Check data

DT::datatable(psych::describe(Sample_1_Nielsen))
DT::datatable(psych::describe(UofA_Sample))

Concatenate data

Sample_1_Nielsen$sample_group = "Nielsen"
UofA_Sample$sample_group = "UofA"

combined <- rbind(UofA_Sample, Sample_1_Nielsen)

Set up CFA model

model <-'
DISC =~ DISC1 + DISC2 + DISC3 + DISC4 + DISC5 + DISC6
JOB =~ JOB1 + JOB2 +JOB3 + JOB4 + JOB5
CARE =~ CARE1 + CARE2 + CARE3 + CARE4
RISK =~ RISK1 + RISK2 + RISK3
SOC =~ SOC1 + SOC2
EMO =~ EMO1 + EMO2 + EMO3
IND =~ IND1 + IND2
'

Set up Multi-group CFA

## configural invariance
config <- cfa(model, data = combined, group = "sample_group")

## Metric invariance
metric <- cfa(model, data = combined, group = "sample_group",
              #set factor loadings to be equal between groups
              group.equal="loadings")

## Scalar invarance
scalar <- cfa(model, data = combined, group = "sample_group",
              #set factor loadings and intercepts (means) to be equal between groups
              group.equal=c("loadings", "intercepts", "means"))

Summary of CFA results for configural, metric, and scalar invarance models

Notes: “Std.lv” standardizes to the latent factors, while the “std.all” uses all path information to determine the standardized estimates for paths

Configural model*

summary(config, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 114 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        192
##                                                       
##   Number of observations per group:                   
##     UofA                                          2445
##     Nielsen                                       2009
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              2841.424
##   Degrees of freedom                               508
##   P-value (Chi-square)                           0.000
##   Test statistic for each group:
##     UofA                                      1478.213
##     Nielsen                                   1363.210
## 
## Model Test Baseline Model:
## 
##   Test statistic                             60554.335
##   Degrees of freedom                               600
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.961
##   Tucker-Lewis Index (TLI)                       0.954
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)            -149205.136
##   Loglikelihood unrestricted model (H1)             NA
##                                                       
##   Akaike (AIC)                              298794.273
##   Bayesian (BIC)                            300023.372
##   Sample-size adjusted Bayesian (BIC)       299413.271
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.045
##   90 Percent confidence interval - lower         0.044
##   90 Percent confidence interval - upper         0.047
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.038
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## 
## Group 1 [UofA]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.831    0.811
##     DISC2             1.022    0.022   45.557    0.000    0.849    0.804
##     DISC3             1.036    0.022   46.854    0.000    0.861    0.820
##     DISC4             1.085    0.022   48.923    0.000    0.901    0.845
##     DISC5             1.129    0.022   52.464    0.000    0.938    0.887
##     DISC6             0.959    0.023   41.211    0.000    0.797    0.747
##   JOB =~                                                                
##     JOB1              1.000                               1.180    0.872
##     JOB2              1.038    0.019   55.804    0.000    1.225    0.852
##     JOB3              0.946    0.016   59.152    0.000    1.116    0.880
##     JOB4              0.913    0.016   58.744    0.000    1.078    0.877
##     JOB5              2.766    0.091   30.358    0.000    3.265    0.566
##   CARE =~                                                               
##     CARE1             1.000                               0.985    0.957
##     CARE2             0.997    0.009  111.654    0.000    0.981    0.964
##     CARE3             0.976    0.011   90.359    0.000    0.961    0.918
##     CARE4             2.674    0.110   24.364    0.000    2.633    0.452
##   RISK =~                                                               
##     RISK1             1.000                               0.811    0.820
##     RISK2             1.029    0.031   33.218    0.000    0.835    0.747
##     RISK3             0.980    0.030   33.021    0.000    0.796    0.739
##   SOC =~                                                                
##     SOC1              1.000                               1.013    0.829
##     SOC2              0.889    0.086   10.283    0.000    0.900    0.705
##   EMO =~                                                                
##     EMO1              1.000                               0.604    0.597
##     EMO2              1.333    0.069   19.454    0.000    0.805    0.851
##     EMO3              0.859    0.047   18.106    0.000    0.519    0.460
##   IND =~                                                                
##     IND1              1.000                               0.760    0.926
##     IND2              0.695    0.115    6.054    0.000    0.528    0.625
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.330    0.023   14.260    0.000    0.336    0.336
##     CARE              0.260    0.019   13.966    0.000    0.318    0.318
##     RISK              0.129    0.016    8.046    0.000    0.192    0.192
##     SOC               0.004    0.020    0.205    0.838    0.005    0.005
##     EMO               0.154    0.014   10.974    0.000    0.307    0.307
##     IND              -0.016    0.014   -1.145    0.252   -0.026   -0.026
##   JOB ~~                                                                
##     CARE              0.218    0.025    8.618    0.000    0.188    0.188
##     RISK              0.217    0.023    9.451    0.000    0.227    0.227
##     SOC               0.088    0.029    3.049    0.002    0.074    0.074
##     EMO               0.191    0.019    9.934    0.000    0.268    0.268
##     IND               0.032    0.020    1.582    0.114    0.036    0.036
##   CARE ~~                                                               
##     RISK              0.134    0.018    7.278    0.000    0.168    0.168
##     SOC               0.085    0.024    3.576    0.000    0.085    0.085
##     EMO               0.125    0.015    8.302    0.000    0.210    0.210
##     IND               0.013    0.017    0.786    0.432    0.017    0.017
##   RISK ~~                                                               
##     SOC               0.172    0.022    7.769    0.000    0.209    0.209
##     EMO               0.119    0.014    8.721    0.000    0.244    0.244
##     IND               0.101    0.015    6.681    0.000    0.163    0.163
##   SOC ~~                                                                
##     EMO               0.122    0.017    6.998    0.000    0.200    0.200
##     IND               0.002    0.019    0.093    0.926    0.002    0.002
##   EMO ~~                                                                
##     IND               0.000    0.011    0.009    0.993    0.000    0.000
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             1.923    0.021   92.760    0.000    1.923    1.876
##    .DISC2             1.780    0.021   83.271    0.000    1.780    1.684
##    .DISC3             1.719    0.021   80.977    0.000    1.719    1.638
##    .DISC4             1.680    0.022   77.890    0.000    1.680    1.575
##    .DISC5             1.854    0.021   86.649    0.000    1.854    1.752
##    .DISC6             1.663    0.022   77.080    0.000    1.663    1.559
##    .JOB1              2.315    0.027   84.548    0.000    2.315    1.710
##    .JOB2              2.445    0.029   84.107    0.000    2.445    1.701
##    .JOB3              2.120    0.026   82.623    0.000    2.120    1.671
##    .JOB4              2.045    0.025   82.239    0.000    2.045    1.663
##    .JOB5              5.818    0.117   49.883    0.000    5.818    1.009
##    .CARE1             1.508    0.021   72.468    0.000    1.508    1.466
##    .CARE2             1.506    0.021   73.205    0.000    1.506    1.480
##    .CARE3             1.506    0.021   71.128    0.000    1.506    1.438
##    .CARE4             3.452    0.118   29.334    0.000    3.452    0.593
##    .RISK1             2.670    0.020  133.316    0.000    2.670    2.696
##    .RISK2             2.609    0.023  115.411    0.000    2.609    2.334
##    .RISK3             2.881    0.022  132.346    0.000    2.881    2.677
##    .SOC1              3.380    0.025  136.625    0.000    3.380    2.763
##    .SOC2              2.975    0.026  115.250    0.000    2.975    2.331
##    .EMO1              2.883    0.020  140.893    0.000    2.883    2.849
##    .EMO2              2.451    0.019  128.080    0.000    2.451    2.590
##    .EMO3              2.652    0.023  116.366    0.000    2.652    2.353
##    .IND1              4.061    0.017  244.589    0.000    4.061    4.946
##    .IND2              4.207    0.017  246.215    0.000    4.207    4.979
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.360    0.012   29.915    0.000    0.360    0.343
##    .DISC2             0.395    0.013   30.159    0.000    0.395    0.354
##    .DISC3             0.361    0.012   29.550    0.000    0.361    0.327
##    .DISC4             0.325    0.011   28.342    0.000    0.325    0.285
##    .DISC5             0.238    0.009   25.166    0.000    0.238    0.213
##    .DISC6             0.503    0.016   31.663    0.000    0.503    0.442
##    .JOB1              0.440    0.017   26.249    0.000    0.440    0.240
##    .JOB2              0.565    0.020   27.695    0.000    0.565    0.273
##    .JOB3              0.364    0.014   25.524    0.000    0.364    0.226
##    .JOB4              0.350    0.014   25.834    0.000    0.350    0.232
##    .JOB5             22.603    0.671   33.710    0.000   22.603    0.680
##    .CARE1             0.089    0.005   19.709    0.000    0.089    0.084
##    .CARE2             0.073    0.004   17.139    0.000    0.073    0.070
##    .CARE3             0.173    0.006   28.260    0.000    0.173    0.158
##    .CARE4            26.924    0.777   34.662    0.000   26.924    0.795
##    .RISK1             0.322    0.018   18.224    0.000    0.322    0.328
##    .RISK2             0.552    0.023   24.370    0.000    0.552    0.442
##    .RISK3             0.526    0.021   24.947    0.000    0.526    0.454
##    .SOC1              0.469    0.099    4.757    0.000    0.469    0.313
##    .SOC2              0.818    0.081   10.156    0.000    0.818    0.502
##    .EMO1              0.659    0.025   26.181    0.000    0.659    0.644
##    .EMO2              0.247    0.029    8.387    0.000    0.247    0.276
##    .EMO3              1.001    0.032   31.559    0.000    1.001    0.788
##    .IND1              0.096    0.094    1.016    0.310    0.096    0.142
##    .IND2              0.435    0.047    9.195    0.000    0.435    0.609
##     DISC              0.690    0.029   23.888    0.000    1.000    1.000
##     JOB               1.393    0.052   26.753    0.000    1.000    1.000
##     CARE              0.969    0.030   31.901    0.000    1.000    1.000
##     RISK              0.658    0.030   21.605    0.000    1.000    1.000
##     SOC               1.027    0.106    9.708    0.000    1.000    1.000
##     EMO               0.365    0.028   13.056    0.000    1.000    1.000
##     IND               0.578    0.096    6.000    0.000    1.000    1.000
## 
## 
## Group 2 [Nielsen]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.807    0.850
##     DISC2             0.813    0.023   35.440    0.000    0.656    0.707
##     DISC3             0.878    0.022   40.403    0.000    0.708    0.776
##     DISC4             0.841    0.023   36.824    0.000    0.679    0.727
##     DISC5             1.008    0.022   45.823    0.000    0.814    0.846
##     DISC6             0.751    0.024   31.538    0.000    0.607    0.648
##   JOB =~                                                                
##     JOB1              1.000                               1.173    0.864
##     JOB2              0.972    0.022   43.757    0.000    1.141    0.821
##     JOB3              0.808    0.019   41.618    0.000    0.948    0.792
##     JOB4              0.776    0.019   40.330    0.000    0.910    0.775
##     JOB5              1.486    0.062   24.001    0.000    1.743    0.520
##   CARE =~                                                               
##     CARE1             1.000                               0.982    0.941
##     CARE2             1.033    0.012   86.085    0.000    1.015    0.953
##     CARE3             1.118    0.015   73.896    0.000    1.098    0.910
##     CARE4             1.800    0.051   35.166    0.000    1.768    0.643
##   RISK =~                                                               
##     RISK1             1.000                               0.787    0.837
##     RISK2             0.952    0.040   24.054    0.000    0.749    0.672
##     RISK3             0.914    0.039   23.646    0.000    0.719    0.649
##   SOC =~                                                                
##     SOC1              1.000                               1.065    0.896
##     SOC2              0.696    0.067   10.369    0.000    0.741    0.610
##   EMO =~                                                                
##     EMO1              1.000                               0.485    0.513
##     EMO2              1.401    0.087   16.172    0.000    0.680    0.745
##     EMO3              1.406    0.087   16.142    0.000    0.682    0.593
##   IND =~                                                                
##     IND1              1.000                               0.746    0.793
##     IND2              0.934    0.081   11.508    0.000    0.697    0.758
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.089    0.024    3.787    0.000    0.094    0.094
##     CARE              0.103    0.019    5.375    0.000    0.130    0.130
##     RISK              0.031    0.017    1.880    0.060    0.050    0.050
##     SOC               0.012    0.022    0.529    0.597    0.014    0.014
##     EMO               0.082    0.012    6.827    0.000    0.208    0.208
##     IND               0.019    0.016    1.146    0.252    0.031    0.031
##   JOB ~~                                                                
##     CARE              0.120    0.028    4.314    0.000    0.105    0.105
##     RISK              0.202    0.025    8.061    0.000    0.219    0.219
##     SOC               0.028    0.032    0.851    0.395    0.022    0.022
##     EMO               0.074    0.017    4.437    0.000    0.130    0.130
##     IND               0.132    0.025    5.383    0.000    0.151    0.151
##   CARE ~~                                                               
##     RISK              0.033    0.020    1.675    0.094    0.043    0.043
##     SOC               0.091    0.026    3.457    0.001    0.087    0.087
##     EMO               0.064    0.014    4.732    0.000    0.135    0.135
##     IND               0.052    0.019    2.697    0.007    0.071    0.071
##   RISK ~~                                                               
##     SOC               0.104    0.023    4.445    0.000    0.124    0.124
##     EMO               0.092    0.013    7.283    0.000    0.240    0.240
##     IND               0.150    0.018    8.200    0.000    0.256    0.256
##   SOC ~~                                                                
##     EMO               0.190    0.018   10.346    0.000    0.368    0.368
##     IND              -0.052    0.023   -2.299    0.022   -0.065   -0.065
##   EMO ~~                                                                
##     IND              -0.036    0.011   -3.110    0.002   -0.099   -0.099
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             1.967    0.021   92.849    0.000    1.967    2.072
##    .DISC2             1.591    0.021   76.847    0.000    1.591    1.714
##    .DISC3             1.636    0.020   80.362    0.000    1.636    1.793
##    .DISC4             1.528    0.021   73.331    0.000    1.528    1.636
##    .DISC5             1.897    0.021   88.421    0.000    1.897    1.973
##    .DISC6             1.577    0.021   75.506    0.000    1.577    1.685
##    .JOB1              2.791    0.030   92.100    0.000    2.791    2.055
##    .JOB2              2.837    0.031   91.510    0.000    2.837    2.042
##    .JOB3              2.296    0.027   86.036    0.000    2.296    1.920
##    .JOB4              2.180    0.026   83.240    0.000    2.180    1.857
##    .JOB5              6.732    0.075   89.993    0.000    6.732    2.008
##    .CARE1             1.577    0.023   67.745    0.000    1.577    1.511
##    .CARE2             1.595    0.024   67.127    0.000    1.595    1.498
##    .CARE3             1.670    0.027   62.021    0.000    1.670    1.384
##    .CARE4             1.666    0.061   27.168    0.000    1.666    0.606
##    .RISK1             2.742    0.021  130.781    0.000    2.742    2.918
##    .RISK2             2.642    0.025  106.209    0.000    2.642    2.370
##    .RISK3             3.046    0.025  123.126    0.000    3.046    2.747
##    .SOC1              3.562    0.027  134.315    0.000    3.562    2.997
##    .SOC2              2.959    0.027  109.259    0.000    2.959    2.438
##    .EMO1              3.232    0.021  152.960    0.000    3.232    3.413
##    .EMO2              2.600    0.020  127.603    0.000    2.600    2.847
##    .EMO3              2.636    0.026  102.704    0.000    2.636    2.291
##    .IND1              3.810    0.021  181.709    0.000    3.810    4.054
##    .IND2              4.053    0.020  197.770    0.000    4.053    4.412
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.250    0.011   22.729    0.000    0.250    0.277
##    .DISC2             0.430    0.015   28.315    0.000    0.430    0.500
##    .DISC3             0.331    0.012   26.535    0.000    0.331    0.397
##    .DISC4             0.411    0.015   27.898    0.000    0.411    0.471
##    .DISC5             0.263    0.011   23.031    0.000    0.263    0.284
##    .DISC6             0.508    0.017   29.262    0.000    0.508    0.580
##    .JOB1              0.469    0.023   20.426    0.000    0.469    0.254
##    .JOB2              0.629    0.027   23.718    0.000    0.629    0.326
##    .JOB3              0.532    0.021   25.238    0.000    0.532    0.372
##    .JOB4              0.550    0.021   25.957    0.000    0.550    0.399
##    .JOB5              8.203    0.271   30.323    0.000    8.203    0.730
##    .CARE1             0.124    0.006   19.510    0.000    0.124    0.114
##    .CARE2             0.104    0.006   16.674    0.000    0.104    0.092
##    .CARE3             0.251    0.010   24.596    0.000    0.251    0.172
##    .CARE4             4.427    0.144   30.720    0.000    4.427    0.586
##    .RISK1             0.264    0.022   11.822    0.000    0.264    0.299
##    .RISK2             0.683    0.029   23.562    0.000    0.683    0.549
##    .RISK3             0.712    0.029   24.707    0.000    0.712    0.579
##    .SOC1              0.279    0.105    2.647    0.008    0.279    0.197
##    .SOC2              0.925    0.059   15.804    0.000    0.925    0.628
##    .EMO1              0.661    0.025   26.512    0.000    0.661    0.737
##    .EMO2              0.371    0.026   14.137    0.000    0.371    0.445
##    .EMO3              0.858    0.037   23.289    0.000    0.858    0.648
##    .IND1              0.328    0.048    6.827    0.000    0.328    0.371
##    .IND2              0.359    0.042    8.451    0.000    0.359    0.425
##     DISC              0.652    0.028   22.961    0.000    1.000    1.000
##     JOB               1.376    0.059   23.327    0.000    1.000    1.000
##     CARE              0.965    0.035   27.967    0.000    1.000    1.000
##     RISK              0.619    0.034   18.354    0.000    1.000    1.000
##     SOC               1.134    0.114    9.985    0.000    1.000    1.000
##     EMO               0.236    0.024   10.027    0.000    1.000    1.000
##     IND               0.556    0.054   10.383    0.000    1.000    1.000

Metric model

summary(metric, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 79 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        192
##   Number of equality constraints                    18
##                                                       
##   Number of observations per group:                   
##     UofA                                          2445
##     Nielsen                                       2009
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              3240.443
##   Degrees of freedom                               526
##   P-value (Chi-square)                           0.000
##   Test statistic for each group:
##     UofA                                      1682.479
##     Nielsen                                   1557.964
## 
## Model Test Baseline Model:
## 
##   Test statistic                             60554.335
##   Degrees of freedom                               600
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.955
##   Tucker-Lewis Index (TLI)                       0.948
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)            -149404.646
##   Loglikelihood unrestricted model (H1)             NA
##                                                       
##   Akaike (AIC)                              299157.292
##   Bayesian (BIC)                            300271.163
##   Sample-size adjusted Bayesian (BIC)       299718.259
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.048
##   90 Percent confidence interval - lower         0.047
##   90 Percent confidence interval - upper         0.050
##   P-value RMSEA <= 0.05                          0.972
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.046
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## 
## Group 1 [UofA]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.883    0.829
##     DISC2   (.p2.)    0.937    0.016   58.360    0.000    0.828    0.795
##     DISC3   (.p3.)    0.969    0.016   61.957    0.000    0.856    0.818
##     DISC4   (.p4.)    0.989    0.016   62.299    0.000    0.873    0.835
##     DISC5   (.p5.)    1.073    0.015   69.544    0.000    0.948    0.890
##     DISC6   (.p6.)    0.873    0.017   52.336    0.000    0.771    0.735
##   JOB =~                                                                
##     JOB1              1.000                               1.224    0.883
##     JOB2    (.p8.)    1.016    0.014   70.549    0.000    1.244    0.858
##     JOB3    (.p9.)    0.901    0.012   72.591    0.000    1.104    0.876
##     JOB4    (.10.)    0.869    0.012   71.551    0.000    1.064    0.871
##     JOB5    (.11.)    1.978    0.054   36.665    0.000    2.422    0.446
##   CARE =~                                                               
##     CARE1             1.000                               0.970    0.955
##     CARE2   (.13.)    1.011    0.007  140.631    0.000    0.981    0.965
##     CARE3   (.14.)    1.027    0.009  115.941    0.000    0.996    0.924
##     CARE4   (.15.)    1.909    0.045   42.122    0.000    1.852    0.332
##   RISK =~                                                               
##     RISK1             1.000                               0.823    0.827
##     RISK2   (.17.)    1.002    0.024   41.089    0.000    0.825    0.741
##     RISK3   (.18.)    0.957    0.024   40.694    0.000    0.788    0.734
##   SOC =~                                                                
##     SOC1              1.000                               1.100    0.899
##     SOC2    (.20.)    0.752    0.053   14.288    0.000    0.827    0.649
##   EMO =~                                                                
##     EMO1              1.000                               0.579    0.580
##     EMO2    (.22.)    1.349    0.053   25.556    0.000    0.781    0.829
##     EMO3    (.23.)    1.042    0.042   24.713    0.000    0.603    0.521
##   IND =~                                                                
##     IND1              1.000                               0.678    0.827
##     IND2    (.25.)    0.874    0.066   13.232    0.000    0.593    0.701
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.361    0.025   14.387    0.000    0.334    0.334
##     CARE              0.272    0.019   14.082    0.000    0.317    0.317
##     RISK              0.139    0.017    8.058    0.000    0.191    0.191
##     SOC              -0.012    0.022   -0.553    0.580   -0.013   -0.013
##     EMO               0.157    0.014   11.447    0.000    0.307    0.307
##     IND              -0.021    0.014   -1.435    0.151   -0.035   -0.035
##   JOB ~~                                                                
##     CARE              0.221    0.026    8.560    0.000    0.186    0.186
##     RISK              0.226    0.024    9.434    0.000    0.225    0.225
##     SOC               0.078    0.031    2.512    0.012    0.058    0.058
##     EMO               0.189    0.019   10.185    0.000    0.266    0.266
##     IND               0.034    0.020    1.704    0.088    0.041    0.041
##   CARE ~~                                                               
##     RISK              0.134    0.018    7.295    0.000    0.168    0.168
##     SOC               0.085    0.024    3.511    0.000    0.079    0.079
##     EMO               0.119    0.014    8.512    0.000    0.212    0.212
##     IND               0.006    0.016    0.411    0.681    0.010    0.010
##   RISK ~~                                                               
##     SOC               0.169    0.023    7.481    0.000    0.187    0.187
##     EMO               0.122    0.013    9.290    0.000    0.256    0.256
##     IND               0.094    0.015    6.425    0.000    0.169    0.169
##   SOC ~~                                                                
##     EMO               0.131    0.017    7.684    0.000    0.205    0.205
##     IND               0.009    0.019    0.491    0.624    0.013    0.013
##   EMO ~~                                                                
##     IND               0.006    0.011    0.581    0.561    0.016    0.016
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             1.923    0.022   89.284    0.000    1.923    1.806
##    .DISC2             1.780    0.021   84.557    0.000    1.780    1.710
##    .DISC3             1.719    0.021   81.191    0.000    1.719    1.642
##    .DISC4             1.680    0.021   79.374    0.000    1.680    1.605
##    .DISC5             1.854    0.022   86.089    0.000    1.854    1.741
##    .DISC6             1.663    0.021   78.320    0.000    1.663    1.584
##    .JOB1              2.315    0.028   82.520    0.000    2.315    1.669
##    .JOB2              2.445    0.029   83.397    0.000    2.445    1.687
##    .JOB3              2.120    0.025   83.156    0.000    2.120    1.682
##    .JOB4              2.045    0.025   82.854    0.000    2.045    1.676
##    .JOB5              5.818    0.110   52.991    0.000    5.818    1.072
##    .CARE1             1.508    0.021   73.333    0.000    1.508    1.483
##    .CARE2             1.506    0.021   73.256    0.000    1.506    1.482
##    .CARE3             1.506    0.022   69.052    0.000    1.506    1.396
##    .CARE4             3.452    0.113   30.624    0.000    3.452    0.619
##    .RISK1             2.670    0.020  132.651    0.000    2.670    2.683
##    .RISK2             2.609    0.023  115.906    0.000    2.609    2.344
##    .RISK3             2.881    0.022  132.727    0.000    2.881    2.684
##    .SOC1              3.380    0.025  136.554    0.000    3.380    2.762
##    .SOC2              2.975    0.026  115.428    0.000    2.975    2.334
##    .EMO1              2.883    0.020  142.786    0.000    2.883    2.888
##    .EMO2              2.451    0.019  128.670    0.000    2.451    2.602
##    .EMO3              2.652    0.023  113.351    0.000    2.652    2.292
##    .IND1              4.061    0.017  244.848    0.000    4.061    4.952
##    .IND2              4.207    0.017  245.794    0.000    4.207    4.971
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.354    0.012   29.294    0.000    0.354    0.312
##    .DISC2             0.398    0.013   30.539    0.000    0.398    0.367
##    .DISC3             0.363    0.012   29.774    0.000    0.363    0.331
##    .DISC4             0.332    0.011   29.023    0.000    0.332    0.303
##    .DISC5             0.235    0.009   25.048    0.000    0.235    0.207
##    .DISC6             0.508    0.016   31.973    0.000    0.508    0.460
##    .JOB1              0.425    0.017   25.433    0.000    0.425    0.221
##    .JOB2              0.555    0.020   27.484    0.000    0.555    0.264
##    .JOB3              0.371    0.014   26.100    0.000    0.371    0.233
##    .JOB4              0.358    0.014   26.441    0.000    0.358    0.241
##    .JOB5             23.611    0.688   34.333    0.000   23.611    0.801
##    .CARE1             0.092    0.004   20.924    0.000    0.092    0.089
##    .CARE2             0.072    0.004   17.382    0.000    0.072    0.069
##    .CARE3             0.171    0.006   27.665    0.000    0.171    0.147
##    .CARE4            27.634    0.794   34.822    0.000   27.634    0.890
##    .RISK1             0.312    0.017   18.394    0.000    0.312    0.316
##    .RISK2             0.559    0.022   25.492    0.000    0.559    0.451
##    .RISK3             0.531    0.021   25.911    0.000    0.531    0.461
##    .SOC1              0.288    0.087    3.322    0.001    0.288    0.192
##    .SOC2              0.940    0.056   16.867    0.000    0.940    0.579
##    .EMO1              0.662    0.023   28.539    0.000    0.662    0.664
##    .EMO2              0.278    0.024   11.660    0.000    0.278    0.313
##    .EMO3              0.975    0.032   30.566    0.000    0.975    0.728
##    .IND1              0.212    0.037    5.780    0.000    0.212    0.316
##    .IND2              0.364    0.030   12.321    0.000    0.364    0.509
##     DISC              0.780    0.029   27.093    0.000    1.000    1.000
##     JOB               1.499    0.052   28.690    0.000    1.000    1.000
##     CARE              0.942    0.029   32.496    0.000    1.000    1.000
##     RISK              0.678    0.029   23.552    0.000    1.000    1.000
##     SOC               1.210    0.094   12.815    0.000    1.000    1.000
##     EMO               0.335    0.022   15.215    0.000    1.000    1.000
##     IND               0.460    0.039   11.775    0.000    1.000    1.000
## 
## 
## Group 2 [Nielsen]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.740    0.816
##     DISC2   (.p2.)    0.937    0.016   58.360    0.000    0.694    0.729
##     DISC3   (.p3.)    0.969    0.016   61.957    0.000    0.717    0.783
##     DISC4   (.p4.)    0.989    0.016   62.299    0.000    0.732    0.757
##     DISC5   (.p5.)    1.073    0.015   69.544    0.000    0.794    0.835
##     DISC6   (.p6.)    0.873    0.017   52.336    0.000    0.646    0.674
##   JOB =~                                                                
##     JOB1              1.000                               1.087    0.832
##     JOB2    (.p8.)    1.016    0.014   70.549    0.000    1.104    0.806
##     JOB3    (.p9.)    0.901    0.012   72.591    0.000    0.980    0.810
##     JOB4    (.10.)    0.869    0.012   71.551    0.000    0.945    0.793
##     JOB5    (.11.)    1.978    0.054   36.665    0.000    2.151    0.600
##   CARE =~                                                               
##     CARE1             1.000                               1.005    0.946
##     CARE2   (.13.)    1.011    0.007  140.631    0.000    1.016    0.953
##     CARE3   (.14.)    1.027    0.009  115.941    0.000    1.031    0.894
##     CARE4   (.15.)    1.909    0.045   42.122    0.000    1.917    0.674
##   RISK =~                                                               
##     RISK1             1.000                               0.767    0.821
##     RISK2   (.17.)    1.002    0.024   41.089    0.000    0.768    0.685
##     RISK3   (.18.)    0.957    0.024   40.694    0.000    0.734    0.659
##   SOC =~                                                                
##     SOC1              1.000                               1.026    0.864
##     SOC2    (.20.)    0.752    0.053   14.288    0.000    0.772    0.635
##   EMO =~                                                                
##     EMO1              1.000                               0.531    0.550
##     EMO2    (.22.)    1.349    0.053   25.556    0.000    0.716    0.778
##     EMO3    (.23.)    1.042    0.042   24.713    0.000    0.553    0.496
##   IND =~                                                                
##     IND1              1.000                               0.770    0.818
##     IND2    (.25.)    0.874    0.066   13.232    0.000    0.673    0.734
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.081    0.020    4.004    0.000    0.100    0.100
##     CARE              0.099    0.018    5.514    0.000    0.134    0.134
##     RISK              0.030    0.015    1.976    0.048    0.052    0.052
##     SOC               0.010    0.020    0.507    0.612    0.013    0.013
##     EMO               0.086    0.012    7.423    0.000    0.218    0.218
##     IND               0.017    0.015    1.125    0.260    0.030    0.030
##   JOB ~~                                                                
##     CARE              0.112    0.026    4.221    0.000    0.102    0.102
##     RISK              0.185    0.023    8.137    0.000    0.221    0.221
##     SOC               0.022    0.030    0.732    0.464    0.020    0.020
##     EMO               0.073    0.017    4.429    0.000    0.127    0.127
##     IND               0.123    0.023    5.308    0.000    0.146    0.146
##   CARE ~~                                                               
##     RISK              0.033    0.020    1.679    0.093    0.043    0.043
##     SOC               0.095    0.027    3.558    0.000    0.092    0.092
##     EMO               0.070    0.015    4.748    0.000    0.132    0.132
##     IND               0.057    0.020    2.799    0.005    0.073    0.073
##   RISK ~~                                                               
##     SOC               0.103    0.023    4.554    0.000    0.130    0.130
##     EMO               0.091    0.013    7.141    0.000    0.223    0.223
##     IND               0.150    0.018    8.378    0.000    0.254    0.254
##   SOC ~~                                                                
##     EMO               0.195    0.018   10.777    0.000    0.359    0.359
##     IND              -0.058    0.023   -2.551    0.011   -0.074   -0.074
##   EMO ~~                                                                
##     IND              -0.042    0.013   -3.345    0.001   -0.104   -0.104
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             1.967    0.020   97.197    0.000    1.967    2.169
##    .DISC2             1.591    0.021   74.967    0.000    1.591    1.673
##    .DISC3             1.636    0.020   80.060    0.000    1.636    1.786
##    .DISC4             1.528    0.022   70.877    0.000    1.528    1.581
##    .DISC5             1.897    0.021   89.426    0.000    1.897    1.995
##    .DISC6             1.577    0.021   73.720    0.000    1.577    1.645
##    .JOB1              2.791    0.029   95.732    0.000    2.791    2.136
##    .JOB2              2.837    0.031   92.746    0.000    2.837    2.069
##    .JOB3              2.296    0.027   85.031    0.000    2.296    1.897
##    .JOB4              2.180    0.027   82.058    0.000    2.180    1.831
##    .JOB5              6.732    0.080   84.183    0.000    6.732    1.878
##    .CARE1             1.577    0.024   66.559    0.000    1.577    1.485
##    .CARE2             1.595    0.024   67.052    0.000    1.595    1.496
##    .CARE3             1.670    0.026   64.907    0.000    1.670    1.448
##    .CARE4             1.666    0.063   26.240    0.000    1.666    0.585
##    .RISK1             2.742    0.021  131.596    0.000    2.742    2.936
##    .RISK2             2.642    0.025  105.553    0.000    2.642    2.355
##    .RISK3             3.046    0.025  122.596    0.000    3.046    2.735
##    .SOC1              3.562    0.026  134.425    0.000    3.562    2.999
##    .SOC2              2.959    0.027  109.047    0.000    2.959    2.433
##    .EMO1              3.232    0.022  150.294    0.000    3.232    3.353
##    .EMO2              2.600    0.021  126.696    0.000    2.600    2.827
##    .EMO3              2.636    0.025  105.962    0.000    2.636    2.364
##    .IND1              3.810    0.021  181.464    0.000    3.810    4.049
##    .IND2              4.053    0.020  198.142    0.000    4.053    4.421
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.275    0.011   25.125    0.000    0.275    0.334
##    .DISC2             0.424    0.015   28.005    0.000    0.424    0.468
##    .DISC3             0.324    0.012   26.496    0.000    0.324    0.387
##    .DISC4             0.398    0.015   27.324    0.000    0.398    0.427
##    .DISC5             0.273    0.011   24.127    0.000    0.273    0.302
##    .DISC6             0.501    0.017   28.992    0.000    0.501    0.546
##    .JOB1              0.526    0.022   23.491    0.000    0.526    0.308
##    .JOB2              0.660    0.026   24.964    0.000    0.660    0.351
##    .JOB3              0.504    0.020   24.767    0.000    0.504    0.344
##    .JOB4              0.526    0.021   25.550    0.000    0.526    0.371
##    .JOB5              8.224    0.278   29.621    0.000    8.224    0.640
##    .CARE1             0.119    0.006   18.702    0.000    0.119    0.106
##    .CARE2             0.105    0.006   17.004    0.000    0.105    0.093
##    .CARE3             0.266    0.010   26.045    0.000    0.266    0.200
##    .CARE4             4.422    0.145   30.550    0.000    4.422    0.546
##    .RISK1             0.284    0.018   15.539    0.000    0.284    0.326
##    .RISK2             0.668    0.027   24.537    0.000    0.668    0.531
##    .RISK3             0.701    0.027   25.615    0.000    0.701    0.566
##    .SOC1              0.358    0.075    4.750    0.000    0.358    0.254
##    .SOC2              0.884    0.051   17.497    0.000    0.884    0.597
##    .EMO1              0.648    0.025   26.413    0.000    0.648    0.697
##    .EMO2              0.334    0.024   13.657    0.000    0.334    0.395
##    .EMO3              0.938    0.034   27.908    0.000    0.938    0.754
##    .IND1              0.293    0.045    6.464    0.000    0.293    0.330
##    .IND2              0.387    0.036   10.755    0.000    0.387    0.461
##     DISC              0.548    0.022   25.040    0.000    1.000    1.000
##     JOB               1.182    0.046   25.625    0.000    1.000    1.000
##     CARE              1.009    0.034   29.447    0.000    1.000    1.000
##     RISK              0.588    0.027   21.524    0.000    1.000    1.000
##     SOC               1.053    0.084   12.501    0.000    1.000    1.000
##     EMO               0.281    0.020   14.229    0.000    1.000    1.000
##     IND               0.593    0.051   11.688    0.000    1.000    1.000

Scalar model

summary(scalar, standardized = TRUE, fit.measures = TRUE)
## lavaan 0.6-7 ended normally after 123 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                        192
##   Number of equality constraints                    43
##                                                       
##   Number of observations per group:                   
##     UofA                                          2445
##     Nielsen                                       2009
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                              4238.009
##   Degrees of freedom                               551
##   P-value (Chi-square)                           0.000
##   Test statistic for each group:
##     UofA                                      2222.815
##     Nielsen                                   2015.193
## 
## Model Test Baseline Model:
## 
##   Test statistic                             60554.335
##   Degrees of freedom                               600
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.939
##   Tucker-Lewis Index (TLI)                       0.933
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)            -149903.429
##   Loglikelihood unrestricted model (H1)             NA
##                                                       
##   Akaike (AIC)                              300104.858
##   Bayesian (BIC)                            301058.690
##   Sample-size adjusted Bayesian (BIC)       300585.227
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.055
##   90 Percent confidence interval - lower         0.053
##   90 Percent confidence interval - upper         0.056
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.053
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## 
## Group 1 [UofA]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.881    0.828
##     DISC2   (.p2.)    0.941    0.016   58.034    0.000    0.829    0.794
##     DISC3   (.p3.)    0.973    0.016   61.816    0.000    0.857    0.818
##     DISC4   (.p4.)    0.993    0.016   62.032    0.000    0.875    0.834
##     DISC5   (.p5.)    1.073    0.016   69.066    0.000    0.946    0.889
##     DISC6   (.p6.)    0.877    0.017   52.274    0.000    0.773    0.735
##   JOB =~                                                                
##     JOB1              1.000                               1.246    0.885
##     JOB2    (.p8.)    1.012    0.014   71.439    0.000    1.261    0.862
##     JOB3    (.p9.)    0.887    0.012   72.791    0.000    1.105    0.874
##     JOB4    (.10.)    0.853    0.012   71.580    0.000    1.063    0.869
##     JOB5    (.11.)    1.979    0.053   37.263    0.000    2.465    0.452
##   CARE =~                                                               
##     CARE1             1.000                               0.971    0.954
##     CARE2   (.13.)    1.011    0.007  140.698    0.000    0.982    0.965
##     CARE3   (.14.)    1.028    0.009  115.772    0.000    0.998    0.923
##     CARE4   (.15.)    1.875    0.046   40.840    0.000    1.820    0.313
##   RISK =~                                                               
##     RISK1             1.000                               0.824    0.828
##     RISK2   (.17.)    1.000    0.024   41.106    0.000    0.824    0.740
##     RISK3   (.18.)    0.960    0.024   40.750    0.000    0.791    0.735
##   SOC =~                                                                
##     SOC1              1.000                               1.131    0.923
##     SOC2    (.20.)    0.710    0.051   14.004    0.000    0.803    0.630
##   EMO =~                                                                
##     EMO1              1.000                               0.593    0.586
##     EMO2    (.22.)    1.323    0.051   25.886    0.000    0.785    0.831
##     EMO3    (.23.)    1.002    0.041   24.708    0.000    0.595    0.515
##   IND =~                                                                
##     IND1              1.000                               0.689    0.834
##     IND2    (.25.)    0.861    0.067   12.921    0.000    0.593    0.699
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.361    0.025   14.205    0.000    0.329    0.329
##     CARE              0.271    0.019   14.051    0.000    0.317    0.317
##     RISK              0.138    0.017    8.028    0.000    0.190    0.190
##     SOC              -0.018    0.022   -0.808    0.419   -0.018   -0.018
##     EMO               0.159    0.014   11.417    0.000    0.305    0.305
##     IND              -0.020    0.015   -1.366    0.172   -0.033   -0.033
##   JOB ~~                                                                
##     CARE              0.229    0.026    8.712    0.000    0.189    0.189
##     RISK              0.236    0.024    9.643    0.000    0.230    0.230
##     SOC               0.084    0.032    2.646    0.008    0.060    0.060
##     EMO               0.205    0.019   10.569    0.000    0.277    0.277
##     IND               0.021    0.021    1.001    0.317    0.024    0.024
##   CARE ~~                                                               
##     RISK              0.136    0.018    7.384    0.000    0.170    0.170
##     SOC               0.087    0.024    3.584    0.000    0.079    0.079
##     EMO               0.124    0.014    8.658    0.000    0.216    0.216
##     IND               0.003    0.016    0.192    0.847    0.005    0.005
##   RISK ~~                                                               
##     SOC               0.169    0.023    7.417    0.000    0.181    0.181
##     EMO               0.127    0.013    9.416    0.000    0.259    0.259
##     IND               0.091    0.015    6.148    0.000    0.160    0.160
##   SOC ~~                                                                
##     EMO               0.138    0.018    7.868    0.000    0.206    0.206
##     IND               0.008    0.019    0.403    0.687    0.010    0.010
##   EMO ~~                                                                
##     IND               0.000    0.011    0.035    0.972    0.001    0.001
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1   (.79.)    1.964    0.015  134.079    0.000    1.964    1.845
##    .DISC2   (.80.)    1.712    0.015  115.255    0.000    1.712    1.640
##    .DISC3   (.81.)    1.696    0.015  116.154    0.000    1.696    1.619
##    .DISC4   (.82.)    1.633    0.015  109.215    0.000    1.633    1.557
##    .DISC5   (.83.)    1.887    0.015  126.343    0.000    1.887    1.774
##    .DISC6   (.84.)    1.638    0.015  109.501    0.000    1.638    1.559
##    .JOB1    (.85.)    2.539    0.020  125.086    0.000    2.539    1.805
##    .JOB2    (.86.)    2.637    0.021  124.698    0.000    2.637    1.802
##    .JOB3    (.87.)    2.223    0.018  121.050    0.000    2.223    1.759
##    .JOB4    (.88.)    2.134    0.018  119.394    0.000    2.134    1.745
##    .JOB5    (.89.)    6.355    0.064   99.360    0.000    6.355    1.166
##    .CARE1   (.90.)    1.545    0.015  100.255    0.000    1.545    1.519
##    .CARE2   (.91.)    1.551    0.015  100.486    0.000    1.551    1.524
##    .CARE3   (.92.)    1.577    0.017   95.433    0.000    1.577    1.459
##    .CARE4   (.93.)    1.887    0.052   36.456    0.000    1.887    0.325
##    .RISK1   (.94.)    2.710    0.014  187.724    0.000    2.710    2.721
##    .RISK2   (.95.)    2.633    0.017  158.025    0.000    2.633    2.365
##    .RISK3   (.96.)    2.956    0.016  181.432    0.000    2.956    2.747
##    .SOC1    (.97.)    3.456    0.018  191.071    0.000    3.456    2.819
##    .SOC2    (.98.)    2.964    0.019  158.819    0.000    2.964    2.325
##    .EMO1    (.99.)    3.043    0.015  204.097    0.000    3.043    3.007
##    .EMO2    (.100)    2.520    0.014  181.032    0.000    2.520    2.668
##    .EMO3    (.101)    2.645    0.017  155.549    0.000    2.645    2.289
##    .IND1    (.102)    3.967    0.013  302.749    0.000    3.967    4.805
##    .IND2    (.103)    4.148    0.013  315.748    0.000    4.148    4.889
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.356    0.012   29.323    0.000    0.356    0.315
##    .DISC2             0.402    0.013   30.542    0.000    0.402    0.369
##    .DISC3             0.363    0.012   29.722    0.000    0.363    0.331
##    .DISC4             0.334    0.012   28.997    0.000    0.334    0.304
##    .DISC5             0.237    0.009   25.120    0.000    0.237    0.210
##    .DISC6             0.508    0.016   31.943    0.000    0.508    0.460
##    .JOB1              0.429    0.017   25.261    0.000    0.429    0.216
##    .JOB2              0.552    0.020   27.282    0.000    0.552    0.258
##    .JOB3              0.376    0.014   26.265    0.000    0.376    0.235
##    .JOB4              0.365    0.014   26.668    0.000    0.365    0.244
##    .JOB5             23.609    0.688   34.315    0.000   23.609    0.795
##    .CARE1             0.092    0.004   20.924    0.000    0.092    0.089
##    .CARE2             0.072    0.004   17.311    0.000    0.072    0.069
##    .CARE3             0.172    0.006   27.687    0.000    0.172    0.147
##    .CARE4            30.413    0.873   34.840    0.000   30.413    0.902
##    .RISK1             0.312    0.017   18.376    0.000    0.312    0.315
##    .RISK2             0.560    0.022   25.549    0.000    0.560    0.452
##    .RISK3             0.532    0.021   25.868    0.000    0.532    0.460
##    .SOC1              0.223    0.093    2.391    0.017    0.223    0.148
##    .SOC2              0.980    0.055   17.939    0.000    0.980    0.603
##    .EMO1              0.672    0.024   28.349    0.000    0.672    0.656
##    .EMO2              0.276    0.024   11.623    0.000    0.276    0.310
##    .EMO3              0.982    0.032   30.809    0.000    0.982    0.735
##    .IND1              0.207    0.039    5.369    0.000    0.207    0.304
##    .IND2              0.369    0.030   12.218    0.000    0.369    0.512
##     DISC              0.777    0.029   27.027    0.000    1.000    1.000
##     JOB               1.551    0.054   28.787    0.000    1.000    1.000
##     CARE              0.942    0.029   32.494    0.000    1.000    1.000
##     RISK              0.679    0.029   23.570    0.000    1.000    1.000
##     SOC               1.280    0.101   12.673    0.000    1.000    1.000
##     EMO               0.352    0.023   15.405    0.000    1.000    1.000
##     IND               0.474    0.041   11.564    0.000    1.000    1.000
## 
## 
## Group 2 [Nielsen]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC =~                                                               
##     DISC1             1.000                               0.739    0.814
##     DISC2   (.p2.)    0.941    0.016   58.034    0.000    0.696    0.727
##     DISC3   (.p3.)    0.973    0.016   61.816    0.000    0.719    0.784
##     DISC4   (.p4.)    0.993    0.016   62.032    0.000    0.734    0.756
##     DISC5   (.p5.)    1.073    0.016   69.066    0.000    0.794    0.833
##     DISC6   (.p6.)    0.877    0.017   52.274    0.000    0.648    0.675
##   JOB =~                                                                
##     JOB1              1.000                               1.106    0.834
##     JOB2    (.p8.)    1.012    0.014   71.439    0.000    1.120    0.810
##     JOB3    (.p9.)    0.887    0.012   72.791    0.000    0.982    0.809
##     JOB4    (.10.)    0.853    0.012   71.580    0.000    0.944    0.790
##     JOB5    (.11.)    1.979    0.053   37.263    0.000    2.189    0.607
##   CARE =~                                                               
##     CARE1             1.000                               1.006    0.946
##     CARE2   (.13.)    1.011    0.007  140.698    0.000    1.017    0.953
##     CARE3   (.14.)    1.028    0.009  115.772    0.000    1.034    0.894
##     CARE4   (.15.)    1.875    0.046   40.840    0.000    1.886    0.664
##   RISK =~                                                               
##     RISK1             1.000                               0.768    0.821
##     RISK2   (.17.)    1.000    0.024   41.106    0.000    0.768    0.684
##     RISK3   (.18.)    0.960    0.024   40.750    0.000    0.737    0.660
##   SOC =~                                                                
##     SOC1              1.000                               1.056    0.885
##     SOC2    (.20.)    0.710    0.051   14.004    0.000    0.750    0.616
##   EMO =~                                                                
##     EMO1              1.000                               0.545    0.555
##     EMO2    (.22.)    1.323    0.051   25.886    0.000    0.721    0.781
##     EMO3    (.23.)    1.002    0.041   24.708    0.000    0.546    0.489
##   IND =~                                                                
##     IND1              1.000                               0.787    0.825
##     IND2    (.25.)    0.861    0.067   12.921    0.000    0.677    0.735
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DISC ~~                                                               
##     JOB               0.073    0.020    3.578    0.000    0.089    0.089
##     CARE              0.097    0.018    5.401    0.000    0.131    0.131
##     RISK              0.028    0.015    1.854    0.064    0.049    0.049
##     SOC               0.005    0.020    0.261    0.794    0.007    0.007
##     EMO               0.084    0.012    7.103    0.000    0.207    0.207
##     IND               0.024    0.016    1.514    0.130    0.041    0.041
##   JOB ~~                                                                
##     CARE              0.119    0.027    4.411    0.000    0.107    0.107
##     RISK              0.192    0.023    8.315    0.000    0.226    0.226
##     SOC               0.035    0.031    1.141    0.254    0.030    0.030
##     EMO               0.087    0.017    5.015    0.000    0.144    0.144
##     IND               0.102    0.024    4.304    0.000    0.117    0.117
##   CARE ~~                                                               
##     RISK              0.035    0.020    1.764    0.078    0.045    0.045
##     SOC               0.098    0.027    3.628    0.000    0.092    0.092
##     EMO               0.075    0.015    4.908    0.000    0.136    0.136
##     IND               0.051    0.021    2.491    0.013    0.065    0.065
##   RISK ~~                                                               
##     SOC               0.105    0.023    4.616    0.000    0.130    0.130
##     EMO               0.095    0.013    7.272    0.000    0.227    0.227
##     IND               0.145    0.018    7.998    0.000    0.240    0.240
##   SOC ~~                                                                
##     EMO               0.208    0.019   11.078    0.000    0.362    0.362
##     IND              -0.068    0.024   -2.884    0.004   -0.082   -0.082
##   EMO ~~                                                                
##     IND              -0.054    0.013   -4.085    0.000   -0.127   -0.127
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1   (.79.)    1.964    0.015  134.079    0.000    1.964    2.163
##    .DISC2   (.80.)    1.712    0.015  115.255    0.000    1.712    1.789
##    .DISC3   (.81.)    1.696    0.015  116.154    0.000    1.696    1.849
##    .DISC4   (.82.)    1.633    0.015  109.215    0.000    1.633    1.682
##    .DISC5   (.83.)    1.887    0.015  126.343    0.000    1.887    1.981
##    .DISC6   (.84.)    1.638    0.015  109.501    0.000    1.638    1.707
##    .JOB1    (.85.)    2.539    0.020  125.086    0.000    2.539    1.913
##    .JOB2    (.86.)    2.637    0.021  124.698    0.000    2.637    1.907
##    .JOB3    (.87.)    2.223    0.018  121.050    0.000    2.223    1.831
##    .JOB4    (.88.)    2.134    0.018  119.394    0.000    2.134    1.786
##    .JOB5    (.89.)    6.355    0.064   99.360    0.000    6.355    1.761
##    .CARE1   (.90.)    1.545    0.015  100.255    0.000    1.545    1.453
##    .CARE2   (.91.)    1.551    0.015  100.486    0.000    1.551    1.453
##    .CARE3   (.92.)    1.577    0.017   95.433    0.000    1.577    1.363
##    .CARE4   (.93.)    1.887    0.052   36.456    0.000    1.887    0.664
##    .RISK1   (.94.)    2.710    0.014  187.724    0.000    2.710    2.899
##    .RISK2   (.95.)    2.633    0.017  158.025    0.000    2.633    2.347
##    .RISK3   (.96.)    2.956    0.016  181.432    0.000    2.956    2.646
##    .SOC1    (.97.)    3.456    0.018  191.071    0.000    3.456    2.897
##    .SOC2    (.98.)    2.964    0.019  158.819    0.000    2.964    2.437
##    .EMO1    (.99.)    3.043    0.015  204.097    0.000    3.043    3.100
##    .EMO2    (.100)    2.520    0.014  181.032    0.000    2.520    2.730
##    .EMO3    (.101)    2.645    0.017  155.549    0.000    2.645    2.369
##    .IND1    (.102)    3.967    0.013  302.749    0.000    3.967    4.158
##    .IND2    (.103)    4.148    0.013  315.748    0.000    4.148    4.500
##     DISC              0.000                               0.000    0.000
##     JOB               0.000                               0.000    0.000
##     CARE              0.000                               0.000    0.000
##     RISK              0.000                               0.000    0.000
##     SOC               0.000                               0.000    0.000
##     EMO               0.000                               0.000    0.000
##     IND               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .DISC1             0.278    0.011   25.155    0.000    0.278    0.337
##    .DISC2             0.432    0.015   28.024    0.000    0.432    0.471
##    .DISC3             0.324    0.012   26.421    0.000    0.324    0.385
##    .DISC4             0.403    0.015   27.318    0.000    0.403    0.428
##    .DISC5             0.278    0.011   24.204    0.000    0.278    0.306
##    .DISC6             0.502    0.017   28.956    0.000    0.502    0.544
##    .JOB1              0.538    0.023   23.439    0.000    0.538    0.305
##    .JOB2              0.659    0.027   24.801    0.000    0.659    0.344
##    .JOB3              0.510    0.021   24.870    0.000    0.510    0.346
##    .JOB4              0.536    0.021   25.708    0.000    0.536    0.375
##    .JOB5              8.235    0.279   29.560    0.000    8.235    0.632
##    .CARE1             0.119    0.006   18.664    0.000    0.119    0.106
##    .CARE2             0.105    0.006   16.864    0.000    0.105    0.092
##    .CARE3             0.269    0.010   26.087    0.000    0.269    0.201
##    .CARE4             4.513    0.147   30.611    0.000    4.513    0.559
##    .RISK1             0.284    0.018   15.517    0.000    0.284    0.325
##    .RISK2             0.670    0.027   24.568    0.000    0.670    0.532
##    .RISK3             0.705    0.028   25.606    0.000    0.705    0.565
##    .SOC1              0.307    0.081    3.812    0.000    0.307    0.216
##    .SOC2              0.917    0.050   18.471    0.000    0.917    0.620
##    .EMO1              0.667    0.025   26.345    0.000    0.667    0.692
##    .EMO2              0.333    0.024   13.594    0.000    0.333    0.390
##    .EMO3              0.948    0.034   28.111    0.000    0.948    0.761
##    .IND1              0.291    0.048    6.024    0.000    0.291    0.319
##    .IND2              0.391    0.037   10.508    0.000    0.391    0.460
##     DISC              0.547    0.022   24.985    0.000    1.000    1.000
##     JOB               1.224    0.048   25.680    0.000    1.000    1.000
##     CARE              1.011    0.034   29.447    0.000    1.000    1.000
##     RISK              0.589    0.027   21.535    0.000    1.000    1.000
##     SOC               1.115    0.090   12.422    0.000    1.000    1.000
##     EMO               0.297    0.021   14.367    0.000    1.000    1.000
##     IND               0.620    0.054   11.507    0.000    1.000    1.000

Chi-squared Difference test

Notes on interpretation: If p-value > 0.05, the constrained model is equivalent to the unconstrained/free model (the coefficients and intercepts do not vary by group). Thus, it would be fair to analyse the pooled data in a single global model.

If p< 0.05, the free model is significantly different from the constrained model, implying differences in coefficients/intercepts between the two groups.

*Difference between config and metric

anova(config, metric)
## Chi-Squared Difference Test
## 
##         Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## config 508 298794 300023 2841.4                                  
## metric 526 299157 300271 3240.4     399.02      18  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

*Difference between metric and scalar

anova(metric, scalar)
## Chi-Squared Difference Test
## 
##         Df    AIC    BIC  Chisq Chisq diff Df diff Pr(>Chisq)    
## metric 526 299157 300271 3240.4                                  
## scalar 551 300105 301059 4238.0     997.57      25  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Examining differences among items to identify scalar non-equality issues

# Transform the data into long format
# Put all variables in the same column except `sample_group`, the grouping variable\
combined <- combined[,-1]
combined.long <- combined %>%
  pivot_longer(-sample_group, names_to = "variables", values_to = "value")
stat.test <- combined.long%>%
  group_by(variables) %>%
  t_test(value ~ sample_group) %>%
  adjust_pvalue(method = "fdr") %>%
  add_significance()
DT::datatable(stat.test)
# # Create the plot
# myplot <- ggboxplot(
#   combined.long, x = "sample_group", y = "value",
#   fill = "sample_group", palette = "npg", legend = "none",
#   ggtheme = theme_pubr(border = TRUE)
#   ) +
#   facet_wrap(~variables)
# # Add statistical test p-values
# stat.test <- stat.test %>% add_xy_position(x = "sample_group")
# myplot + stat_pvalue_manual(stat.test, label = "p.adj.signif")

Subscale Scores

#z-scores for all items
Sample_1_Nielsen_scaled <- as.data.frame(scale(Sample_1_Nielsen[2:26]))
UofA_Sample_scaled <- as.data.frame(scale(UofA_Sample[2:26]))

Sample_1_Nielsen_scaled$sample_group = "Nielsen"
UofA_Sample_scaled$sample_group = "UofA"

combined_scaled <- rbind(UofA_Sample_scaled, Sample_1_Nielsen_scaled)
#Create subscale scores

combined_scaled$DISC <- rowMeans(combined_scaled[1:6])
combined_scaled$JOB <- rowMeans(combined_scaled[7:11])
combined_scaled$CARE <- rowMeans(combined_scaled[12:15])
combined_scaled$RISK <- rowMeans(combined_scaled[16:18])
combined_scaled$SOC <- rowMeans(combined_scaled[19:20])
combined_scaled$EMO <- rowMeans(combined_scaled[21:23])
combined_scaled$IND <- rowMeans(combined_scaled[24:25])
combined_scaled$CASE <- combined$CASE
## Warning: Unknown or uninitialised column: `CASE`.