_sha_att_f1 =~ 1*t3_inf_sha_att_01 + e*t3_inf_sha_att_02
t3_inf_sha_att_f2 =~ 1*t3_inf_sha_att_03 + f*t3_inf_sha_att_04
t3_inf_sha_att_f3 =~ 1*t3_inf_sha_att_05 + g*t3_inf_sha_att_06
t3_inf_sha_att_f4 =~ 1*t3_inf_sha_att_07 + h*t3_inf_sha_att_08
t3_inf_sha_att_f5 =~ 1*t3_inf_sha_att_10 + i*t3_inf_sha_att_11
t4_inf_sha_att_f1 =~ 1*t4_inf_sha_att_01 + e*t4_inf_sha_att_02
t4_inf_sha_att_f2 =~ 1*t4_inf_sha_att_03 + f*t4_inf_sha_att_04
t4_inf_sha_att_f3 =~ 1*t4_inf_sha_att_05 + g*t4_inf_sha_att_06
t4_inf_sha_att_f4 =~ 1*t4_inf_sha_att_07 + h*t4_inf_sha_att_08
t4_inf_sha_att_f5 =~ 1*t4_inf_sha_att_10 + i*t4_inf_sha_att_11
t5_inf_sha_att_f1 =~ 1*t5_inf_sha_att_01 + e*t5_inf_sha_att_02
t5_inf_sha_att_f2 =~ 1*t5_inf_sha_att_03 + f*t5_inf_sha_att_04
t5_inf_sha_att_f3 =~ 1*t5_inf_sha_att_05 + g*t5_inf_sha_att_06
t5_inf_sha_att_f4 =~ 1*t5_inf_sha_att_07 + h*t5_inf_sha_att_08
t5_inf_sha_att_f5 =~ 1*t5_inf_sha_att_10 + i*t5_inf_sha_att_11

# factor covariance
t5_inf_sha_att_f ~~ t1_inf_sha_att_f + t3_inf_sha_att_f + t4_inf_sha_att_f
t1_inf_sha_att_f ~~ t3_inf_sha_att_f + t4_inf_sha_att_f
t3_inf_sha_att_f ~~ t4_inf_sha_att_f

# item error covariance
t5_inf_sha_att_01 ~~ t1_inf_sha_att_01 + t3_inf_sha_att_01 + t4_inf_sha_att_01
t1_inf_sha_att_01 ~~ t3_inf_sha_att_01 + t4_inf_sha_att_01
t3_inf_sha_att_01 ~~ t4_inf_sha_att_01
t5_inf_sha_att_02 ~~ t1_inf_sha_att_02 + t3_inf_sha_att_02 + t4_inf_sha_att_02
t1_inf_sha_att_02 ~~ t3_inf_sha_att_02 + t4_inf_sha_att_02
t3_inf_sha_att_02 ~~ t4_inf_sha_att_02
t5_inf_sha_att_03 ~~ t1_inf_sha_att_03 + t3_inf_sha_att_03 + t4_inf_sha_att_03
t1_inf_sha_att_03 ~~ t3_inf_sha_att_03 + t4_inf_sha_att_03
t3_inf_sha_att_03 ~~ t4_inf_sha_att_03
t5_inf_sha_att_04 ~~ t1_inf_sha_att_04 + t3_inf_sha_att_04 + t4_inf_sha_att_04
t1_inf_sha_att_04 ~~ t3_inf_sha_att_04 + t4_inf_sha_att_04
t3_inf_sha_att_04 ~~ t4_inf_sha_att_04
t5_inf_sha_att_05 ~~ t1_inf_sha_att_05 + t3_inf_sha_att_05 + t4_inf_sha_att_05
t1_inf_sha_att_05 ~~ t3_inf_sha_att_05 + t4_inf_sha_att_05
t3_inf_sha_att_05 ~~ t4_inf_sha_att_05
t5_inf_sha_att_06 ~~ t1_inf_sha_att_06 + t3_inf_sha_att_06 + t4_inf_sha_att_06
t1_inf_sha_att_06 ~~ t3_inf_sha_att_06 + t4_inf_sha_att_06
t3_inf_sha_att_06 ~~ t4_inf_sha_att_06
t5_inf_sha_att_07 ~~ t1_inf_sha_att_07 + t3_inf_sha_att_07 + t4_inf_sha_att_07
t1_inf_sha_att_07 ~~ t3_inf_sha_att_07 + t4_inf_sha_att_07
t3_inf_sha_att_07 ~~ t4_inf_sha_att_07
t5_inf_sha_att_08 ~~ t1_inf_sha_att_08 + t3_inf_sha_att_08 + t4_inf_sha_att_08
t1_inf_sha_att_08 ~~ t3_inf_sha_att_08 + t4_inf_sha_att_08
t3_inf_sha_att_08 ~~ t4_inf_sha_att_08
t5_inf_sha_att_10 ~~ t1_inf_sha_att_10 + t3_inf_sha_att_10 + t4_inf_sha_att_10
t1_inf_sha_att_10 ~~ t3_inf_sha_att_10 + t4_inf_sha_att_10
t3_inf_sha_att_10 ~~ t4_inf_sha_att_10
t5_inf_sha_att_11 ~~ t1_inf_sha_att_11 + t3_inf_sha_att_11 + t4_inf_sha_att_11
t1_inf_sha_att_11 ~~ t3_inf_sha_att_11 + t4_inf_sha_att_11
t3_inf_sha_att_11 ~~ t4_inf_sha_att_11

# information sharing behavior
# create factors
t1_inf_sha_beh_f =~ 1*t1_inf_sha_beh_f1 + o2*t1_inf_sha_beh_f2 + o3*t1_inf_sha_beh_f3 + o4*t1_inf_sha_beh_f4 + o5*t1_inf_sha_beh_f5
t3_inf_sha_beh_f =~ 1*t3_inf_sha_beh_f1 + o2*t3_inf_sha_beh_f2 + o3*t3_inf_sha_beh_f3 + o4*t3_inf_sha_beh_f4 + o5*t3_inf_sha_beh_f5
t4_inf_sha_beh_f =~ 1*t4_inf_sha_beh_f1 + o2*t4_inf_sha_beh_f2 + o3*t4_inf_sha_beh_f3 + o4*t4_inf_sha_beh_f4 + o5*t4_inf_sha_beh_f5
t5_inf_sha_beh_f =~ 1*t5_inf_sha_beh_f1 + o2*t5_inf_sha_beh_f2 + o3*t5_inf_sha_beh_f3 + o4*t5_inf_sha_beh_f4 + o5*t5_inf_sha_beh_f5
t1_inf_sha_beh_f1 =~ 1*t1_inf_sha_beh_01 + j2*t1_inf_sha_beh_02
t1_inf_sha_beh_f2 =~ 1*t1_inf_sha_beh_03 + k2*t1_inf_sha_beh_04
t1_inf_sha_beh_f3 =~ 1*t1_inf_sha_beh_05 + l2*t1_inf_sha_beh_06
t1_inf_sha_beh_f4 =~ 1*t1_inf_sha_beh_07 + m2*t1_inf_sha_beh_08
t1_inf_sha_beh_f5 =~ 1*t1_inf_sha_beh_10 + n2*t1_inf_sha_beh_11
t3_inf_sha_beh_f1 =~ 1*t3_inf_sha_beh_01 + j2*t3_inf_sha_beh_02
t3_inf_sha_beh_f2 =~ 1*t3_inf_sha_beh_03 + k2*t3_inf_sha_beh_04
t3_inf_sha_beh_f3 =~ 1*t3_inf_sha_beh_05 + l2*t3_inf_sha_beh_06
t3_inf_sha_beh_f4 =~ 1*t3_inf_sha_beh_07 + m2*t3_inf_sha_beh_08
t3_inf_sha_beh_f5 =~ 1*t3_inf_sha_beh_10 + n2*t3_inf_sha_beh_11
t4_inf_sha_beh_f1 =~ 1*t4_inf_sha_beh_01 + j2*t4_inf_sha_beh_02
t4_inf_sha_beh_f2 =~ 1*t4_inf_sha_beh_03 + k2*t4_inf_sha_beh_04
t4_inf_sha_beh_f3 =~ 1*t4_inf_sha_beh_05 + l2*t4_inf_sha_beh_06
t4_inf_sha_beh_f4 =~ 1*t4_inf_sha_beh_07 + m2*t4_inf_sha_beh_08
t4_inf_sha_beh_f5 =~ 1*t4_inf_sha_beh_10 + n2*t4_inf_sha_beh_11
t5_inf_sha_beh_f1 =~ 1*t5_inf_sha_beh_01 + j2*t5_inf_sha_beh_02
t5_inf_sha_beh_f2 =~ 1*t5_inf_sha_beh_03 + k2*t5_inf_sha_beh_04
t5_inf_sha_beh_f3 =~ 1*t5_inf_sha_beh_05 + l2*t5_inf_sha_beh_06
t5_inf_sha_beh_f4 =~ 1*t5_inf_sha_beh_07 + m2*t5_inf_sha_beh_08
t5_inf_sha_beh_f5 =~ 1*t5_inf_sha_beh_10 + n2*t5_inf_sha_beh_11

# factor covariance
t5_inf_sha_beh_f ~~ t1_inf_sha_beh_f + t3_inf_sha_beh_f + t4_inf_sha_beh_f
t1_inf_sha_beh_f ~~ t3_inf_sha_beh_f + t4_inf_sha_beh_f
t3_inf_sha_beh_f ~~ t4_inf_sha_beh_f

# item error covariance
t5_inf_sha_beh_01 ~~ t1_inf_sha_beh_01 + t3_inf_sha_beh_01 + t4_inf_sha_beh_01
t1_inf_sha_beh_01 ~~ t3_inf_sha_beh_01 + t4_inf_sha_beh_01
t3_inf_sha_beh_01 ~~ t4_inf_sha_beh_01
t5_inf_sha_beh_02 ~~ t1_inf_sha_beh_02 + t3_inf_sha_beh_02 + t4_inf_sha_beh_02
t1_inf_sha_beh_02 ~~ t3_inf_sha_beh_02 + t4_inf_sha_beh_02
t3_inf_sha_beh_02 ~~ t4_inf_sha_beh_02
t5_inf_sha_beh_03 ~~ t1_inf_sha_beh_03 + t3_inf_sha_beh_03 + t4_inf_sha_beh_03
t1_inf_sha_beh_03 ~~ t3_inf_sha_beh_03 + t4_inf_sha_beh_03
t3_inf_sha_beh_03 ~~ t4_inf_sha_beh_03
t5_inf_sha_beh_04 ~~ t1_inf_sha_beh_04 + t3_inf_sha_beh_04 + t4_inf_sha_beh_04
t1_inf_sha_beh_04 ~~ t3_inf_sha_beh_04 + t4_inf_sha_beh_04
t3_inf_sha_beh_04 ~~ t4_inf_sha_beh_04
t5_inf_sha_beh_05 ~~ t1_inf_sha_beh_05 + t3_inf_sha_beh_05 + t4_inf_sha_beh_05
t1_inf_sha_beh_05 ~~ t3_inf_sha_beh_05 + t4_inf_sha_beh_05
t3_inf_sha_beh_05 ~~ t4_inf_sha_beh_05
t5_inf_sha_beh_06 ~~ t1_inf_sha_beh_06 + t3_inf_sha_beh_06 + t4_inf_sha_beh_06
t1_inf_sha_beh_06 ~~ t3_inf_sha_beh_06 + t4_inf_sha_beh_06
t3_inf_sha_beh_06 ~~ t4_inf_sha_beh_06
t5_inf_sha_beh_07 ~~ t1_inf_sha_beh_07 + t3_inf_sha_beh_07 + t4_inf_sha_beh_07
t1_inf_sha_beh_07 ~~ t3_inf_sha_beh_07 + t4_inf_sha_beh_07
t3_inf_sha_beh_07 ~~ t4_inf_sha_beh_07
t5_inf_sha_beh_08 ~~ t1_inf_sha_beh_08 + t3_inf_sha_beh_08 + t4_inf_sha_beh_08
t1_inf_sha_beh_08 ~~ t3_inf_sha_beh_08 + t4_inf_sha_beh_08
t3_inf_sha_beh_08 ~~ t4_inf_sha_beh_08
t5_inf_sha_beh_10 ~~ t1_inf_sha_beh_10 + t3_inf_sha_beh_10 + t4_inf_sha_beh_10
t1_inf_sha_beh_10 ~~ t3_inf_sha_beh_10 + t4_inf_sha_beh_10
t3_inf_sha_beh_10 ~~ t4_inf_sha_beh_10
t5_inf_sha_beh_11 ~~ t1_inf_sha_beh_11 + t3_inf_sha_beh_11 + t4_inf_sha_beh_11
t1_inf_sha_beh_11 ~~ t3_inf_sha_beh_11 + t4_inf_sha_beh_11
t3_inf_sha_beh_11 ~~ t4_inf_sha_beh_11

## Correlations Attitude and Behavior-Items
t1_inf_sha_beh_01 ~~ t1_inf_sha_att_01
t1_inf_sha_beh_02 ~~ t1_inf_sha_att_02
t1_inf_sha_beh_03 ~~ t1_inf_sha_att_03
t1_inf_sha_beh_04 ~~ t1_inf_sha_att_04
t1_inf_sha_beh_05 ~~ t1_inf_sha_att_05
t1_inf_sha_beh_06 ~~ t1_inf_sha_att_06
t1_inf_sha_beh_07 ~~ t1_inf_sha_att_07
t1_inf_sha_beh_08 ~~ t1_inf_sha_att_08
t1_inf_sha_beh_10 ~~ t1_inf_sha_att_10
t1_inf_sha_beh_11 ~~ t1_inf_sha_att_11
t3_inf_sha_beh_01 ~~ t3_inf_sha_att_01
t3_inf_sha_beh_02 ~~ t3_inf_sha_att_02
t3_inf_sha_beh_03 ~~ t3_inf_sha_att_03
t3_inf_sha_beh_04 ~~ t3_inf_sha_att_04
t3_inf_sha_beh_05 ~~ t3_inf_sha_att_05
t3_inf_sha_beh_06 ~~ t3_inf_sha_att_06
t3_inf_sha_beh_07 ~~ t3_inf_sha_att_07
t3_inf_sha_beh_08 ~~ t3_inf_sha_att_08
t3_inf_sha_beh_10 ~~ t3_inf_sha_att_10
t3_inf_sha_beh_11 ~~ t3_inf_sha_att_11
t4_inf_sha_beh_01 ~~ t4_inf_sha_att_01
t4_inf_sha_beh_02 ~~ t4_inf_sha_att_02
t4_inf_sha_beh_03 ~~ t4_inf_sha_att_03
t4_inf_sha_beh_04 ~~ t4_inf_sha_att_04
t4_inf_sha_beh_05 ~~ t4_inf_sha_att_05
t4_inf_sha_beh_06 ~~ t4_inf_sha_att_06
t4_inf_sha_beh_07 ~~ t4_inf_sha_att_07
t4_inf_sha_beh_08 ~~ t4_inf_sha_att_08
t4_inf_sha_beh_10 ~~ t4_inf_sha_att_10
t4_inf_sha_beh_11 ~~ t4_inf_sha_att_11
t5_inf_sha_beh_01 ~~ t5_inf_sha_att_01
t5_inf_sha_beh_02 ~~ t5_inf_sha_att_02
t5_inf_sha_beh_03 ~~ t5_inf_sha_att_03
t5_inf_sha_beh_04 ~~ t5_inf_sha_att_04
t5_inf_sha_beh_05 ~~ t5_inf_sha_att_05
t5_inf_sha_beh_06 ~~ t5_inf_sha_att_06
t5_inf_sha_beh_07 ~~ t5_inf_sha_att_07
t5_inf_sha_beh_08 ~~ t5_inf_sha_att_08
t5_inf_sha_beh_10 ~~ t5_inf_sha_att_10
t5_inf_sha_beh_11 ~~ t5_inf_sha_att_11
'
assign(paste("fit", name, sep = "_"), cfa(model, d_wide_all, missing = "ML"))
summary(get(paste("fit", name, sep = "_")), standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 439 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        622
##   Number of equality constraints                    69
##                                                       
##   Number of observations                           893
##   Number of missing patterns                       110
##                                                       
## Model Test User Model:
##                                                        
##   Test statistic                              13924.019
##   Degrees of freedom                               5011
##   P-value (Chi-square)                            0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             90895.859
##   Degrees of freedom                              5356
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.896
##   Tucker-Lewis Index (TLI)                       0.889
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -98960.788
##   Loglikelihood unrestricted model (H1)     -91998.778
##                                                       
##   Akaike (AIC)                              199027.576
##   Bayesian (BIC)                            201678.982
##   Sample-size adjusted Bayesian (BIC)       199922.755
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.045
##   90 Percent confidence interval - lower         0.044
##   90 Percent confidence interval - upper         0.046
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.071
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   t1_pri_con_f =~                                                           
##     t1_pr_c_1             1.000                               0.932    0.932
##     t1_pr_c_2 (a2)        1.158    0.032   36.640    0.000    0.945    0.945
##   t3_pri_con_f =~                                                           
##     t3_pr_c_1             1.000                               0.988    0.988
##     t3_pr_c_2 (a2)        1.158    0.032   36.640    0.000    0.944    0.944
##   t4_pri_con_f =~                                                           
##     t4_pr_c_1             1.000                               0.963    0.963
##     t4_pr_c_2 (a2)        1.158    0.032   36.640    0.000    0.968    0.968
##   t5_pri_con_f =~                                                           
##     t5_pr_c_1             1.000                               0.949    0.949
##     t5_pr_c_2 (a2)        1.158    0.032   36.640    0.000    0.971    0.971
##   t1_pri_con_f1 =~                                                          
##     t1_pr__04             1.000                               0.878    0.830
##     t1_pr__05 (b2)        0.974    0.030   32.777    0.000    0.855    0.654
##     t1_pr__06 (b3)        1.009    0.025   40.371    0.000    0.886    0.755
##   t1_pri_con_f2 =~                                                          
##     t1_pr__07             1.000                               1.002    0.798
##     t1_pr__08 (c2)        0.970    0.021   46.262    0.000    0.973    0.833
##     t1_pr__09 (c3)        0.878    0.019   45.198    0.000    0.880    0.841
##   t3_pri_con_f1 =~                                                          
##     t3_pr__04             1.000                               0.846    0.801
##     t3_pr__05 (b2)        0.974    0.030   32.777    0.000    0.825    0.631
##     t3_pr__06 (b3)        1.009    0.025   40.371    0.000    0.854    0.756
##   t3_pri_con_f2 =~                                                          
##     t3_pr__07             1.000                               1.026    0.828
##     t3_pr__08 (c2)        0.970    0.021   46.262    0.000    0.995    0.857
##     t3_pr__09 (c3)        0.878    0.019   45.198    0.000    0.901    0.840
##   t4_pri_con_f1 =~                                                          
##     t4_pr__04             1.000                               0.870    0.818
##     t4_pr__05 (b2)        0.974    0.030   32.777    0.000    0.847    0.657
##     t4_pr__06 (b3)        1.009    0.025   40.371    0.000    0.878    0.776
##   t4_pri_con_f2 =~                                                          
##     t4_pr__07             1.000                               1.002    0.813
##     t4_pr__08 (c2)        0.970    0.021   46.262    0.000    0.972    0.850
##     t4_pr__09 (c3)        0.878    0.019   45.198    0.000    0.879    0.826
##   t5_pri_con_f1 =~                                                          
##     t5_pr__04             1.000                               0.905    0.849
##     t5_pr__05 (b2)        0.974    0.030   32.777    0.000    0.881    0.667
##     t5_pr__06 (b3)        1.009    0.025   40.371    0.000    0.913    0.794
##   t5_pri_con_f2 =~                                                          
##     t5_pr__07             1.000                               1.024    0.816
##     t5_pr__08 (c2)        0.970    0.021   46.262    0.000    0.994    0.856
##     t5_pr__09 (c3)        0.878    0.019   45.198    0.000    0.899    0.842
##   t1_inf_sha_att_f =~                                                       
##     t1_nf___1             1.000                               0.468    0.468
##     t1_nf___2 (d2)        2.544    0.165   15.405    0.000    0.960    0.960
##     t1_nf___3 (d3)        2.610    0.169   15.421    0.000    0.931    0.931
##     t1_nf___4 (d4)        2.116    0.141   14.977    0.000    0.893    0.893
##     t1_nf___5 (d5)        1.426    0.104   13.771    0.000    0.517    0.517
##   t3_inf_sha_att_f =~                                                       
##     t3_nf___1             1.000                               0.480    0.480
##     t3_nf___2 (d2)        2.544    0.165   15.405    0.000    0.919    0.919
##     t3_nf___3 (d3)        2.610    0.169   15.421    0.000    0.939    0.939
##     t3_nf___4 (d4)        2.116    0.141   14.977    0.000    0.924    0.924
##     t3_nf___5 (d5)        1.426    0.104   13.771    0.000    0.502    0.502
##   t4_inf_sha_att_f =~                                                       
##     t4_nf___1             1.000                               0.422    0.422
##     t4_nf___2 (d2)        2.544    0.165   15.405    0.000    0.976    0.976
##     t4_nf___3 (d3)        2.610    0.169   15.421    0.000    0.917    0.917
##     t4_nf___4 (d4)        2.116    0.141   14.977    0.000    0.912    0.912
##     t4_nf___5 (d5)        1.426    0.104   13.771    0.000    0.488    0.488
##   t5_inf_sha_att_f =~                                                       
##     t5_nf___1             1.000                               0.417    0.417
##     t5_nf___2 (d2)        2.544    0.165   15.405    0.000    1.022    1.022
##     t5_nf___3 (d3)        2.610    0.169   15.421    0.000    0.901    0.901
##     t5_nf___4 (d4)        2.116    0.141   14.977    0.000    0.945    0.945
##     t5_nf___5 (d5)        1.426    0.104   13.771    0.000    0.493    0.493
##   t1_inf_sha_att_f1 =~                                                      
##     t1_n___01             1.000                               0.761    0.677
##     t1_n___02  (e)        0.906    0.064   14.093    0.000    0.689    0.625
##   t1_inf_sha_att_f2 =~                                                      
##     t1_n___03             1.000                               0.944    0.912
##     t1_n___04  (f)        0.980    0.016   61.381    0.000    0.926    0.902
##   t1_inf_sha_att_f3 =~                                                      
##     t1_n___05             1.000                               0.999    0.949
##     t1_n___06  (g)        0.959    0.015   65.861    0.000    0.958    0.883
##   t1_inf_sha_att_f4 =~                                                      
##     t1_n___07             1.000                               0.844    0.778
##     t1_n___08  (h)        0.881    0.027   32.760    0.000    0.744    0.700
##   t1_inf_sha_att_f5 =~                                                      
##     t1_n___10             1.000                               0.982    0.912
##     t1_n___11  (i)        0.977    0.023   43.310    0.000    0.960    0.912
##   t3_inf_sha_att_f1 =~                                                      
##     t3_n___01             1.000                               0.712    0.636
##     t3_n___02  (e)        0.906    0.064   14.093    0.000    0.645    0.610
##   t3_inf_sha_att_f2 =~                                                      
##     t3_n___03             1.000                               0.946    0.927
##     t3_n___04  (f)        0.980    0.016   61.381    0.000    0.927    0.902
##   t3_inf_sha_att_f3 =~                                                      
##     t3_n___05             1.000                               0.950    0.921
##     t3_n___06  (g)        0.959    0.015   65.861    0.000    0.911    0.859
##   t3_inf_sha_att_f4 =~                                                      
##     t3_n___07             1.000                               0.783    0.743
##     t3_n___08  (h)        0.881    0.027   32.760    0.000    0.690    0.667
##   t3_inf_sha_att_f5 =~                                                      
##     t3_n___10             1.000                               0.972    0.937
##     t3_n___11  (i)        0.977    0.023   43.310    0.000    0.950    0.914
##   t4_inf_sha_att_f1 =~                                                      
##     t4_n___01             1.000                               0.756    0.625
##     t4_n___02  (e)        0.906    0.064   14.093    0.000    0.685    0.634
##   t4_inf_sha_att_f2 =~                                                      
##     t4_n___03             1.000                               0.831    0.761
##     t4_n___04  (f)        0.980    0.016   61.381    0.000    0.815    0.800
##   t4_inf_sha_att_f3 =~                                                      
##     t4_n___05             1.000                               0.908    0.923
##     t4_n___06  (g)        0.959    0.015   65.861    0.000    0.870    0.848
##   t4_inf_sha_att_f4 =~                                                      
##     t4_n___07             1.000                               0.740    0.721
##     t4_n___08  (h)        0.881    0.027   32.760    0.000    0.652    0.640
##   t4_inf_sha_att_f5 =~                                                      
##     t4_n___10             1.000                               0.932    0.928
##     t4_n___11  (i)        0.977    0.023   43.310    0.000    0.911    0.915
##   t5_inf_sha_att_f1 =~                                                      
##     t5_n___01             1.000                               0.784    0.647
##     t5_n___02  (e)        0.906    0.064   14.093    0.000    0.710    0.648
##   t5_inf_sha_att_f2 =~                                                      
##     t5_n___03             1.000                               0.814    0.749
##     t5_n___04  (f)        0.980    0.016   61.381    0.000    0.798    0.786
##   t5_inf_sha_att_f3 =~                                                      
##     t5_n___05             1.000                               0.947    0.949
##     t5_n___06  (g)        0.959    0.015   65.861    0.000    0.908    0.850
##   t5_inf_sha_att_f4 =~                                                      
##     t5_n___07             1.000                               0.733    0.712
##     t5_n___08  (h)        0.881    0.027   32.760    0.000    0.646    0.635
##   t5_inf_sha_att_f5 =~                                                      
##     t5_n___10             1.000                               0.947    0.947
##     t5_n___11  (i)        0.977    0.023   43.310    0.000    0.926    0.916
##   t1_inf_sha_beh_f =~                                                       
##     t1_nf___1             1.000                               0.616    0.616
##     t1_nf___2 (o2)        2.365    0.109   21.642    0.000    0.931    0.931
##     t1_nf___3 (o3)        2.328    0.107   21.777    0.000    0.948    0.948
##     t1_nf___4 (o4)        2.149    0.101   21.195    0.000    0.991    0.991
##     t1_nf___5 (o5)        1.236    0.067   18.328    0.000    0.567    0.567
##   t3_inf_sha_beh_f =~                                                       
##     t3_nf___1             1.000                               0.666    0.666
##     t3_nf___2 (o2)        2.365    0.109   21.642    0.000    0.931    0.931
##     t3_nf___3 (o3)        2.328    0.107   21.777    0.000    0.938    0.938
##     t3_nf___4 (o4)        2.149    0.101   21.195    0.000    0.948    0.948
##     t3_nf___5 (o5)        1.236    0.067   18.328    0.000    0.545    0.545
##   t4_inf_sha_beh_f =~                                                       
##     t4_nf___1             1.000                               0.522    0.522
##     t4_nf___2 (o2)        2.365    0.109   21.642    0.000    0.924    0.924
##     t4_nf___3 (o3)        2.328    0.107   21.777    0.000    0.922    0.922
##     t4_nf___4 (o4)        2.149    0.101   21.195    0.000    0.993    0.993
##     t4_nf___5 (o5)        1.236    0.067   18.328    0.000    0.544    0.544
##   t5_inf_sha_beh_f =~                                                       
##     t5_nf___1             1.000                               0.254    0.254
##     t5_nf___2 (o2)        2.365    0.109   21.642    0.000    0.993    0.993
##     t5_nf___3 (o3)        2.328    0.107   21.777    0.000    0.965    0.965
##     t5_nf___4 (o4)        2.149    0.101   21.195    0.000    0.991    0.991
##     t5_nf___5 (o5)        1.236    0.067   18.328    0.000    0.472    0.472
##   t1_inf_sha_beh_f1 =~                                                      
##     t1_n___01             1.000                               0.625    0.575
##     t1_n___02 (j2)        0.426    0.031   13.889    0.000    0.266    0.436
##   t1_inf_sha_beh_f2 =~                                                      
##     t1_n___03             1.000                               0.978    0.964
##     t1_n___04 (k2)        0.996    0.008  129.672    0.000    0.974    0.967
##   t1_inf_sha_beh_f3 =~                                                      
##     t1_n___05             1.000                               0.945    0.973
##     t1_n___06 (l2)        0.958    0.009  112.672    0.000    0.905    0.918
##   t1_inf_sha_beh_f4 =~                                                      
##     t1_n___07             1.000                               0.835    0.812
##     t1_n___08 (m2)        0.865    0.019   44.433    0.000    0.722    0.709
##   t1_inf_sha_beh_f5 =~                                                      
##     t1_n___10             1.000                               0.839    0.927
##     t1_n___11 (n2)        0.884    0.018   50.156    0.000    0.742    0.860
##   t3_inf_sha_beh_f1 =~                                                      
##     t3_n___01             1.000                               0.535    0.485
##     t3_n___02 (j2)        0.426    0.031   13.889    0.000    0.228    0.423
##   t3_inf_sha_beh_f2 =~                                                      
##     t3_n___03             1.000                               0.905    0.960
##     t3_n___04 (k2)        0.996    0.008  129.672    0.000    0.902    0.959
##   t3_inf_sha_beh_f3 =~                                                      
##     t3_n___05             1.000                               0.885    0.966
##     t3_n___06 (l2)        0.958    0.009  112.672    0.000    0.847    0.912
##   t3_inf_sha_beh_f4 =~                                                      
##     t3_n___07             1.000                               0.808    0.807
##     t3_n___08 (m2)        0.865    0.019   44.433    0.000    0.699    0.727
##   t3_inf_sha_beh_f5 =~                                                      
##     t3_n___10             1.000                               0.808    0.928
##     t3_n___11 (n2)        0.884    0.018   50.156    0.000    0.715    0.881
##   t4_inf_sha_beh_f1 =~                                                      
##     t4_n___01             1.000                               0.683    0.556
##     t4_n___02 (j2)        0.426    0.031   13.889    0.000    0.291    0.503
##   t4_inf_sha_beh_f2 =~                                                      
##     t4_n___03             1.000                               0.913    0.930
##     t4_n___04 (k2)        0.996    0.008  129.672    0.000    0.910    0.926
##   t4_inf_sha_beh_f3 =~                                                      
##     t4_n___05             1.000                               0.900    0.947
##     t4_n___06 (l2)        0.958    0.009  112.672    0.000    0.862    0.889
##   t4_inf_sha_beh_f4 =~                                                      
##     t4_n___07             1.000                               0.771    0.766
##     t4_n___08 (m2)        0.865    0.019   44.433    0.000    0.667    0.679
##   t4_inf_sha_beh_f5 =~                                                      
##     t4_n___10             1.000                               0.810    0.917
##     t4_n___11 (n2)        0.884    0.018   50.156    0.000    0.717    0.876
##   t5_inf_sha_beh_f1 =~                                                      
##     t5_n___01             1.000                               2.142    1.465
##     t5_n___02 (j2)        0.426    0.031   13.889    0.000    0.912    0.561
##   t5_inf_sha_beh_f2 =~                                                      
##     t5_n___03             1.000                               1.297    0.977
##     t5_n___04 (k2)        0.996    0.008  129.672    0.000    1.293    0.971
##   t5_inf_sha_beh_f3 =~                                                      
##     t5_n___05             1.000                               1.314    0.998
##     t5_n___06 (l2)        0.958    0.009  112.672    0.000    1.258    0.950
##   t5_inf_sha_beh_f4 =~                                                      
##     t5_n___07             1.000                               1.180    0.898
##     t5_n___08 (m2)        0.865    0.019   44.433    0.000    1.021    0.760
##   t5_inf_sha_beh_f5 =~                                                      
##     t5_n___10             1.000                               1.425    1.034
##     t5_n___11 (n2)        0.884    0.018   50.156    0.000    1.261    0.910
## 
## Covariances:
##                        Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .t4_pri_con_04 ~~                                                          
##    .t5_pri_con_04         0.073    0.016    4.520    0.000    0.073    0.213
##  .t3_pri_con_04 ~~                                                          
##    .t5_pri_con_04         0.056    0.016    3.460    0.001    0.056    0.158
##  .t1_pri_con_04 ~~                                                          
##    .t5_pri_con_04         0.049    0.016    3.067    0.002    0.049    0.148
##  .t4_pri_con_05 ~~                                                          
##    .t5_pri_con_05         0.414    0.039   10.685    0.000    0.414    0.432
##  .t3_pri_con_05 ~~                                                          
##    .t5_pri_con_05         0.401    0.040   10.116    0.000    0.401    0.402
##  .t1_pri_con_05 ~~                                                          
##    .t5_pri_con_05         0.407    0.039   10.302    0.000    0.407    0.418
##  .t4_pri_con_06 ~~                                                          
##    .t5_pri_con_06         0.127    0.021    5.920    0.000    0.127    0.255
##  .t3_pri_con_06 ~~                                                          
##    .t5_pri_con_06         0.140    0.022    6.392    0.000    0.140    0.271
##  .t1_pri_con_06 ~~                                                          
##    .t5_pri_con_06         0.156    0.023    6.781    0.000    0.156    0.290
##  .t4_pri_con_07 ~~                                                          
##    .t5_pri_con_07         0.172    0.023    7.525    0.000    0.172    0.331
##  .t3_pri_con_07 ~~                                                          
##    .t5_pri_con_07         0.141    0.022    6.387    0.000    0.141    0.279
##  .t1_pri_con_07 ~~                                                          
##    .t5_pri_con_07         0.124    0.023    5.312    0.000    0.124    0.227
##  .t4_pri_con_08 ~~                                                          
##    .t5_pri_con_08         0.136    0.017    7.787    0.000    0.136    0.375
##  .t3_pri_con_08 ~~                                                          
##    .t5_pri_con_08         0.121    0.017    7.075    0.000    0.121    0.336
##  .t1_pri_con_08 ~~                                                          
##    .t5_pri_con_08         0.125    0.018    6.901    0.000    0.125    0.321
##  .t4_pri_con_09 ~~                                                          
##    .t5_pri_con_09         0.101    0.016    6.452    0.000    0.101    0.293
##  .t3_pri_con_09 ~~                                                          
##    .t5_pri_con_09         0.088    0.015    5.756    0.000    0.088    0.261
##  .t1_pri_con_09 ~~                                                          
##    .t5_pri_con_09         0.075    0.015    5.001    0.000    0.075    0.230
##  .t3_pri_con_04 ~~                                                          
##    .t4_pri_con_04         0.094    0.017    5.399    0.000    0.094    0.242
##  .t1_pri_con_04 ~~                                                          
##    .t4_pri_con_04         0.043    0.017    2.534    0.011    0.043    0.118
##  .t3_pri_con_05 ~~                                                          
##    .t4_pri_con_05         0.428    0.040   10.751    0.000    0.428    0.434
##  .t1_pri_con_05 ~~                                                          
##    .t4_pri_con_05         0.451    0.040   11.406    0.000    0.451    0.469
##  .t3_pri_con_06 ~~                                                          
##    .t4_pri_con_06         0.165    0.022    7.349    0.000    0.165    0.313
##  .t1_pri_con_06 ~~                                                          
##    .t4_pri_con_06         0.150    0.023    6.484    0.000    0.150    0.274
##  .t3_pri_con_07 ~~                                                          
##    .t4_pri_con_07         0.180    0.022    8.021    0.000    0.180    0.361
##  .t1_pri_con_07 ~~                                                          
##    .t4_pri_con_07         0.144    0.024    6.053    0.000    0.144    0.266
##  .t3_pri_con_08 ~~                                                          
##    .t4_pri_con_08         0.112    0.017    6.558    0.000    0.112    0.311
##  .t1_pri_con_08 ~~                                                          
##    .t4_pri_con_08         0.080    0.018    4.501    0.000    0.080    0.206
##  .t3_pri_con_09 ~~                                                          
##    .t4_pri_con_09         0.075    0.016    4.784    0.000    0.075    0.214
##  .t1_pri_con_09 ~~                                                          
##    .t4_pri_con_09         0.059    0.015    3.865    0.000    0.059    0.173
##  .t1_pri_con_04 ~~                                                          
##    .t3_pri_con_04         0.083    0.017    4.728    0.000    0.083    0.222
##  .t1_pri_con_05 ~~                                                          
##    .t3_pri_con_05         0.537    0.042   12.707    0.000    0.537    0.536
##  .t1_pri_con_06 ~~                                                          
##    .t3_pri_con_06         0.192    0.024    7.939    0.000    0.192    0.337
##  .t1_pri_con_07 ~~                                                          
##    .t3_pri_con_07         0.202    0.024    8.501    0.000    0.202    0.386
##  .t1_pri_con_08 ~~                                                          
##    .t3_pri_con_08         0.099    0.018    5.472    0.000    0.099    0.255
##  .t1_pri_con_09 ~~                                                          
##    .t3_pri_con_09         0.053    0.015    3.535    0.000    0.053    0.162
##   t1_pri_con_f ~~                                                           
##     t5_pri_con_f          0.516    0.036   14.152    0.000    0.735    0.735
##   t3_pri_con_f ~~                                                           
##     t5_pri_con_f          0.550    0.038   14.621    0.000    0.766    0.766
##   t4_pri_con_f ~~                                                           
##     t5_pri_con_f          0.579    0.039   15.021    0.000    0.805    0.805
##   t1_pri_con_f ~~                                                           
##     t3_pri_con_f          0.566    0.038   15.061    0.000    0.827    0.827
##     t4_pri_con_f          0.526    0.036   14.493    0.000    0.768    0.768
##   t3_pri_con_f ~~                                                           
##     t4_pri_con_f          0.542    0.037   14.705    0.000    0.775    0.775
##   t1_inf_sha_att_f ~~                                                       
##     t5_inf_sh_tt_f        0.053    0.008    6.448    0.000    0.454    0.454
##   t3_inf_sha_att_f ~~                                                       
##     t5_inf_sh_tt_f        0.061    0.009    6.744    0.000    0.548    0.548
##   t4_inf_sha_att_f ~~                                                       
##     t5_inf_sh_tt_f        0.065    0.009    6.874    0.000    0.620    0.620
##   t1_inf_sha_att_f ~~                                                       
##     t3_inf_sh_tt_f        0.068    0.010    6.808    0.000    0.557    0.557
##     t4_inf_sh_tt_f        0.061    0.009    6.704    0.000    0.534    0.534
##   t3_inf_sha_att_f ~~                                                       
##     t4_inf_sh_tt_f        0.061    0.009    6.755    0.000    0.558    0.558
##  .t1_inf_sha_att_01 ~~                                                      
##    .t5_nf_sh_tt_01        0.314    0.038    8.288    0.000    0.314    0.410
##  .t3_inf_sha_att_01 ~~                                                      
##    .t5_nf_sh_tt_01        0.373    0.040    9.344    0.000    0.373    0.466
##  .t4_inf_sha_att_01 ~~                                                      
##    .t5_nf_sh_tt_01        0.436    0.044    9.816    0.000    0.436    0.500
##  .t1_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_tt_01        0.253    0.035    7.224    0.000    0.253    0.353
##    .t4_nf_sh_tt_01        0.273    0.038    7.199    0.000    0.273    0.349
##  .t3_inf_sha_att_01 ~~                                                      
##    .t4_nf_sh_tt_01        0.311    0.040    7.716    0.000    0.311    0.381
##  .t1_inf_sha_att_02 ~~                                                      
##    .t5_nf_sh_tt_02        0.317    0.034    9.235    0.000    0.317    0.442
##  .t3_inf_sha_att_02 ~~                                                      
##    .t5_nf_sh_tt_02        0.371    0.035   10.667    0.000    0.371    0.531
##  .t4_inf_sha_att_02 ~~                                                      
##    .t5_nf_sh_tt_02        0.374    0.036   10.304    0.000    0.374    0.537
##  .t1_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_tt_02        0.299    0.034    8.886    0.000    0.299    0.414
##    .t4_nf_sh_tt_02        0.333    0.034    9.709    0.000    0.333    0.463
##  .t3_inf_sha_att_02 ~~                                                      
##    .t4_nf_sh_tt_02        0.387    0.035   11.146    0.000    0.387    0.554
##  .t1_inf_sha_att_03 ~~                                                      
##    .t5_nf_sh_tt_03        0.067    0.014    4.864    0.000    0.067    0.218
##  .t3_inf_sha_att_03 ~~                                                      
##    .t5_nf_sh_tt_03        0.072    0.013    5.597    0.000    0.072    0.261
##  .t4_inf_sha_att_03 ~~                                                      
##    .t5_nf_sh_tt_03        0.161    0.021    7.633    0.000    0.161    0.314
##  .t1_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_tt_03        0.060    0.010    6.257    0.000    0.060    0.370
##    .t4_nf_sh_tt_03        0.054    0.014    3.904    0.000    0.054    0.179
##  .t3_inf_sha_att_03 ~~                                                      
##    .t4_nf_sh_tt_03        0.069    0.013    5.155    0.000    0.069    0.254
##  .t1_inf_sha_att_04 ~~                                                      
##    .t5_nf_sh_tt_04        0.093    0.013    7.342    0.000    0.093    0.333
##  .t3_inf_sha_att_04 ~~                                                      
##    .t5_nf_sh_tt_04        0.097    0.012    7.809    0.000    0.097    0.349
##  .t4_inf_sha_att_04 ~~                                                      
##    .t5_nf_sh_tt_04        0.131    0.017    7.838    0.000    0.131    0.340
##  .t1_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_tt_04        0.056    0.010    5.366    0.000    0.056    0.283
##    .t4_nf_sh_tt_04        0.066    0.013    5.266    0.000    0.066    0.244
##  .t3_inf_sha_att_04 ~~                                                      
##    .t4_nf_sh_tt_04        0.101    0.013    7.880    0.000    0.101    0.374
##  .t1_inf_sha_att_05 ~~                                                      
##    .t5_nf_sh_tt_05       -0.000    0.008   -0.059    0.953   -0.000   -0.005
##  .t3_inf_sha_att_05 ~~                                                      
##    .t5_nf_sh_tt_05       -0.000    0.009   -0.036    0.971   -0.000   -0.003
##  .t4_inf_sha_att_05 ~~                                                      
##    .t5_nf_sh_tt_05        0.011    0.009    1.218    0.223    0.011    0.096
##  .t1_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_tt_05        0.033    0.009    3.470    0.001    0.033    0.243
##    .t4_nf_sh_tt_05        0.026    0.009    2.876    0.004    0.026    0.203
##  .t3_inf_sha_att_05 ~~                                                      
##    .t4_nf_sh_tt_05        0.050    0.010    4.981    0.000    0.050    0.331
##  .t1_inf_sha_att_06 ~~                                                      
##    .t5_nf_sh_tt_06        0.134    0.013   10.236    0.000    0.134    0.467
##  .t3_inf_sha_att_06 ~~                                                      
##    .t5_nf_sh_tt_06        0.142    0.014   10.008    0.000    0.142    0.464
##  .t4_inf_sha_att_06 ~~                                                      
##    .t5_nf_sh_tt_06        0.153    0.014   10.673    0.000    0.153    0.499
##  .t1_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_tt_06        0.126    0.013    9.371    0.000    0.126    0.455
##    .t4_nf_sh_tt_06        0.110    0.013    8.637    0.000    0.110    0.395
##  .t3_inf_sha_att_06 ~~                                                      
##    .t4_nf_sh_tt_06        0.138    0.014    9.696    0.000    0.138    0.469
##  .t1_inf_sha_att_07 ~~                                                      
##    .t5_nf_sh_tt_07        0.205    0.022    9.294    0.000    0.205    0.416
##  .t3_inf_sha_att_07 ~~                                                      
##    .t5_nf_sh_tt_07        0.199    0.022    9.068    0.000    0.199    0.391
##  .t4_inf_sha_att_07 ~~                                                      
##    .t5_nf_sh_tt_07        0.216    0.022    9.588    0.000    0.216    0.419
##  .t1_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_tt_07        0.193    0.022    8.828    0.000    0.193    0.401
##    .t4_nf_sh_tt_07        0.205    0.022    9.295    0.000    0.205    0.422
##  .t3_inf_sha_att_07 ~~                                                      
##    .t4_nf_sh_tt_07        0.158    0.021    7.374    0.000    0.158    0.315
##  .t1_inf_sha_att_08 ~~                                                      
##    .t5_nf_sh_tt_08        0.231    0.024    9.471    0.000    0.231    0.388
##  .t3_inf_sha_att_08 ~~                                                      
##    .t5_nf_sh_tt_08        0.227    0.024    9.288    0.000    0.227    0.375
##  .t4_inf_sha_att_08 ~~                                                      
##    .t5_nf_sh_tt_08        0.276    0.025   10.861    0.000    0.276    0.448
##  .t1_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_tt_08        0.231    0.025    9.433    0.000    0.231    0.396
##    .t4_nf_sh_tt_08        0.229    0.025    9.281    0.000    0.229    0.385
##  .t3_inf_sha_att_08 ~~                                                      
##    .t4_nf_sh_tt_08        0.216    0.025    8.704    0.000    0.216    0.358
##  .t1_inf_sha_att_10 ~~                                                      
##    .t5_nf_sh_tt_10        0.032    0.013    2.410    0.016    0.032    0.228
##  .t3_inf_sha_att_10 ~~                                                      
##    .t5_nf_sh_tt_10        0.023    0.013    1.865    0.062    0.023    0.201
##  .t4_inf_sha_att_10 ~~                                                      
##    .t5_nf_sh_tt_10        0.050    0.012    4.061    0.000    0.050    0.418
##  .t1_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_tt_10        0.011    0.015    0.743    0.458    0.011    0.067
##    .t4_nf_sh_tt_10        0.033    0.014    2.329    0.020    0.033    0.200
##  .t3_inf_sha_att_10 ~~                                                      
##    .t4_nf_sh_tt_10        0.027    0.013    1.986    0.047    0.027    0.197
##  .t1_inf_sha_att_11 ~~                                                      
##    .t5_nf_sh_tt_11        0.062    0.013    4.706    0.000    0.062    0.357
##  .t3_inf_sha_att_11 ~~                                                      
##    .t5_nf_sh_tt_11        0.034    0.013    2.647    0.008    0.034    0.201
##  .t4_inf_sha_att_11 ~~                                                      
##    .t5_nf_sh_tt_11        0.054    0.012    4.403    0.000    0.054    0.335
##  .t1_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_tt_11        0.050    0.014    3.537    0.000    0.050    0.275
##    .t4_nf_sh_tt_11        0.054    0.014    3.978    0.000    0.054    0.311
##  .t3_inf_sha_att_11 ~~                                                      
##    .t4_nf_sh_tt_11        0.046    0.013    3.466    0.001    0.046    0.273
##   t1_inf_sha_beh_f ~~                                                       
##     t5_inf_sh_bh_f       -0.035    0.008   -4.323    0.000   -0.168   -0.168
##   t3_inf_sha_beh_f ~~                                                       
##     t5_inf_sh_bh_f       -0.031    0.007   -4.117    0.000   -0.158   -0.158
##   t4_inf_sha_beh_f ~~                                                       
##     t5_inf_sh_bh_f       -0.041    0.008   -5.172    0.000   -0.213   -0.213
##   t1_inf_sha_beh_f ~~                                                       
##     t3_inf_sh_bh_f        0.084    0.010    8.860    0.000    0.614    0.614
##     t4_inf_sh_bh_f        0.076    0.009    8.549    0.000    0.551    0.551
##   t3_inf_sha_beh_f ~~                                                       
##     t4_inf_sh_bh_f        0.080    0.009    8.862    0.000    0.626    0.626
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t5_nf_sh_bh_01       -0.088    0.026   -3.411    0.001   -0.088   -0.063
##  .t3_inf_sha_beh_01 ~~                                                      
##    .t5_nf_sh_bh_01       -0.075    0.027   -2.804    0.005   -0.075   -0.050
##  .t4_inf_sha_beh_01 ~~                                                      
##    .t5_nf_sh_bh_01       -0.059    0.030   -1.942    0.052   -0.059   -0.037
##  .t1_inf_sha_beh_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.359    0.037    9.697    0.000    0.359    0.417
##    .t4_nf_sh_bh_01        0.378    0.041    9.313    0.000    0.378    0.416
##  .t3_inf_sha_beh_01 ~~                                                      
##    .t4_nf_sh_bh_01        0.435    0.043   10.048    0.000    0.435    0.440
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t5_nf_sh_bh_02       -0.008    0.017   -0.440    0.660   -0.008   -0.010
##  .t3_inf_sha_beh_02 ~~                                                      
##    .t5_nf_sh_bh_02       -0.043    0.016   -2.768    0.006   -0.043   -0.065
##  .t4_inf_sha_beh_02 ~~                                                      
##    .t5_nf_sh_bh_02       -0.041    0.017   -2.445    0.014   -0.041   -0.060
##  .t1_inf_sha_beh_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.075    0.010    7.380    0.000    0.075    0.281
##    .t4_nf_sh_bh_02        0.061    0.011    5.786    0.000    0.061    0.224
##  .t3_inf_sha_beh_02 ~~                                                      
##    .t4_nf_sh_bh_02        0.064    0.010    6.613    0.000    0.064    0.263
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t5_nf_sh_bh_03       -0.002    0.005   -0.516    0.606   -0.002   -0.032
##  .t3_inf_sha_beh_03 ~~                                                      
##    .t5_nf_sh_bh_03        0.002    0.004    0.461    0.645    0.002    0.028
##  .t4_inf_sha_beh_03 ~~                                                      
##    .t5_nf_sh_bh_03       -0.002    0.006   -0.326    0.744   -0.002   -0.019
##  .t1_inf_sha_beh_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.021    0.005    4.359    0.000    0.021    0.295
##    .t4_nf_sh_bh_03        0.008    0.006    1.300    0.194    0.008    0.079
##  .t3_inf_sha_beh_03 ~~                                                      
##    .t4_nf_sh_bh_03        0.028    0.006    4.777    0.000    0.028    0.296
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t5_nf_sh_bh_04       -0.016    0.005   -3.183    0.001   -0.016   -0.189
##  .t3_inf_sha_beh_04 ~~                                                      
##    .t5_nf_sh_bh_04       -0.009    0.005   -1.917    0.055   -0.009   -0.108
##  .t4_inf_sha_beh_04 ~~                                                      
##    .t5_nf_sh_bh_04       -0.035    0.006   -5.340    0.000   -0.035   -0.290
##  .t1_inf_sha_beh_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.020    0.005    4.295    0.000    0.020    0.295
##    .t4_nf_sh_bh_04        0.021    0.006    3.619    0.000    0.021    0.221
##  .t3_inf_sha_beh_04 ~~                                                      
##    .t4_nf_sh_bh_04        0.036    0.006    5.977    0.000    0.036    0.362
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t5_nf_sh_bh_05       -0.004    0.004   -0.965    0.335   -0.004   -0.228
##  .t3_inf_sha_beh_05 ~~                                                      
##    .t5_nf_sh_bh_05       -0.001    0.004   -0.136    0.892   -0.001   -0.030
##  .t4_inf_sha_beh_05 ~~                                                      
##    .t5_nf_sh_bh_05       -0.013    0.005   -2.583    0.010   -0.013   -0.544
##  .t1_inf_sha_beh_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.010    0.005    1.951    0.051    0.010    0.184
##    .t4_nf_sh_bh_05        0.013    0.006    2.280    0.023    0.013    0.193
##  .t3_inf_sha_beh_05 ~~                                                      
##    .t4_nf_sh_bh_05       -0.001    0.006   -0.212    0.832   -0.001   -0.017
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t5_nf_sh_bh_06       -0.022    0.007   -3.185    0.001   -0.022   -0.134
##  .t3_inf_sha_beh_06 ~~                                                      
##    .t5_nf_sh_bh_06       -0.020    0.007   -3.041    0.002   -0.020   -0.129
##  .t4_inf_sha_beh_06 ~~                                                      
##    .t5_nf_sh_bh_06       -0.029    0.008   -3.638    0.000   -0.029   -0.156
##  .t1_inf_sha_beh_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.047    0.007    6.608    0.000    0.047    0.313
##    .t4_nf_sh_bh_06        0.043    0.008    5.445    0.000    0.043    0.245
##  .t3_inf_sha_beh_06 ~~                                                      
##    .t4_nf_sh_bh_06        0.078    0.008    9.644    0.000    0.078    0.460
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t5_nf_sh_bh_07       -0.020    0.014   -1.435    0.151   -0.020   -0.057
##  .t3_inf_sha_beh_07 ~~                                                      
##    .t5_nf_sh_bh_07       -0.043    0.014   -3.015    0.003   -0.043   -0.125
##  .t4_inf_sha_beh_07 ~~                                                      
##    .t5_nf_sh_bh_07       -0.033    0.015   -2.202    0.028   -0.033   -0.088
##  .t1_inf_sha_beh_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.122    0.015    8.119    0.000    0.122    0.344
##    .t4_nf_sh_bh_07        0.124    0.016    7.957    0.000    0.124    0.319
##  .t3_inf_sha_beh_07 ~~                                                      
##    .t4_nf_sh_bh_07        0.126    0.016    7.925    0.000    0.126    0.329
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t5_nf_sh_bh_08       -0.084    0.023   -3.686    0.000   -0.084   -0.134
##  .t3_inf_sha_beh_08 ~~                                                      
##    .t5_nf_sh_bh_08       -0.038    0.022   -1.785    0.074   -0.038   -0.067
##  .t4_inf_sha_beh_08 ~~                                                      
##    .t5_nf_sh_bh_08       -0.049    0.023   -2.145    0.032   -0.049   -0.079
##  .t1_inf_sha_beh_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.159    0.019    8.535    0.000    0.159    0.337
##    .t4_nf_sh_bh_08        0.183    0.020    9.331    0.000    0.183    0.353
##  .t3_inf_sha_beh_08 ~~                                                      
##    .t4_nf_sh_bh_08        0.196    0.019   10.299    0.000    0.196    0.412
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t5_nf_sh_bh_10       -0.028    0.012   -2.431    0.015   -0.028   -0.228
##  .t3_inf_sha_beh_10 ~~                                                      
##    .t5_nf_sh_bh_10       -0.028    0.011   -2.526    0.012   -0.028   -0.237
##  .t4_inf_sha_beh_10 ~~                                                      
##    .t5_nf_sh_bh_10       -0.020    0.011   -1.744    0.081   -0.020   -0.153
##  .t1_inf_sha_beh_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.019    0.011    1.747    0.081    0.019    0.174
##    .t4_nf_sh_bh_10        0.036    0.012    3.109    0.002    0.036    0.300
##  .t3_inf_sha_beh_10 ~~                                                      
##    .t4_nf_sh_bh_10        0.047    0.011    4.304    0.000    0.047    0.407
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t5_nf_sh_bh_11       -0.010    0.012   -0.854    0.393   -0.010   -0.040
##  .t3_inf_sha_beh_11 ~~                                                      
##    .t5_nf_sh_bh_11        0.005    0.011    0.429    0.668    0.005    0.021
##  .t4_inf_sha_beh_11 ~~                                                      
##    .t5_nf_sh_bh_11       -0.018    0.011   -1.648    0.099   -0.018   -0.079
##  .t1_inf_sha_beh_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.026    0.010    2.557    0.011    0.026    0.153
##    .t4_nf_sh_bh_11        0.055    0.010    5.251    0.000    0.055    0.315
##  .t3_inf_sha_beh_11 ~~                                                      
##    .t4_nf_sh_bh_11        0.038    0.010    3.967    0.000    0.038    0.254
##  .t1_inf_sha_att_01 ~~                                                      
##    .t1_nf_sh_bh_01        0.171    0.030    5.685    0.000    0.171    0.233
##  .t1_inf_sha_att_02 ~~                                                      
##    .t1_nf_sh_bh_02        0.082    0.017    4.775    0.000    0.082    0.174
##  .t1_inf_sha_att_03 ~~                                                      
##    .t1_nf_sh_bh_03        0.019    0.006    2.975    0.003    0.019    0.166
##  .t1_inf_sha_att_04 ~~                                                      
##    .t1_nf_sh_bh_04        0.030    0.006    4.608    0.000    0.030    0.258
##  .t1_inf_sha_att_05 ~~                                                      
##    .t1_nf_sh_bh_05        0.019    0.006    3.023    0.003    0.019    0.254
##  .t1_inf_sha_att_06 ~~                                                      
##    .t1_nf_sh_bh_06        0.046    0.008    5.602    0.000    0.046    0.229
##  .t1_inf_sha_att_07 ~~                                                      
##    .t1_nf_sh_bh_07        0.062    0.015    4.167    0.000    0.062    0.151
##  .t1_inf_sha_att_08 ~~                                                      
##    .t1_nf_sh_bh_08        0.112    0.018    6.129    0.000    0.112    0.206
##  .t1_inf_sha_att_10 ~~                                                      
##    .t1_nf_sh_bh_10       -0.002    0.013   -0.168    0.867   -0.002   -0.015
##  .t1_inf_sha_att_11 ~~                                                      
##    .t1_nf_sh_bh_11        0.036    0.012    2.941    0.003    0.036    0.189
##  .t3_inf_sha_att_01 ~~                                                      
##    .t3_nf_sh_bh_01        0.192    0.031    6.099    0.000    0.192    0.229
##  .t3_inf_sha_att_02 ~~                                                      
##    .t3_nf_sh_bh_02        0.064    0.014    4.520    0.000    0.064    0.157
##  .t3_inf_sha_att_03 ~~                                                      
##    .t3_nf_sh_bh_03        0.032    0.006    5.266    0.000    0.032    0.319
##  .t3_inf_sha_att_04 ~~                                                      
##    .t3_nf_sh_bh_04        0.023    0.006    3.637    0.000    0.023    0.193
##  .t3_inf_sha_att_05 ~~                                                      
##    .t3_nf_sh_bh_05        0.022    0.007    3.287    0.001    0.022    0.233
##  .t3_inf_sha_att_06 ~~                                                      
##    .t3_nf_sh_bh_06        0.018    0.008    2.266    0.023    0.018    0.088
##  .t3_inf_sha_att_07 ~~                                                      
##    .t3_nf_sh_bh_07        0.098    0.016    6.194    0.000    0.098    0.236
##  .t3_inf_sha_att_08 ~~                                                      
##    .t3_nf_sh_bh_08        0.094    0.018    5.342    0.000    0.094    0.185
##  .t3_inf_sha_att_10 ~~                                                      
##    .t3_nf_sh_bh_10        0.025    0.012    2.130    0.033    0.025    0.211
##  .t3_inf_sha_att_11 ~~                                                      
##    .t3_nf_sh_bh_11        0.012    0.011    1.058    0.290    0.012    0.074
##  .t4_inf_sha_att_01 ~~                                                      
##    .t4_nf_sh_bh_01        0.160    0.036    4.398    0.000    0.160    0.166
##  .t4_inf_sha_att_02 ~~                                                      
##    .t4_nf_sh_bh_02        0.050    0.015    3.332    0.001    0.050    0.120
##  .t4_inf_sha_att_03 ~~                                                      
##    .t4_nf_sh_bh_03        0.042    0.011    3.685    0.000    0.042    0.163
##  .t4_inf_sha_att_04 ~~                                                      
##    .t4_nf_sh_bh_04        0.051    0.010    5.080    0.000    0.051    0.222
##  .t4_inf_sha_att_05 ~~                                                      
##    .t4_nf_sh_bh_05        0.018    0.008    2.332    0.020    0.018    0.157
##  .t4_inf_sha_att_06 ~~                                                      
##    .t4_nf_sh_bh_06        0.048    0.009    5.162    0.000    0.048    0.198
##  .t4_inf_sha_att_07 ~~                                                      
##    .t4_nf_sh_bh_07        0.098    0.016    5.991    0.000    0.098    0.213
##  .t4_inf_sha_att_08 ~~                                                      
##    .t4_nf_sh_bh_08        0.107    0.018    5.933    0.000    0.107    0.189
##  .t4_inf_sha_att_10 ~~                                                      
##    .t4_nf_sh_bh_10        0.004    0.011    0.381    0.703    0.004    0.033
##  .t4_inf_sha_att_11 ~~                                                      
##    .t4_nf_sh_bh_11        0.026    0.011    2.513    0.012    0.026    0.167
##  .t5_inf_sha_att_01 ~~                                                      
##    .t5_nf_sh_bh_01       -0.048    0.027   -1.795    0.073   -0.048   -0.033
##  .t5_inf_sha_att_02 ~~                                                      
##    .t5_nf_sh_bh_02       -0.011    0.028   -0.399    0.690   -0.011   -0.010
##  .t5_inf_sha_att_03 ~~                                                      
##    .t5_nf_sh_bh_03       -0.028    0.009   -3.107    0.002   -0.028   -0.137
##  .t5_inf_sha_att_04 ~~                                                      
##    .t5_nf_sh_bh_04       -0.024    0.008   -2.938    0.003   -0.024   -0.119
##  .t5_inf_sha_att_05 ~~                                                      
##    .t5_nf_sh_bh_05       -0.013    0.006   -2.300    0.021   -0.013   -0.523
##  .t5_inf_sha_att_06 ~~                                                      
##    .t5_nf_sh_bh_06        0.015    0.009    1.696    0.090    0.015    0.063
##  .t5_inf_sha_att_07 ~~                                                      
##    .t5_nf_sh_bh_07        0.027    0.015    1.777    0.076    0.027    0.065
##  .t5_inf_sha_att_08 ~~                                                      
##    .t5_nf_sh_bh_08       -0.039    0.023   -1.744    0.081   -0.039   -0.057
##  .t5_inf_sha_att_10 ~~                                                      
##    .t5_nf_sh_bh_10       -0.005    0.012   -0.442    0.658   -0.005   -0.046
##  .t5_inf_sha_att_11 ~~                                                      
##    .t5_nf_sh_bh_11       -0.009    0.013   -0.739    0.460   -0.009   -0.041
##   t1_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.065    0.012   -5.363    0.000   -0.222   -0.222
##     t3_inf_sh_tt_f       -0.040    0.011   -3.572    0.000   -0.142   -0.142
##     t4_inf_sh_tt_f       -0.065    0.011   -5.787    0.000   -0.247   -0.247
##     t5_inf_sh_tt_f       -0.064    0.011   -5.615    0.000   -0.238   -0.238
##     t1_inf_sh_bh_f       -0.035    0.012   -2.920    0.003   -0.111   -0.111
##     t3_inf_sh_bh_f       -0.021    0.011   -1.856    0.063   -0.070   -0.070
##     t4_inf_sh_bh_f       -0.036    0.011   -3.229    0.001   -0.125   -0.125
##     t5_inf_sh_bh_f        0.013    0.016    0.795    0.426    0.029    0.029
##   t3_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.050    0.012   -4.229    0.000   -0.167   -0.167
##     t3_inf_sh_tt_f       -0.041    0.011   -3.652    0.000   -0.143   -0.143
##     t4_inf_sh_tt_f       -0.040    0.011   -3.793    0.000   -0.151   -0.151
##     t5_inf_sh_tt_f       -0.044    0.011   -4.053    0.000   -0.161   -0.161
##     t1_inf_sh_bh_f       -0.030    0.012   -2.472    0.013   -0.093   -0.093
##     t3_inf_sh_bh_f       -0.017    0.011   -1.484    0.138   -0.055   -0.055
##     t4_inf_sh_bh_f       -0.031    0.011   -2.745    0.006   -0.105   -0.105
##     t5_inf_sh_bh_f       -0.006    0.017   -0.383    0.701   -0.014   -0.014
##   t4_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.059    0.012   -4.960    0.000   -0.199   -0.199
##     t3_inf_sh_tt_f       -0.048    0.011   -4.268    0.000   -0.169   -0.169
##     t4_inf_sh_tt_f       -0.056    0.011   -5.095    0.000   -0.210   -0.210
##     t5_inf_sh_tt_f       -0.051    0.011   -4.609    0.000   -0.185   -0.185
##     t1_inf_sh_bh_f       -0.034    0.012   -2.790    0.005   -0.105   -0.105
##     t3_inf_sh_bh_f       -0.034    0.011   -3.004    0.003   -0.113   -0.113
##     t4_inf_sh_bh_f       -0.040    0.011   -3.485    0.000   -0.133   -0.133
##     t5_inf_sh_bh_f        0.013    0.017    0.785    0.433    0.029    0.029
##   t5_pri_con_f ~~                                                           
##     t1_inf_sh_tt_f       -0.053    0.012   -4.413    0.000   -0.174   -0.174
##     t3_inf_sh_tt_f       -0.040    0.011   -3.468    0.001   -0.135   -0.135
##     t4_inf_sh_tt_f       -0.051    0.011   -4.618    0.000   -0.187   -0.187
##     t5_inf_sh_tt_f       -0.068    0.012   -5.820    0.000   -0.243   -0.243
##     t1_inf_sh_bh_f       -0.028    0.012   -2.293    0.022   -0.085   -0.085
##     t3_inf_sh_bh_f       -0.019    0.011   -1.643    0.100   -0.061   -0.061
##     t4_inf_sh_bh_f       -0.031    0.012   -2.714    0.007   -0.103   -0.103
##     t5_inf_sh_bh_f        0.021    0.017    1.215    0.224    0.044    0.044
##   t1_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.062    0.007    8.498    0.000    0.452    0.452
##     t3_inf_sh_bh_f        0.051    0.006    7.973    0.000    0.398    0.398
##     t4_inf_sh_bh_f        0.042    0.006    7.118    0.000    0.330    0.330
##     t5_inf_sh_bh_f       -0.024    0.007   -3.328    0.001   -0.124   -0.124
##   t3_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.048    0.006    7.575    0.000    0.364    0.364
##     t3_inf_sh_bh_f        0.061    0.007    8.833    0.000    0.500    0.500
##     t4_inf_sh_bh_f        0.040    0.006    7.062    0.000    0.330    0.330
##     t5_inf_sh_bh_f       -0.036    0.007   -4.886    0.000   -0.193   -0.193
##   t4_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.046    0.006    7.630    0.000    0.374    0.374
##     t3_inf_sh_bh_f        0.047    0.006    8.049    0.000    0.414    0.414
##     t4_inf_sh_bh_f        0.053    0.006    8.450    0.000    0.462    0.462
##     t5_inf_sh_bh_f       -0.033    0.007   -4.735    0.000   -0.188   -0.188
##   t5_inf_sha_att_f ~~                                                       
##     t1_inf_sh_bh_f        0.048    0.006    7.717    0.000    0.377    0.377
##     t3_inf_sh_bh_f        0.046    0.006    7.877    0.000    0.395    0.395
##     t4_inf_sh_bh_f        0.048    0.006    8.027    0.000    0.412    0.412
##     t5_inf_sh_bh_f       -0.031    0.007   -4.509    0.000   -0.176   -0.176
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     3.706    0.035  104.702    0.000    3.706    3.506
##    .t1_pri_con_05     3.780    0.044   86.154    0.000    3.780    2.892
##    .t1_pri_con_06     3.285    0.039   83.582    0.000    3.285    2.799
##    .t1_pri_con_07     3.612    0.042   85.909    0.000    3.612    2.877
##    .t1_pri_con_08     3.615    0.039   92.412    0.000    3.615    3.094
##    .t1_pri_con_09     4.094    0.035  116.793    0.000    4.094    3.911
##    .t3_pri_con_04     3.674    0.035  103.711    0.000    3.674    3.478
##    .t3_pri_con_05     3.683    0.044   83.818    0.000    3.683    2.818
##    .t3_pri_con_06     3.212    0.038   84.812    0.000    3.212    2.844
##    .t3_pri_con_07     3.482    0.042   83.833    0.000    3.482    2.811
##    .t3_pri_con_08     3.562    0.039   91.437    0.000    3.562    3.068
##    .t3_pri_con_09     3.985    0.036  110.746    0.000    3.985    3.715
##    .t4_pri_con_04     3.580    0.036  100.345    0.000    3.580    3.369
##    .t4_pri_con_05     3.689    0.043   85.018    0.000    3.689    2.861
##    .t4_pri_con_06     3.156    0.038   83.074    0.000    3.156    2.791
##    .t4_pri_con_07     3.322    0.041   80.327    0.000    3.322    2.697
##    .t4_pri_con_08     3.505    0.038   91.273    0.000    3.505    3.066
##    .t4_pri_con_09     3.910    0.036  109.434    0.000    3.910    3.675
##    .t5_pri_con_04     3.590    0.036  100.643    0.000    3.590    3.369
##    .t5_pri_con_05     3.597    0.044   81.186    0.000    3.597    2.721
##    .t5_pri_con_06     3.120    0.038   81.062    0.000    3.120    2.715
##    .t5_pri_con_07     3.282    0.042   78.096    0.000    3.282    2.615
##    .t5_pri_con_08     3.434    0.039   88.333    0.000    3.434    2.958
##    .t5_pri_con_09     3.874    0.036  108.380    0.000    3.874    3.629
##    .t1_nf_sh_tt_01    1.710    0.038   45.395    0.000    1.710    1.521
##    .t1_nf_sh_tt_02    1.937    0.037   52.388    0.000    1.937    1.756
##    .t1_nf_sh_tt_03    2.845    0.035   82.072    0.000    2.845    2.748
##    .t1_nf_sh_tt_04    3.018    0.034   87.793    0.000    3.018    2.940
##    .t1_nf_sh_tt_05    2.722    0.035   77.209    0.000    2.722    2.585
##    .t1_nf_sh_tt_06    2.468    0.036   67.932    0.000    2.468    2.275
##    .t1_nf_sh_tt_07    3.059    0.036   84.155    0.000    3.059    2.818
##    .t1_nf_sh_tt_08    2.361    0.036   66.357    0.000    2.361    2.222
##    .t1_nf_sh_tt_10    2.265    0.036   62.773    0.000    2.265    2.103
##    .t1_nf_sh_tt_11    2.303    0.035   65.314    0.000    2.303    2.188
##    .t3_nf_sh_tt_01    1.802    0.037   48.063    0.000    1.802    1.609
##    .t3_nf_sh_tt_02    1.911    0.035   54.045    0.000    1.911    1.809
##    .t3_nf_sh_tt_03    3.035    0.034   88.811    0.000    3.035    2.973
##    .t3_nf_sh_tt_04    3.132    0.034   91.055    0.000    3.132    3.047
##    .t3_nf_sh_tt_05    2.842    0.035   82.346    0.000    2.842    2.756
##    .t3_nf_sh_tt_06    2.556    0.035   72.064    0.000    2.556    2.412
##    .t3_nf_sh_tt_07    3.214    0.035   91.096    0.000    3.214    3.051
##    .t3_nf_sh_tt_08    2.457    0.035   70.979    0.000    2.457    2.377
##    .t3_nf_sh_tt_10    2.319    0.035   66.764    0.000    2.319    2.236
##    .t3_nf_sh_tt_11    2.393    0.035   68.843    0.000    2.393    2.305
##    .t4_nf_sh_tt_01    1.937    0.041   47.765    0.000    1.937    1.601
##    .t4_nf_sh_tt_02    1.940    0.036   53.578    0.000    1.940    1.796
##    .t4_nf_sh_tt_03    2.831    0.037   77.249    0.000    2.831    2.590
##    .t4_nf_sh_tt_04    3.000    0.034   87.968    0.000    3.000    2.944
##    .t4_nf_sh_tt_05    2.681    0.033   81.450    0.000    2.681    2.726
##    .t4_nf_sh_tt_06    2.368    0.034   68.962    0.000    2.368    2.308
##    .t4_nf_sh_tt_07    3.125    0.034   90.916    0.000    3.125    3.042
##    .t4_nf_sh_tt_08    2.261    0.034   66.244    0.000    2.261    2.218
##    .t4_nf_sh_tt_10    2.215    0.034   65.894    0.000    2.215    2.205
##    .t4_nf_sh_tt_11    2.296    0.033   68.947    0.000    2.296    2.307
##    .t5_nf_sh_tt_01    1.996    0.041   49.046    0.000    1.996    1.646
##    .t5_nf_sh_tt_02    1.985    0.037   54.042    0.000    1.985    1.812
##    .t5_nf_sh_tt_03    2.840    0.036   77.951    0.000    2.840    2.612
##    .t5_nf_sh_tt_04    3.046    0.034   89.607    0.000    3.046    3.000
##    .t5_nf_sh_tt_05    2.727    0.033   81.571    0.000    2.727    2.731
##    .t5_nf_sh_tt_06    2.421    0.036   67.652    0.000    2.421    2.265
##    .t5_nf_sh_tt_07    3.161    0.034   91.747    0.000    3.161    3.072
##    .t5_nf_sh_tt_08    2.320    0.034   68.148    0.000    2.320    2.282
##    .t5_nf_sh_tt_10    2.269    0.034   67.717    0.000    2.269    2.268
##    .t5_nf_sh_tt_11    2.332    0.034   68.877    0.000    2.332    2.307
##    .t1_nf_sh_bh_01    1.743    0.036   47.799    0.000    1.743    1.602
##    .t1_nf_sh_bh_02    1.260    0.020   61.591    0.000    1.260    2.064
##    .t1_nf_sh_bh_03    2.732    0.034   80.480    0.000    2.732    2.693
##    .t1_nf_sh_bh_04    2.774    0.034   82.232    0.000    2.774    2.752
##    .t1_nf_sh_bh_05    2.599    0.032   79.995    0.000    2.599    2.678
##    .t1_nf_sh_bh_06    2.494    0.033   75.548    0.000    2.494    2.529
##    .t1_nf_sh_bh_07    2.951    0.034   85.761    0.000    2.951    2.870
##    .t1_nf_sh_bh_08    2.234    0.034   65.520    0.000    2.234    2.195
##    .t1_nf_sh_bh_10    1.796    0.030   59.220    0.000    1.796    1.984
##    .t1_nf_sh_bh_11    1.728    0.029   59.764    0.000    1.728    2.002
##    .t3_nf_sh_bh_01    1.777    0.037   48.057    0.000    1.777    1.609
##    .t3_nf_sh_bh_02    1.246    0.018   69.171    0.000    1.246    2.315
##    .t3_nf_sh_bh_03    2.677    0.032   84.861    0.000    2.677    2.840
##    .t3_nf_sh_bh_04    2.742    0.031   87.082    0.000    2.742    2.914
##    .t3_nf_sh_bh_05    2.566    0.031   83.726    0.000    2.566    2.802
##    .t3_nf_sh_bh_06    2.450    0.031   78.827    0.000    2.450    2.638
##    .t3_nf_sh_bh_07    2.944    0.034   87.791    0.000    2.944    2.939
##    .t3_nf_sh_bh_08    2.239    0.032   69.539    0.000    2.239    2.330
##    .t3_nf_sh_bh_10    1.785    0.029   61.200    0.000    1.785    2.049
##    .t3_nf_sh_bh_11    1.719    0.027   63.285    0.000    1.719    2.119
##    .t4_nf_sh_bh_01    1.915    0.041   46.493    0.000    1.915    1.558
##    .t4_nf_sh_bh_02    1.249    0.019   64.576    0.000    1.249    2.161
##    .t4_nf_sh_bh_03    2.727    0.033   82.974    0.000    2.727    2.778
##    .t4_nf_sh_bh_04    2.812    0.033   85.450    0.000    2.812    2.861
##    .t4_nf_sh_bh_05    2.590    0.032   81.356    0.000    2.590    2.724
##    .t4_nf_sh_bh_06    2.450    0.032   75.484    0.000    2.450    2.528
##    .t4_nf_sh_bh_07    2.966    0.034   87.943    0.000    2.966    2.945
##    .t4_nf_sh_bh_08    2.231    0.033   67.860    0.000    2.231    2.273
##    .t4_nf_sh_bh_10    1.808    0.030   61.109    0.000    1.808    2.046
##    .t4_nf_sh_bh_11    1.757    0.027   64.129    0.000    1.757    2.147
##    .t5_nf_sh_bh_01    2.958    0.049   60.056    0.000    2.958    2.023
##    .t5_nf_sh_bh_02    3.084    0.055   56.215    0.000    3.084    1.897
##    .t5_nf_sh_bh_03    2.507    0.045   56.063    0.000    2.507    1.888
##    .t5_nf_sh_bh_04    2.493    0.045   55.591    0.000    2.493    1.872
##    .t5_nf_sh_bh_05    2.565    0.044   57.862    0.000    2.565    1.949
##    .t5_nf_sh_bh_06    2.604    0.045   58.311    0.000    2.604    1.965
##    .t5_nf_sh_bh_07    2.482    0.044   56.031    0.000    2.482    1.888
##    .t5_nf_sh_bh_08    2.725    0.045   60.170    0.000    2.725    2.030
##    .t5_nf_sh_bh_10    2.832    0.046   60.926    0.000    2.832    2.055
##    .t5_nf_sh_bh_11    2.857    0.047   61.091    0.000    2.857    2.061
##     t1_pri_con_f      0.000                               0.000    0.000
##     t3_pri_con_f      0.000                               0.000    0.000
##     t4_pri_con_f      0.000                               0.000    0.000
##     t5_pri_con_f      0.000                               0.000    0.000
##    .t1_pri_con_f1     0.000                               0.000    0.000
##    .t1_pri_con_f2     0.000                               0.000    0.000
##    .t3_pri_con_f1     0.000                               0.000    0.000
##    .t3_pri_con_f2     0.000                               0.000    0.000
##    .t4_pri_con_f1     0.000                               0.000    0.000
##    .t4_pri_con_f2     0.000                               0.000    0.000
##    .t5_pri_con_f1     0.000                               0.000    0.000
##    .t5_pri_con_f2     0.000                               0.000    0.000
##     t1_inf_sh_tt_f    0.000                               0.000    0.000
##     t3_inf_sh_tt_f    0.000                               0.000    0.000
##     t4_inf_sh_tt_f    0.000                               0.000    0.000
##     t5_inf_sh_tt_f    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t1_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t3_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t4_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t4_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t4_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t4_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t4_nf_sh_tt_f5    0.000                               0.000    0.000
##    .t5_nf_sh_tt_f1    0.000                               0.000    0.000
##    .t5_nf_sh_tt_f2    0.000                               0.000    0.000
##    .t5_nf_sh_tt_f3    0.000                               0.000    0.000
##    .t5_nf_sh_tt_f4    0.000                               0.000    0.000
##    .t5_nf_sh_tt_f5    0.000                               0.000    0.000
##     t1_inf_sh_bh_f    0.000                               0.000    0.000
##     t3_inf_sh_bh_f    0.000                               0.000    0.000
##     t4_inf_sh_bh_f    0.000                               0.000    0.000
##     t5_inf_sh_bh_f    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t1_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t3_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t4_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t4_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t4_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t4_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t4_nf_sh_bh_f5    0.000                               0.000    0.000
##    .t5_nf_sh_bh_f1    0.000                               0.000    0.000
##    .t5_nf_sh_bh_f2    0.000                               0.000    0.000
##    .t5_nf_sh_bh_f3    0.000                               0.000    0.000
##    .t5_nf_sh_bh_f4    0.000                               0.000    0.000
##    .t5_nf_sh_bh_f5    0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .t1_pri_con_04     0.347    0.024   14.322    0.000    0.347    0.311
##    .t1_pri_con_05     0.977    0.053   18.566    0.000    0.977    0.572
##    .t1_pri_con_06     0.593    0.035   17.043    0.000    0.593    0.430
##    .t1_pri_con_07     0.572    0.034   16.821    0.000    0.572    0.363
##    .t1_pri_con_08     0.419    0.027   15.608    0.000    0.419    0.307
##    .t1_pri_con_09     0.321    0.021   15.357    0.000    0.321    0.293
##    .t3_pri_con_04     0.399    0.025   15.980    0.000    0.399    0.358
##    .t3_pri_con_05     1.028    0.054   19.021    0.000    1.028    0.602
##    .t3_pri_con_06     0.546    0.032   17.239    0.000    0.546    0.428
##    .t3_pri_con_07     0.481    0.029   16.369    0.000    0.481    0.314
##    .t3_pri_con_08     0.358    0.024   15.045    0.000    0.358    0.266
##    .t3_pri_con_09     0.339    0.021   15.970    0.000    0.339    0.295
##    .t4_pri_con_04     0.373    0.024   15.375    0.000    0.373    0.330
##    .t4_pri_con_05     0.945    0.050   18.790    0.000    0.945    0.568
##    .t4_pri_con_06     0.509    0.030   16.962    0.000    0.509    0.398
##    .t4_pri_con_07     0.514    0.031   16.639    0.000    0.514    0.339
##    .t4_pri_con_08     0.363    0.024   15.086    0.000    0.363    0.278
##    .t4_pri_con_09     0.359    0.022   16.267    0.000    0.359    0.317
##    .t5_pri_con_04     0.318    0.022   14.204    0.000    0.318    0.280
##    .t5_pri_con_05     0.970    0.051   18.902    0.000    0.970    0.555
##    .t5_pri_con_06     0.488    0.029   16.860    0.000    0.488    0.369
##    .t5_pri_con_07     0.526    0.031   16.995    0.000    0.526    0.334
##    .t5_pri_con_08     0.360    0.024   15.331    0.000    0.360    0.267
##    .t5_pri_con_09     0.331    0.021   15.833    0.000    0.331    0.291
##    .t1_nf_sh_tt_01    0.684    0.058   11.812    0.000    0.684    0.541
##    .t1_nf_sh_tt_02    0.742    0.054   13.838    0.000    0.742    0.610
##    .t1_nf_sh_tt_03    0.180    0.014   12.905    0.000    0.180    0.168
##    .t1_nf_sh_tt_04    0.197    0.014   14.107    0.000    0.197    0.187
##    .t1_nf_sh_tt_05    0.111    0.013    8.796    0.000    0.111    0.100
##    .t1_nf_sh_tt_06    0.260    0.016   16.243    0.000    0.260    0.221
##    .t1_nf_sh_tt_07    0.466    0.032   14.613    0.000    0.466    0.395
##    .t1_nf_sh_tt_08    0.576    0.032   17.903    0.000    0.576    0.510
##    .t1_nf_sh_tt_10    0.195    0.026    7.401    0.000    0.195    0.168
##    .t1_nf_sh_tt_11    0.186    0.025    7.396    0.000    0.186    0.168
##    .t3_nf_sh_tt_01    0.747    0.057   13.194    0.000    0.747    0.596
##    .t3_nf_sh_tt_02    0.700    0.050   14.083    0.000    0.700    0.627
##    .t3_nf_sh_tt_03    0.147    0.013   11.116    0.000    0.147    0.141
##    .t3_nf_sh_tt_04    0.196    0.014   13.963    0.000    0.196    0.186
##    .t3_nf_sh_tt_05    0.161    0.015   10.847    0.000    0.161    0.151
##    .t3_nf_sh_tt_06    0.294    0.019   15.894    0.000    0.294    0.262
##    .t3_nf_sh_tt_07    0.497    0.032   15.629    0.000    0.497    0.448
##    .t3_nf_sh_tt_08    0.592    0.032   18.279    0.000    0.592    0.554
##    .t3_nf_sh_tt_10    0.131    0.025    5.317    0.000    0.131    0.122
##    .t3_nf_sh_tt_11    0.177    0.024    7.245    0.000    0.177    0.164
##    .t4_nf_sh_tt_01    0.892    0.066   13.463    0.000    0.892    0.610
##    .t4_nf_sh_tt_02    0.697    0.055   12.663    0.000    0.697    0.598
##    .t4_nf_sh_tt_03    0.504    0.030   16.843    0.000    0.504    0.422
##    .t4_nf_sh_tt_04    0.374    0.025   14.776    0.000    0.374    0.360
##    .t4_nf_sh_tt_05    0.143    0.015    9.849    0.000    0.143    0.148
##    .t4_nf_sh_tt_06    0.296    0.018   16.317    0.000    0.296    0.281
##    .t4_nf_sh_tt_07    0.507    0.032   15.618    0.000    0.507    0.481
##    .t4_nf_sh_tt_08    0.614    0.034   18.105    0.000    0.614    0.591
##    .t4_nf_sh_tt_10    0.141    0.024    5.922    0.000    0.141    0.140
##    .t4_nf_sh_tt_11    0.161    0.022    7.315    0.000    0.161    0.162
##    .t5_nf_sh_tt_01    0.855    0.070   12.237    0.000    0.855    0.582
##    .t5_nf_sh_tt_02    0.696    0.055   12.582    0.000    0.696    0.580
##    .t5_nf_sh_tt_03    0.519    0.030   17.217    0.000    0.519    0.439
##    .t5_nf_sh_tt_04    0.393    0.025   15.883    0.000    0.393    0.382
##    .t5_nf_sh_tt_05    0.099    0.014    7.299    0.000    0.099    0.099
##    .t5_nf_sh_tt_06    0.317    0.019   16.498    0.000    0.317    0.278
##    .t5_nf_sh_tt_07    0.522    0.034   15.484    0.000    0.522    0.493
##    .t5_nf_sh_tt_08    0.616    0.034   17.944    0.000    0.616    0.596
##    .t5_nf_sh_tt_10    0.103    0.023    4.574    0.000    0.103    0.103
##    .t5_nf_sh_tt_11    0.164    0.022    7.430    0.000    0.164    0.161
##    .t1_nf_sh_bh_01    0.793    0.060   13.240    0.000    0.793    0.670
##    .t1_nf_sh_bh_02    0.302    0.016   18.320    0.000    0.302    0.810
##    .t1_nf_sh_bh_03    0.072    0.007   10.563    0.000    0.072    0.070
##    .t1_nf_sh_bh_04    0.067    0.007    9.892    0.000    0.067    0.066
##    .t1_nf_sh_bh_05    0.050    0.007    6.750    0.000    0.050    0.053
##    .t1_nf_sh_bh_06    0.153    0.009   16.308    0.000    0.153    0.158
##    .t1_nf_sh_bh_07    0.360    0.024   15.099    0.000    0.360    0.341
##    .t1_nf_sh_bh_08    0.515    0.027   18.870    0.000    0.515    0.497
##    .t1_nf_sh_bh_10    0.116    0.019    6.138    0.000    0.116    0.141
##    .t1_nf_sh_bh_11    0.194    0.017   11.740    0.000    0.194    0.261
##    .t3_nf_sh_bh_01    0.934    0.061   15.318    0.000    0.934    0.765
##    .t3_nf_sh_bh_02    0.238    0.013   17.882    0.000    0.238    0.821
##    .t3_nf_sh_bh_03    0.069    0.006   10.820    0.000    0.069    0.078
##    .t3_nf_sh_bh_04    0.072    0.007   10.991    0.000    0.072    0.081
##    .t3_nf_sh_bh_05    0.056    0.007    7.581    0.000    0.056    0.066
##    .t3_nf_sh_bh_06    0.145    0.009   15.819    0.000    0.145    0.168
##    .t3_nf_sh_bh_07    0.351    0.023   15.154    0.000    0.351    0.349
##    .t3_nf_sh_bh_08    0.435    0.024   18.404    0.000    0.435    0.471
##    .t3_nf_sh_bh_10    0.105    0.017    6.176    0.000    0.105    0.139
##    .t3_nf_sh_bh_11    0.147    0.014   10.520    0.000    0.147    0.223
##    .t4_nf_sh_bh_01    1.045    0.074   14.181    0.000    1.045    0.691
##    .t4_nf_sh_bh_02    0.249    0.015   16.828    0.000    0.249    0.747
##    .t4_nf_sh_bh_03    0.130    0.011   11.989    0.000    0.130    0.135
##    .t4_nf_sh_bh_04    0.138    0.011   12.613    0.000    0.138    0.143
##    .t4_nf_sh_bh_05    0.094    0.011    8.947    0.000    0.094    0.104
##    .t4_nf_sh_bh_06    0.197    0.012   15.832    0.000    0.197    0.210
##    .t4_nf_sh_bh_07    0.419    0.027   15.719    0.000    0.419    0.413
##    .t4_nf_sh_bh_08    0.519    0.028   18.805    0.000    0.519    0.539
##    .t4_nf_sh_bh_10    0.125    0.017    7.158    0.000    0.125    0.160
##    .t4_nf_sh_bh_11    0.156    0.015   10.783    0.000    0.156    0.233
##    .t5_nf_sh_bh_01   -2.452    0.362   -6.781    0.000   -2.452   -1.147
##    .t5_nf_sh_bh_02    1.813    0.118   15.341    0.000    1.813    0.686
##    .t5_nf_sh_bh_03    0.080    0.007   11.660    0.000    0.080    0.045
##    .t5_nf_sh_bh_04    0.103    0.007   13.710    0.000    0.103    0.058
##    .t5_nf_sh_bh_05    0.006    0.007    0.923    0.356    0.006    0.004
##    .t5_nf_sh_bh_06    0.172    0.010   16.581    0.000    0.172    0.098
##    .t5_nf_sh_bh_07    0.335    0.029   11.685    0.000    0.335    0.194
##    .t5_nf_sh_bh_08    0.760    0.041   18.366    0.000    0.760    0.422
##    .t5_nf_sh_bh_10   -0.133    0.043   -3.073    0.002   -0.133   -0.070
##    .t5_nf_sh_bh_11    0.331    0.039    8.563    0.000    0.331    0.172
##     t1_pri_con_f      0.669    0.043   15.569    0.000    1.000    1.000
##     t3_pri_con_f      0.700    0.044   15.965    0.000    1.000    1.000
##     t4_pri_con_f      0.701    0.044   15.968    0.000    1.000    1.000
##     t5_pri_con_f      0.737    0.046   16.075    0.000    1.000    1.000
##    .t1_pri_con_f1     0.102    0.019    5.459    0.000    0.132    0.132
##    .t1_pri_con_f2     0.108    0.022    4.890    0.000    0.107    0.107
##    .t3_pri_con_f1     0.017    0.015    1.109    0.267    0.024    0.024
##    .t3_pri_con_f2     0.114    0.020    5.735    0.000    0.108    0.108
##    .t4_pri_con_f1     0.056    0.016    3.393    0.001    0.073    0.073
##    .t4_pri_con_f2     0.063    0.019    3.330    0.001    0.063    0.063
##    .t5_pri_con_f1     0.081    0.017    4.649    0.000    0.099    0.099
##    .t5_pri_con_f2     0.060    0.019    3.074    0.002    0.057    0.057
##     t1_inf_sh_tt_f    0.127    0.017    7.326    0.000    1.000    1.000
##     t3_inf_sh_tt_f    0.117    0.016    7.305    0.000    1.000    1.000
##     t4_inf_sh_tt_f    0.102    0.014    7.280    0.000    1.000    1.000
##     t5_inf_sh_tt_f    0.107    0.015    7.269    0.000    1.000    1.000
##    .t1_nf_sh_tt_f1    0.453    0.052    8.774    0.000    0.781    0.781
##    .t1_nf_sh_tt_f2    0.070    0.014    5.027    0.000    0.079    0.079
##    .t1_nf_sh_tt_f3    0.133    0.016    8.137    0.000    0.134    0.134
##    .t1_nf_sh_tt_f4    0.145    0.023    6.340    0.000    0.203    0.203
##    .t1_nf_sh_tt_f5    0.707    0.044   16.071    0.000    0.733    0.733
##    .t3_nf_sh_tt_f1    0.390    0.047    8.377    0.000    0.770    0.770
##    .t3_nf_sh_tt_f2    0.139    0.016    8.865    0.000    0.156    0.156
##    .t3_nf_sh_tt_f3    0.107    0.016    6.464    0.000    0.118    0.118
##    .t3_nf_sh_tt_f4    0.090    0.021    4.208    0.000    0.146    0.146
##    .t3_nf_sh_tt_f5    0.706    0.043   16.422    0.000    0.748    0.748
##    .t4_nf_sh_tt_f1    0.470    0.054    8.634    0.000    0.822    0.822
##    .t4_nf_sh_tt_f2    0.033    0.018    1.799    0.072    0.047    0.047
##    .t4_nf_sh_tt_f3    0.131    0.017    7.630    0.000    0.159    0.159
##    .t4_nf_sh_tt_f4    0.092    0.022    4.298    0.000    0.169    0.169
##    .t4_nf_sh_tt_f5    0.661    0.041   16.309    0.000    0.762    0.762
##    .t5_nf_sh_tt_f1    0.508    0.058    8.782    0.000    0.826    0.826
##    .t5_nf_sh_tt_f2   -0.030    0.017   -1.785    0.074   -0.045   -0.045
##    .t5_nf_sh_tt_f3    0.168    0.018    9.198    0.000    0.187    0.187
##    .t5_nf_sh_tt_f4    0.058    0.021    2.761    0.006    0.107    0.107
##    .t5_nf_sh_tt_f5    0.679    0.041   16.607    0.000    0.757    0.757
##     t1_inf_sh_bh_f    0.148    0.015    9.689    0.000    1.000    1.000
##     t3_inf_sh_bh_f    0.127    0.013    9.666    0.000    1.000    1.000
##     t4_inf_sh_bh_f    0.127    0.013    9.609    0.000    1.000    1.000
##     t5_inf_sh_bh_f    0.297    0.031    9.647    0.000    1.000    1.000
##    .t1_nf_sh_bh_f1    0.243    0.047    5.215    0.000    0.621    0.621
##    .t1_nf_sh_bh_f2    0.127    0.012   10.872    0.000    0.133    0.133
##    .t1_nf_sh_bh_f3    0.090    0.011    8.079    0.000    0.101    0.101
##    .t1_nf_sh_bh_f4    0.013    0.016    0.810    0.418    0.019    0.019
##    .t1_nf_sh_bh_f5    0.478    0.030   15.803    0.000    0.679    0.679
##    .t3_nf_sh_bh_f1    0.159    0.040    3.976    0.000    0.557    0.557
##    .t3_nf_sh_bh_f2    0.109    0.011   10.249    0.000    0.133    0.133
##    .t3_nf_sh_bh_f3    0.094    0.011    8.802    0.000    0.120    0.120
##    .t3_nf_sh_bh_f4    0.066    0.016    4.079    0.000    0.101    0.101
##    .t3_nf_sh_bh_f5    0.460    0.028   16.172    0.000    0.703    0.703
##    .t4_nf_sh_bh_f1    0.340    0.055    6.158    0.000    0.728    0.728
##    .t4_nf_sh_bh_f2    0.122    0.014    8.966    0.000    0.147    0.147
##    .t4_nf_sh_bh_f3    0.121    0.014    8.795    0.000    0.149    0.149
##    .t4_nf_sh_bh_f4    0.008    0.017    0.468    0.640    0.013    0.013
##    .t4_nf_sh_bh_f5    0.462    0.029   15.913    0.000    0.704    0.704
##    .t5_nf_sh_bh_f1    4.293    0.398   10.792    0.000    0.935    0.935
##    .t5_nf_sh_bh_f2    0.024    0.010    2.425    0.015    0.014    0.014
##    .t5_nf_sh_bh_f3    0.119    0.013    9.030    0.000    0.069    0.069
##    .t5_nf_sh_bh_f4    0.024    0.023    1.041    0.298    0.017    0.017
##    .t5_nf_sh_bh_f5    1.579    0.090   17.618    0.000    0.777    0.777

Extract factor scores.

d_fs_all <- lavPredict(get(paste("fit", name, sep = "_")), type = "ov") %>% as.data.frame() %>% mutate(t1_pri_con_fs = rowMeans(select(., 
    starts_with("t1_pri"))), t3_pri_con_fs = rowMeans(select(., starts_with("t3_pri"))), t4_pri_con_fs = rowMeans(select(., 
    starts_with("t4_pri"))), t5_pri_con_fs = rowMeans(select(., starts_with("t5_pri"))), t1_inf_sha_att_fs = rowMeans(select(., 
    starts_with("t1_inf_sha_att"))), t3_inf_sha_att_fs = rowMeans(select(., starts_with("t3_inf_sha_att"))), t4_inf_sha_att_fs = rowMeans(select(., 
    starts_with("t4_inf_sha_att"))), t5_inf_sha_att_fs = rowMeans(select(., starts_with("t5_inf_sha_att"))), t1_inf_sha_beh_fs = rowMeans(select(., 
    starts_with("t1_inf_sha_beh"))), t3_inf_sha_beh_fs = rowMeans(select(., starts_with("t3_inf_sha_beh"))), t4_inf_sha_beh_fs = rowMeans(select(., 
    starts_with("t4_inf_sha_beh"))), t5_inf_sha_beh_fs = rowMeans(select(., starts_with("t5_inf_sha_beh")))) %>% select(contains("_fs"))
d_wide_all <- cbind(d_fs_all, d_wide_all)

Run new model.

model <- '
# between relations
pri_con_b =~ 1*t1_pri_con_fs + 1*t3_pri_con_fs + 1*t4_pri_con_fs + 1*t5_pri_con_fs
inf_sha_beh_b =~ 1*t1_inf_sha_beh_fs + 1*t3_inf_sha_beh_fs + 1*t4_inf_sha_beh_fs  + 1*t5_inf_sha_beh_fs
inf_sha_att_b =~ 1*t1_inf_sha_att_fs + 1*t3_inf_sha_att_fs + 1*t4_inf_sha_att_fs + 1*t5_inf_sha_att_fs

# within person changes
t1_pri_con_w =~ 1*t1_pri_con_fs
t3_pri_con_w =~ 1*t3_pri_con_fs
t4_pri_con_w =~ 1*t4_pri_con_fs
t5_pri_con_w =~ 1*t5_pri_con_fs
t1_inf_sha_beh_w =~ 1*t1_inf_sha_beh_fs
t3_inf_sha_beh_w =~ 1*t3_inf_sha_beh_fs
t4_inf_sha_beh_w =~ 1*t4_inf_sha_beh_fs
t5_inf_sha_beh_w =~ 1*t5_inf_sha_beh_fs
t1_inf_sha_att_w =~ 1*t1_inf_sha_att_fs
t3_inf_sha_att_w =~ 1*t3_inf_sha_att_fs
t4_inf_sha_att_w =~ 1*t4_inf_sha_att_fs
t5_inf_sha_att_w =~ 1*t5_inf_sha_att_fs

# within person effects
t3_pri_con_w ~ a1*t1_pri_con_w + a2*t1_inf_sha_att_w + a3*t1_inf_sha_beh_w
t3_inf_sha_att_w ~ b1*t1_pri_con_w + b2*t1_inf_sha_att_w + b3*t1_inf_sha_beh_w
t3_inf_sha_beh_w ~ c1*t1_pri_con_w + c2*t1_inf_sha_att_w + c3*t1_inf_sha_beh_w
t4_pri_con_w ~ a1*t3_pri_con_w + a2*t3_inf_sha_att_w + a3*t3_inf_sha_beh_w
t4_inf_sha_att_w ~ b1*t3_pri_con_w + b2*t3_inf_sha_att_w + b3*t3_inf_sha_beh_w
t4_inf_sha_beh_w ~ c1*t3_pri_con_w + c2*t3_inf_sha_att_w + c3*t3_inf_sha_beh_w
t5_pri_con_w ~ a1*t4_pri_con_w + a2*t4_inf_sha_att_w + a3*t4_inf_sha_beh_w
t5_inf_sha_att_w ~ b1*t4_pri_con_w + b2*t4_inf_sha_att_w + b3*t4_inf_sha_beh_w
t5_inf_sha_beh_w ~ c1*t4_pri_con_w + c2*t4_inf_sha_att_w + c3*t4_inf_sha_beh_w

# covariances
pri_con_b ~~ cor_b_1*inf_sha_att_b + cor_b_2*inf_sha_beh_b
inf_sha_att_b ~~ cor_b_3*inf_sha_beh_b
t1_pri_con_w ~~ cor_w_1*t1_inf_sha_att_w + cor_w_2*t1_inf_sha_beh_w
t1_inf_sha_att_w ~~ cor_w_3*t1_inf_sha_beh_w
t3_pri_con_w ~~ a*t3_inf_sha_att_w + b*t3_inf_sha_beh_w
t3_inf_sha_att_w ~~ c*t3_inf_sha_beh_w
t4_pri_con_w ~~ a*t4_inf_sha_att_w + b*t4_inf_sha_beh_w
t4_inf_sha_att_w ~~ c*t4_inf_sha_beh_w
t5_pri_con_w ~~ a*t5_inf_sha_att_w + b*t5_inf_sha_beh_w
t5_inf_sha_att_w ~~ c*t5_inf_sha_beh_w

# setting variances of observed variables to zero
t1_pri_con_fs ~~ 0*t1_pri_con_fs
t3_pri_con_fs ~~ 0*t3_pri_con_fs
t4_pri_con_fs ~~ 0*t4_pri_con_fs
t5_pri_con_fs ~~ 0*t5_pri_con_fs
t1_inf_sha_att_fs ~~ 0*t1_inf_sha_att_fs
t3_inf_sha_att_fs ~~ 0*t3_inf_sha_att_fs
t4_inf_sha_att_fs ~~ 0*t4_inf_sha_att_fs
t5_inf_sha_att_fs ~~ 0*t5_inf_sha_att_fs
t1_inf_sha_beh_fs ~~ 0*t1_inf_sha_beh_fs
t3_inf_sha_beh_fs ~~ 0*t3_inf_sha_beh_fs
t4_inf_sha_beh_fs ~~ 0*t4_inf_sha_beh_fs
t5_inf_sha_beh_fs ~~ 0*t5_inf_sha_beh_fs

# control variables
t1_pri_con_fs ~ age + edu_num + male
t3_pri_con_fs ~ age + edu_num + male
t4_pri_con_fs ~ age + edu_num + male
t5_pri_con_fs ~ age + edu_num + male
t1_inf_sha_beh_fs ~ age + edu_num + male
t3_inf_sha_beh_fs ~ age + edu_num + male
t4_inf_sha_beh_fs ~ age + edu_num + male
t5_inf_sha_beh_fs ~ age + edu_num + male
t1_inf_sha_att_fs ~ age + edu_num + male
t3_inf_sha_att_fs ~ age + edu_num + male
t4_inf_sha_att_fs ~ age + edu_num + male
t5_inf_sha_att_fs ~ age + edu_num + male
'
fit <- sem(model, data = d_wide_all, orthogonal = TRUE, missing = "ML")
summary(fit, standardized = TRUE, fit.measures = TRUE, ci = TRUE)
## lavaan 0.6-7 ended normally after 198 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        105
##   Number of equality constraints                    24
##                                                       
##                                                   Used       Total
##   Number of observations                           803         893
##   Number of missing patterns                         1            
##                                                                   
## Model Test User Model:
##                                                       
##   Test statistic                               308.866
##   Degrees of freedom                                45
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5562.601
##   Degrees of freedom                               102
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.952
##   Tucker-Lewis Index (TLI)                       0.890
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -8286.383
##   Loglikelihood unrestricted model (H1)      -8131.950
##                                                       
##   Akaike (AIC)                               16734.767
##   Bayesian (BIC)                             17114.524
##   Sample-size adjusted Bayesian (BIC)        16857.303
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085
##   90 Percent confidence interval - lower         0.077
##   90 Percent confidence interval - upper         0.095
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.082
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b =~                                                                               
##     t1_pri_con_fs        1.000                               1.000    1.000    0.721    0.852
##     t3_pri_con_fs        1.000                               1.000    1.000    0.721    0.842
##     t4_pri_con_fs        1.000                               1.000    1.000    0.721    0.831
##     t5_pri_con_fs        1.000                               1.000    1.000    0.721    0.829
##   inf_sha_beh_b =~                                                                           
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.418    0.649
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.418    0.707
##     t4_nf_sh_bh_fs       1.000                               1.000    1.000    0.418    0.696
##     t5_nf_sh_bh_fs       1.000                               1.000    1.000    0.418    0.284
##   inf_sha_att_b =~                                                                           
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.461    0.668
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.461    0.697
##     t4_nf_sh_tt_fs       1.000                               1.000    1.000    0.461    0.734
##     t5_nf_sh_tt_fs       1.000                               1.000    1.000    0.461    0.711
##   t1_pri_con_w =~                                                                            
##     t1_pri_con_fs        1.000                               1.000    1.000    0.412    0.487
##   t3_pri_con_w =~                                                                            
##     t3_pri_con_fs        1.000                               1.000    1.000    0.432    0.505
##   t4_pri_con_w =~                                                                            
##     t4_pri_con_fs        1.000                               1.000    1.000    0.453    0.522
##   t5_pri_con_w =~                                                                            
##     t5_pri_con_fs        1.000                               1.000    1.000    0.449    0.516
##   t1_inf_sha_beh_w =~                                                                        
##     t1_nf_sh_bh_fs       1.000                               1.000    1.000    0.472    0.732
##   t3_inf_sha_beh_w =~                                                                        
##     t3_nf_sh_bh_fs       1.000                               1.000    1.000    0.390    0.659
##   t4_inf_sha_beh_w =~                                                                        
##     t4_nf_sh_bh_fs       1.000                               1.000    1.000    0.406    0.676
##   t5_inf_sha_beh_w =~                                                                        
##     t5_nf_sh_bh_fs       1.000                               1.000    1.000    1.409    0.955
##   t1_inf_sha_att_w =~                                                                        
##     t1_nf_sh_tt_fs       1.000                               1.000    1.000    0.496    0.719
##   t3_inf_sha_att_w =~                                                                        
##     t3_nf_sh_tt_fs       1.000                               1.000    1.000    0.454    0.686
##   t4_inf_sha_att_w =~                                                                        
##     t4_nf_sh_tt_fs       1.000                               1.000    1.000    0.405    0.644
##   t5_inf_sha_att_w =~                                                                        
##     t5_nf_sh_tt_fs       1.000                               1.000    1.000    0.435    0.670
## 
## Regressions:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   t3_pri_con_w ~                                                                             
##     t1_pr_cn_ (a1)       0.263    0.043    6.163    0.000    0.180    0.347    0.251    0.251
##     t1_nf_s__ (a2)       0.011    0.028    0.408    0.683   -0.043    0.066    0.013    0.013
##     t1_nf_s__ (a3)      -0.039    0.033   -1.202    0.229   -0.104    0.025   -0.043   -0.043
##   t3_inf_sha_att_w ~                                                                         
##     t1_pr_cn_ (b1)       0.084    0.032    2.599    0.009    0.021    0.147    0.076    0.076
##     t1_nf_s__ (b2)       0.075    0.034    2.209    0.027    0.008    0.141    0.082    0.082
##     t1_nf_s__ (b3)       0.049    0.033    1.499    0.134   -0.015    0.114    0.051    0.051
##   t3_inf_sha_beh_w ~                                                                         
##     t1_pr_cn_ (c1)       0.013    0.040    0.332    0.740   -0.065    0.091    0.014    0.014
##     t1_nf_s__ (c2)       0.005    0.032    0.173    0.863   -0.057    0.067    0.007    0.007
##     t1_nf_s__ (c3)       0.110    0.054    2.057    0.040    0.005    0.215    0.133    0.133
##   t4_pri_con_w ~                                                                             
##     t3_pr_cn_ (a1)       0.263    0.043    6.163    0.000    0.180    0.347    0.252    0.252
##     t3_nf_s__ (a2)       0.011    0.028    0.408    0.683   -0.043    0.066    0.011    0.011
##     t3_nf_s__ (a3)      -0.039    0.033   -1.202    0.229   -0.104    0.025   -0.034   -0.034
##   t4_inf_sha_att_w ~                                                                         
##     t3_pr_cn_ (b1)       0.084    0.032    2.599    0.009    0.021    0.147    0.089    0.089
##     t3_nf_s__ (b2)       0.075    0.034    2.209    0.027    0.008    0.141    0.084    0.084
##     t3_nf_s__ (b3)       0.049    0.033    1.499    0.134   -0.015    0.114    0.047    0.047
##   t4_inf_sha_beh_w ~                                                                         
##     t3_pr_cn_ (c1)       0.013    0.040    0.332    0.740   -0.065    0.091    0.014    0.014
##     t3_nf_s__ (c2)       0.005    0.032    0.173    0.863   -0.057    0.067    0.006    0.006
##     t3_nf_s__ (c3)       0.110    0.054    2.057    0.040    0.005    0.215    0.106    0.106
##   t5_pri_con_w ~                                                                             
##     t4_pr_cn_ (a1)       0.263    0.043    6.163    0.000    0.180    0.347    0.265    0.265
##     t4_nf_s__ (a2)       0.011    0.028    0.408    0.683   -0.043    0.066    0.010    0.010
##     t4_nf_s__ (a3)      -0.039    0.033   -1.202    0.229   -0.104    0.025   -0.036   -0.036
##   t5_inf_sha_att_w ~                                                                         
##     t4_pr_cn_ (b1)       0.084    0.032    2.599    0.009    0.021    0.147    0.087    0.087
##     t4_nf_s__ (b2)       0.075    0.034    2.209    0.027    0.008    0.141    0.070    0.070
##     t4_nf_s__ (b3)       0.049    0.033    1.499    0.134   -0.015    0.114    0.046    0.046
##   t5_inf_sha_beh_w ~                                                                         
##     t4_pr_cn_ (c1)       0.013    0.040    0.332    0.740   -0.065    0.091    0.004    0.004
##     t4_nf_s__ (c2)       0.005    0.032    0.173    0.863   -0.057    0.067    0.002    0.002
##     t4_nf_s__ (c3)       0.110    0.054    2.057    0.040    0.005    0.215    0.032    0.032
##   t1_pri_con_fs ~                                                                            
##     age                  0.011    0.002    5.240    0.000    0.007    0.015    0.011    0.187
##     edu_num             -0.029    0.017   -1.678    0.093   -0.062    0.005   -0.029   -0.059
##     male                -0.019    0.061   -0.303    0.762   -0.138    0.101   -0.019   -0.011
##   t3_pri_con_fs ~                                                                            
##     age                  0.011    0.002    5.034    0.000    0.007    0.015    0.011    0.180
##     edu_num             -0.035    0.017   -2.009    0.044   -0.068   -0.001   -0.035   -0.071
##     male                -0.023    0.062   -0.372    0.710   -0.144    0.098   -0.023   -0.013
##   t4_pri_con_fs ~                                                                            
##     age                  0.011    0.002    4.992    0.000    0.007    0.015    0.011    0.178
##     edu_num             -0.045    0.017   -2.596    0.009   -0.079   -0.011   -0.045   -0.091
##     male                -0.014    0.063   -0.220    0.826   -0.137    0.109   -0.014   -0.008
##   t5_pri_con_fs ~                                                                            
##     age                  0.012    0.002    5.736    0.000    0.008    0.016    0.012    0.204
##     edu_num             -0.039    0.017   -2.260    0.024   -0.073   -0.005   -0.039   -0.079
##     male                -0.019    0.062   -0.307    0.759   -0.142    0.103   -0.019   -0.011
##   t1_inf_sha_beh_fs ~                                                                        
##     age                 -0.007    0.002   -4.311    0.000   -0.010   -0.004   -0.007   -0.153
##     edu_num              0.051    0.013    3.984    0.000    0.026    0.077    0.051    0.139
##     male                -0.113    0.046   -2.433    0.015   -0.204   -0.022   -0.113   -0.087
##   t3_inf_sha_beh_fs ~                                                                        
##     age                 -0.006    0.001   -4.397    0.000   -0.009   -0.004   -0.006   -0.155
##     edu_num              0.070    0.012    5.999    0.000    0.047    0.093    0.070    0.207
##     male                -0.097    0.042   -2.307    0.021   -0.180   -0.015   -0.097   -0.082
##   t4_inf_sha_beh_fs ~                                                                        
##     age                 -0.008    0.001   -5.440    0.000   -0.011   -0.005   -0.008   -0.192
##     edu_num              0.058    0.012    4.871    0.000    0.035    0.082    0.058    0.169
##     male                -0.021    0.043   -0.490    0.624   -0.105    0.063   -0.021   -0.017
##   t5_inf_sha_beh_fs ~                                                                        
##     age                  0.007    0.004    1.772    0.076   -0.001    0.014    0.007    0.064
##     edu_num             -0.048    0.030   -1.607    0.108   -0.107    0.011   -0.048   -0.057
##     male                -0.013    0.108   -0.125    0.901   -0.225    0.198   -0.013   -0.005
##   t1_inf_sha_att_fs ~                                                                        
##     age                 -0.003    0.002   -2.018    0.044   -0.007   -0.000   -0.003   -0.072
##     edu_num              0.027    0.014    1.967    0.049    0.000    0.054    0.027    0.069
##     male                -0.239    0.050   -4.786    0.000   -0.336   -0.141   -0.239   -0.172
##   t3_inf_sha_att_fs ~                                                                        
##     age                 -0.005    0.002   -3.208    0.001   -0.008   -0.002   -0.005   -0.114
##     edu_num              0.047    0.013    3.548    0.000    0.021    0.073    0.047    0.124
##     male                -0.188    0.048   -3.945    0.000   -0.281   -0.095   -0.188   -0.141
##   t4_inf_sha_att_fs ~                                                                        
##     age                 -0.006    0.002   -3.664    0.000   -0.009   -0.003   -0.006   -0.130
##     edu_num              0.047    0.013    3.777    0.000    0.023    0.072    0.047    0.132
##     male                -0.178    0.045   -3.940    0.000   -0.266   -0.089   -0.178   -0.141
##   t5_inf_sha_att_fs ~                                                                        
##     age                 -0.006    0.002   -3.766    0.000   -0.009   -0.003   -0.006   -0.134
##     edu_num              0.051    0.013    3.954    0.000    0.026    0.077    0.051    0.138
##     male                -0.165    0.047   -3.531    0.000   -0.256   -0.073   -0.165   -0.126
## 
## Covariances:
##                       Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##   pri_con_b ~~                                                                               
##     in___ (cr_b_1)      -0.118    0.015   -7.810    0.000   -0.148   -0.089   -0.355   -0.355
##     in___ (cr_b_2)      -0.044    0.014   -3.104    0.002   -0.072   -0.016   -0.147   -0.147
##   inf_sha_beh_b ~~                                                                           
##     in___ (cr_b_3)       0.127    0.011   11.406    0.000    0.105    0.149    0.659    0.659
##   t1_pri_con_w ~~                                                                            
##     t1___ (cr_w_1)      -0.013    0.010   -1.274    0.203   -0.033    0.007   -0.063   -0.063
##     t1___ (cr_w_2)      -0.014    0.010   -1.372    0.170   -0.034    0.006   -0.072   -0.072
##   t1_inf_sha_beh_w ~~                                                                        
##     t1___ (cr_w_3)       0.048    0.011    4.299    0.000    0.026    0.070    0.205    0.205
##  .t3_pri_con_w ~~                                                                            
##    .t3___      (a)      -0.012    0.005   -2.134    0.033   -0.022   -0.001   -0.062   -0.062
##    .t3___      (b)      -0.002    0.006   -0.322    0.747   -0.015    0.010   -0.013   -0.013
##  .t3_inf_sha_beh_w ~~                                                                        
##    .t3___      (c)       0.036    0.006    5.724    0.000    0.024    0.048    0.207    0.207
##  .t4_pri_con_w ~~                                                                            
##    .t4___      (a)      -0.012    0.005   -2.134    0.033   -0.022   -0.001   -0.067   -0.067
##    .t4___      (b)      -0.002    0.006   -0.322    0.747   -0.015    0.010   -0.012   -0.012
##  .t4_inf_sha_beh_w ~~                                                                        
##    .t4___      (c)       0.036    0.006    5.724    0.000    0.024    0.048    0.222    0.222
##  .t5_pri_con_w ~~                                                                            
##    .t5___      (a)      -0.012    0.005   -2.134    0.033   -0.022   -0.001   -0.063   -0.063
##    .t5___      (b)      -0.002    0.006   -0.322    0.747   -0.015    0.010   -0.003   -0.003
##  .t5_inf_sha_beh_w ~~                                                                        
##    .t5___      (c)       0.036    0.006    5.724    0.000    0.024    0.048    0.059    0.059
##   pri_con_b ~~                                                                               
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_beh_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##   inf_sha_att_b ~~                                                                           
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
##     t1___                0.000                               0.000    0.000    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     3.243    0.189   17.198    0.000    2.874    3.613    3.243    3.831
##    .t3_pri_con_fs     3.207    0.191   16.797    0.000    2.833    3.581    3.207    3.744
##    .t4_pri_con_fs     3.180    0.193   16.446    0.000    2.801    3.559    3.180    3.663
##    .t5_pri_con_fs     3.024    0.193   15.677    0.000    2.646    3.402    3.024    3.477
##    .t1_nf_sh_bh_fs    2.503    0.143   17.484    0.000    2.222    2.784    2.503    3.882
##    .t3_nf_sh_bh_fs    2.339    0.130   18.010    0.000    2.084    2.593    2.339    3.952
##    .t4_nf_sh_bh_fs    2.429    0.132   18.361    0.000    2.170    2.689    2.429    4.045
##    .t5_nf_sh_bh_fs    2.613    0.334    7.827    0.000    1.958    3.267    2.613    1.771
##    .t1_nf_sh_tt_fs    2.870    0.154   18.653    0.000    2.568    3.172    2.870    4.158
##    .t3_nf_sh_tt_fs    2.887    0.147   19.636    0.000    2.598    3.175    2.887    4.361
##    .t4_nf_sh_tt_fs    2.792    0.139   20.036    0.000    2.519    3.065    2.792    4.440
##    .t5_nf_sh_tt_fs    2.818    0.144   19.575    0.000    2.536    3.100    2.818    4.340
##     pri_con_b         0.000                               0.000    0.000    0.000    0.000
##     inf_sha_beh_b     0.000                               0.000    0.000    0.000    0.000
##     inf_sha_att_b     0.000                               0.000    0.000    0.000    0.000
##     t1_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t4_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##    .t5_pri_con_w      0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_bh_w    0.000                               0.000    0.000    0.000    0.000
##     t1_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t3_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t4_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
##    .t5_inf_sh_tt_w    0.000                               0.000    0.000    0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper   Std.lv  Std.all
##    .t1_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t3_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t4_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t5_pri_con_fs     0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t4_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t5_nf_sh_tt_fs    0.000                               0.000    0.000    0.000    0.000
##    .t1_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t3_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t4_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##    .t5_nf_sh_bh_fs    0.000                               0.000    0.000    0.000    0.000
##     pri_con_b         0.520    0.030   17.329    0.000    0.462    0.579    1.000    1.000
##     inf_sha_beh_b     0.175    0.016   11.151    0.000    0.144    0.206    1.000    1.000
##     inf_sha_att_b     0.213    0.014   14.980    0.000    0.185    0.241    1.000    1.000
##     t1_pri_con_w      0.170    0.013   12.665    0.000    0.143    0.196    1.000    1.000
##    .t3_pri_con_w      0.175    0.012   14.045    0.000    0.150    0.199    0.934    0.934
##    .t4_pri_con_w      0.192    0.014   13.990    0.000    0.165    0.219    0.936    0.936
##    .t5_pri_con_w      0.187    0.012   16.143    0.000    0.165    0.210    0.928    0.928
##     t1_inf_sh_bh_w    0.223    0.017   13.215    0.000    0.190    0.256    1.000    1.000
##    .t3_inf_sh_bh_w    0.149    0.013   11.276    0.000    0.123    0.175    0.982    0.982
##    .t4_inf_sh_bh_w    0.163    0.011   14.544    0.000    0.141    0.185    0.988    0.988
##    .t5_inf_sh_bh_w    1.985    0.101   19.667    0.000    1.787    2.182    0.999    0.999
##     t1_inf_sh_tt_w    0.246    0.015   16.263    0.000    0.217    0.276    1.000    1.000
##    .t3_inf_sh_tt_w    0.203    0.013   15.964    0.000    0.178    0.228    0.985    0.985
##    .t4_inf_sh_tt_w    0.161    0.011   14.001    0.000    0.138    0.183    0.982    0.982
##    .t5_inf_sh_tt_w    0.186    0.012   16.136    0.000    0.164    0.209    0.985    0.985
fit_riclpm_5w <- fit

The results show the same between person effects. Within-person effects disappear, which is understandable given the longer interval. Effects hence remain stable also across longer time intervals and until 2018.

2.2 Mixed Models

In what follows, we also present the results of several mixed models. Using mixed models, we can include more data. However, one downside is that not all research questions can be answered in one single model.

2.2.1 Two Variables

2.2.1.1 Model 1

Measures overall correlation between privacy concerns and information sharing.

fit <- lmer(pri_con_m ~ 1 + inf_sha_beh_m + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: pri_con_m ~ 1 + inf_sha_beh_m + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 16584
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.758 -0.477  0.061  0.516  4.998 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.5807   0.7620  
##  wave     (Intercept) 0.0035   0.0592  
##  Residual             0.2243   0.4736  
## Number of obs: 8191, groups:  id, 2735; wave, 5
## 
## Fixed effects:
##               Estimate Std. Error t value
## (Intercept)    3.65461    0.03721   98.21
## inf_sha_beh_m -0.02822    0.00913   -3.09
## 
## Correlation of Fixed Effects:
##             (Intr)
## inf_sh_bh_m -0.551
std_beta(fit)

2.2.1.2 Model 2

Measures how current levels of information sharing are affected by generel levels of privacy concern und current levels of privacy concern.

fit <- lmer(inf_sha_beh_m ~ pri_con_m_b + pri_con_m_w + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_beh_m ~ pri_con_m_b + pri_con_m_w + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 18196
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -3.589 -0.512 -0.069  0.474  4.228 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.1421   0.377   
##  wave     (Intercept) 0.0749   0.274   
##  Residual             0.4329   0.658   
## Number of obs: 8191, groups:  id, 2735; wave, 5
## 
## Fixed effects:
##             Estimate Std. Error t value
## (Intercept)  2.24448    0.12293   18.26
## pri_con_m_b -0.06339    0.01150   -5.51
## pri_con_m_w -0.00259    0.01881   -0.14
## 
## Correlation of Fixed Effects:
##             (Intr) pr_cn_m_b
## pri_con_m_b 0.002           
## pri_con_m_w 0.004  0.003
std_beta(fit)

Measures how current levels of privacy concern are affected by generel levels of information sharing und current levels of information sharing.

fit <- lmer(pri_con_m ~ inf_sha_beh_m_b + inf_sha_beh_m_w + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: pri_con_m ~ inf_sha_beh_m_b + inf_sha_beh_m_w + (1 | id) + (1 |      wave)
##    Data: d_long
## 
## REML criterion at convergence: 16576
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.726 -0.480  0.059  0.511  5.007 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.57905  0.7610  
##  wave     (Intercept) 0.00345  0.0587  
##  Residual             0.22409  0.4734  
## Number of obs: 8191, groups:  id, 2735; wave, 5
## 
## Fixed effects:
##                 Estimate Std. Error t value
## (Intercept)      3.60976    0.03130  115.32
## inf_sha_beh_m_b -0.11176    0.02451   -4.56
## inf_sha_beh_m_w -0.01542    0.00927   -1.66
## 
## Correlation of Fixed Effects:
##               (Intr) inf_sh_bh_m_b
## inf_sh_bh_m_b -0.091              
## inf_sh_bh_m_w -0.144  0.090
std_beta(fit)

2.2.1.3 Model 3

Includes control variables.

fit <- lmer(inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + male + age + edu_num + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + male + age +      edu_num + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 16456
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -3.762 -0.519 -0.067  0.471  4.271 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.1167   0.342   
##  wave     (Intercept) 0.0786   0.280   
##  Residual             0.4307   0.656   
## Number of obs: 7506, groups:  id, 2521; wave, 5
## 
## Fixed effects:
##              Estimate Std. Error t value
## (Intercept)  2.633209   0.140093   18.80
## pri_con_m_b -0.053749   0.011472   -4.69
## pri_con_m_w -0.006160   0.019520   -0.32
## male        -0.131022   0.021633   -6.06
## age         -0.009026   0.000679  -13.29
## edu_num      0.058070   0.006248    9.29
## 
## Correlation of Fixed Effects:
##             (Intr) pr_cn_m_b pr_cn_m_w male   age   
## pri_con_m_b  0.023                                  
## pri_con_m_w  0.006  0.004                           
## male        -0.295 -0.024     0.001                 
## age         -0.280 -0.066    -0.012     0.156       
## edu_num     -0.228  0.012    -0.001     0.105 -0.077
## optimizer (nloptwrap) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.011047 (tol = 0.002, component 1)
std_beta(fit)
fit <- lmer(pri_con_m ~ 1 + inf_sha_beh_m_b + inf_sha_beh_m_w + male + age + edu_num + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: pri_con_m ~ 1 + inf_sha_beh_m_b + inf_sha_beh_m_w + male + age +      edu_num + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 15113
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.705 -0.474  0.057  0.512  4.953 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.53582  0.7320  
##  wave     (Intercept) 0.00448  0.0669  
##  Residual             0.22597  0.4754  
## Number of obs: 7506, groups:  id, 2521; wave, 5
## 
## Fixed effects:
##                  Estimate Std. Error t value
## (Intercept)      3.029006   0.096670   31.33
## inf_sha_beh_m_b -0.112531   0.025204   -4.46
## inf_sha_beh_m_w -0.007509   0.009735   -0.77
## male             0.031984   0.032493    0.98
## age              0.013018   0.000996   13.07
## edu_num         -0.032105   0.009520   -3.37
## 
## Correlation of Fixed Effects:
##               (Intr) inf_sh_bh_m_b inf_sh_bh_m_w male   age   
## inf_sh_bh_m_b  0.011                                          
## inf_sh_bh_m_w -0.094  0.092                                   
## male          -0.627  0.066         0.022                     
## age           -0.580 -0.017         0.085         0.139       
## edu_num       -0.489 -0.132        -0.026         0.090 -0.077
std_beta(fit)

2.2.2 Three Variables

2.2.2.1 Model 1

Measures how current levels of information sharing are affected by generel levels of privacy concern and current levels of privacy concern, as well as general levels of positive attitude toward information sharing and current levels of positive attitude toward information sharing.

fit <- lmer(inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_att_m_b + inf_sha_att_m_w + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_att_m_b +      inf_sha_att_m_w + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 17959
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -3.771 -0.511 -0.077  0.472  4.344 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.1243   0.353   
##  wave     (Intercept) 0.0743   0.272   
##  Residual             0.4296   0.655   
## Number of obs: 8176, groups:  id, 2732; wave, 5
## 
## Fixed effects:
##                 Estimate Std. Error t value
## (Intercept)      2.23710    0.12236   18.28
## pri_con_m_b     -0.04412    0.01122   -3.93
## pri_con_m_w      0.00227    0.01877    0.12
## inf_sha_att_m_b  0.14891    0.01130   13.18
## inf_sha_att_m_w  0.12581    0.01964    6.40
## 
## Correlation of Fixed Effects:
##               (Intr) pr_cn_m_b pr_cn_m_w inf_sh_tt_m_b
## pri_con_m_b    0.002                                  
## pri_con_m_w    0.004  0.003                           
## inf_sh_tt_m_b -0.004  0.119     0.000                 
## inf_sh_tt_m_w  0.000  0.004     0.031     0.003
std_beta(fit)

Measures how current levels of positive attitude toward information sharing are affected by generel levels of privacy concern and current levels of privacy concern, as well as general levels of information sharing and current levels of information sharing.

fit <- lmer(inf_sha_att_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_beh_m_b + inf_sha_beh_m_w + (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_att_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_beh_m_b +      inf_sha_beh_m_w + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 13896
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.147 -0.528  0.024  0.526  5.917 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.22725  0.4767  
##  wave     (Intercept) 0.00198  0.0445  
##  Residual             0.20112  0.4485  
## Number of obs: 8176, groups:  id, 2732; wave, 5
## 
## Fixed effects:
##                 Estimate Std. Error t value
## (Intercept)       2.2988     0.0232   98.90
## pri_con_m_b      -0.1643     0.0115  -14.33
## pri_con_m_w      -0.0300     0.0129   -2.34
## inf_sha_beh_m_b   0.2216     0.0166   13.36
## inf_sha_beh_m_w   0.1021     0.0085   12.02
## 
## Correlation of Fixed Effects:
##               (Intr) pr_cn_m_b pr_cn_m_w inf_sh_bh_m_b
## pri_con_m_b   -0.005                                  
## pri_con_m_w    0.015  0.000                           
## inf_sh_bh_m_b -0.115  0.100    -0.014                 
## inf_sh_bh_m_w -0.162  0.012     0.010     0.113
std_beta(fit)

Measures how current levels of privacy concern are affected by generel levels of positive attitude toward information sharing and current levels of positive attitude toward information sharing, as well as general levels of information sharing and current levels of information sharing.

fit <- lmer(pri_con_m ~ 1 + inf_sha_beh_m_b + inf_sha_beh_m_w + inf_sha_att_m_b + inf_sha_att_m_w + (1 | id) + (1 | wave), 
    d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: pri_con_m ~ 1 + inf_sha_beh_m_b + inf_sha_beh_m_w + inf_sha_att_m_b +  
##     inf_sha_att_m_w + (1 | id) + (1 | wave)
##    Data: d_long
## 
## REML criterion at convergence: 16518
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.793 -0.479  0.058  0.517  5.013 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.57210  0.756   
##  wave     (Intercept) 0.00372  0.061   
##  Residual             0.22358  0.473   
## Number of obs: 8176, groups:  id, 2732; wave, 5
## 
## Fixed effects:
##                 Estimate Std. Error t value
## (Intercept)      3.60512    0.03212  112.23
## inf_sha_beh_m_b -0.05512    0.02658   -2.07
## inf_sha_beh_m_w -0.00915    0.00932   -0.98
## inf_sha_att_m_b -0.09501    0.01811   -5.25
## inf_sha_att_m_w -0.03141    0.01429   -2.20
## 
## Correlation of Fixed Effects:
##               (Intr) inf_sh_bh_m_b inf_sh_bh_m_w inf_sh_tt_m_b
## inf_sh_bh_m_b -0.090                                          
## inf_sh_bh_m_w -0.142  0.110                                   
## inf_sh_tt_m_b  0.020 -0.398        -0.068                     
## inf_sh_tt_m_w  0.010 -0.006        -0.084         0.005
std_beta(fit)

2.2.2.2 Model 2

Includes control variables

fit <- lmer(pri_con_m ~ 1 + inf_sha_att_m_b + inf_sha_att_m_w + inf_sha_beh_m_b + inf_sha_beh_m_w + male + age + edu_num + 
    (1 | id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: pri_con_m ~ 1 + inf_sha_att_m_b + inf_sha_att_m_w + inf_sha_beh_m_b +  
##     inf_sha_beh_m_w + male + age + edu_num + (1 | id) + (1 |      wave)
##    Data: d_long
## 
## REML criterion at convergence: 15063
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.771 -0.477  0.059  0.517  4.961 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.52997  0.7280  
##  wave     (Intercept) 0.00471  0.0686  
##  Residual             0.22548  0.4749  
## Number of obs: 7492, groups:  id, 2518; wave, 5
## 
## Fixed effects:
##                  Estimate Std. Error t value
## (Intercept)      3.045423   0.096674   31.50
## inf_sha_att_m_b -0.080142   0.018526   -4.33
## inf_sha_att_m_w -0.032246   0.014985   -2.15
## inf_sha_beh_m_b -0.064872   0.027276   -2.38
## inf_sha_beh_m_w -0.001667   0.009786   -0.17
## male             0.024006   0.032450    0.74
## age              0.012723   0.000996   12.77
## edu_num         -0.030699   0.009489   -3.24
## 
## Correlation of Fixed Effects:
##               (Intr) inf_sh_tt_m_b inf_sh_tt_m_w inf_sh_bh_m_b inf_sh_bh_m_w male   age   
## inf_sh_tt_m_b -0.055                                                                      
## inf_sh_tt_m_w  0.007  0.005                                                               
## inf_sh_bh_m_b  0.032 -0.392        -0.006                                                 
## inf_sh_bh_m_w -0.091 -0.059        -0.083         0.109                                   
## male          -0.626  0.075        -0.003         0.031         0.018                     
## age           -0.580  0.087        -0.003        -0.050         0.080         0.146       
## edu_num       -0.483 -0.046         0.001        -0.103        -0.023         0.085 -0.081
std_beta(fit)
fit <- lmer(inf_sha_att_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_beh_m_b + inf_sha_beh_m_w + male + age + edu_num + (1 | 
    id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_att_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_beh_m_b +  
##     inf_sha_beh_m_w + male + age + edu_num + (1 | id) + (1 |      wave)
##    Data: d_long
## 
## REML criterion at convergence: 12590
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -4.144 -0.525  0.026  0.531  5.073 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.20364  0.4513  
##  wave     (Intercept) 0.00202  0.0449  
##  Residual             0.20165  0.4491  
## Number of obs: 7492, groups:  id, 2518; wave, 5
## 
## Fixed effects:
##                  Estimate Std. Error t value
## (Intercept)      2.731029   0.065973   41.40
## pri_con_m_b     -0.162739   0.011542  -14.10
## pri_con_m_w     -0.029148   0.013387   -2.18
## inf_sha_beh_m_b  0.205034   0.016916   12.12
## inf_sha_beh_m_w  0.096022   0.008887   10.81
## male            -0.228948   0.021972  -10.42
## age             -0.004718   0.000682   -6.92
## edu_num          0.032546   0.006417    5.07
## 
## Correlation of Fixed Effects:
##               (Intr) pr_cn_m_b pr_cn_m_w inf_sh_bh_m_b inf_sh_bh_m_w male   age   
## pri_con_m_b    0.051                                                              
## pri_con_m_w    0.009  0.001                                                       
## inf_sh_bh_m_b -0.004  0.105    -0.015                                             
## inf_sh_bh_m_w -0.117  0.002     0.014     0.115                                   
## male          -0.627 -0.022     0.000     0.065         0.028                     
## age           -0.591 -0.074    -0.007    -0.011         0.107         0.147       
## edu_num       -0.482 -0.002     0.002    -0.131        -0.031         0.091 -0.078
std_beta(fit)
fit <- lmer(inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_att_m_b + inf_sha_att_m_w + male + age + edu_num + (1 | 
    id) + (1 | wave), d_long)
summary(fit)
## Linear mixed model fit by REML ['lmerMod']
## Formula: inf_sha_beh_m ~ 1 + pri_con_m_b + pri_con_m_w + inf_sha_att_m_b +  
##     inf_sha_att_m_w + male + age + edu_num + (1 | id) + (1 |      wave)
##    Data: d_long
## 
## REML criterion at convergence: 16276
## 
## Scaled residuals: 
##    Min     1Q Median     3Q    Max 
## -3.947 -0.509 -0.071  0.461  4.383 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  id       (Intercept) 0.1049   0.324   
##  wave     (Intercept) 0.0782   0.280   
##  Residual             0.4271   0.654   
## Number of obs: 7492, groups:  id, 2518; wave, 5
## 
## Fixed effects:
##                  Estimate Std. Error t value
## (Intercept)      2.597421   0.139168   18.66
## pri_con_m_b     -0.036462   0.011298   -3.23
## pri_con_m_w     -0.001456   0.019478   -0.07
## inf_sha_att_m_b  0.125435   0.011555   10.86
## inf_sha_att_m_w  0.124057   0.020446    6.07
## male            -0.107823   0.021206   -5.08
## age             -0.008455   0.000665  -12.72
## edu_num          0.051049   0.006121    8.34
## 
## Correlation of Fixed Effects:
##               (Intr) pr_cn_m_b pr_cn_m_w inf_sh_tt_m_b inf_sh_tt_m_w male   age   
## pri_con_m_b    0.019                                                              
## pri_con_m_w    0.006  0.004                                                       
## inf_sh_tt_m_b -0.024  0.127    -0.001                                             
## inf_sh_tt_m_w  0.000  0.004     0.031     0.003                                   
## male          -0.290 -0.010     0.001     0.104        -0.002                     
## age           -0.277 -0.056    -0.012     0.075         0.004         0.164       
## edu_num       -0.220 -0.001     0.000    -0.101        -0.002         0.093 -0.084
std_beta(fit)