Random Split into Two Sub-Samples

set.seed(888) # Set seed so that same sample can be reproduced in future

# select 50% of data for training and test set
sample <- sample.int(n = nrow(ctoccsv.yn), size = floor(.50*nrow(ctoccsv.yn)), replace = F)
train.dat <- ctoccsv.yn[sample, ]
test.dat  <- ctoccsv.yn[-sample, ]

Primary Theoretical Model

8 Factor CFA

sps.cfa.8 <- '
tacphys =~ A1Q1+ A1Q2+ A1Q3
musclejointbone =~ A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3
soundjr =~ B2Q1+ B2Q2
tactilejr =~ B3Q1+ B3Q2 
inc =~ .90*CQ1
energy =~ .90*DQ1
urge =~ .90*EQ1
'

fit.sps.cfa.8 <- cfa(sps.cfa.8, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1"))
summary(fit.sps.cfa.8, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 33 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        55
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                                56.089      91.394
##   Degrees of freedom                                65          65
##   P-value (Chi-square)                           0.777       0.017
##   Scaling correction factor                                  0.725
##   Shift parameter                                           13.980
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000       0.992
##   Tucker-Lewis Index (TLI)                       1.003       0.986
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000       0.029
##   90 Percent confidence interval - lower         0.000       0.013
##   90 Percent confidence interval - upper         0.019       0.042
##   P-value RMSEA <= 0.05                          1.000       0.998
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.061       0.061
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys =~                                                              
##     A1Q1                0.595    0.069    8.592    0.000    0.595    0.595
##     A1Q2                0.690    0.077    8.904    0.000    0.690    0.690
##     A1Q3                0.673    0.073    9.221    0.000    0.673    0.673
##   musclejointbone =~                                                      
##     A2Q1                0.761    0.072   10.622    0.000    0.761    0.761
##     A2Q2                0.864    0.071   12.208    0.000    0.864    0.864
##   lookjr =~                                                               
##     B1Q1                0.968    0.025   38.202    0.000    0.968    0.968
##     B1Q2                0.952    0.023   42.025    0.000    0.952    0.952
##     B1Q3                0.853    0.032   26.274    0.000    0.853    0.853
##   soundjr =~                                                              
##     B2Q1                0.851    0.051   16.608    0.000    0.851    0.851
##     B2Q2                0.906    0.048   18.734    0.000    0.906    0.906
##   tactilejr =~                                                            
##     B3Q1                0.860    0.061   14.062    0.000    0.860    0.860
##     B3Q2                0.769    0.063   12.192    0.000    0.769    0.769
##   inc =~                                                                  
##     CQ1                 0.900                               0.900    0.900
##   energy =~                                                               
##     DQ1                 0.900                               0.900    0.900
##   urge =~                                                                 
##     EQ1                 0.900                               0.900    0.900
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys ~~                                                              
##     musclejointbon      0.863    0.104    8.293    0.000    0.863    0.863
##     lookjr              0.747    0.072   10.405    0.000    0.747    0.747
##     soundjr             0.753    0.101    7.468    0.000    0.753    0.753
##     tactilejr           0.854    0.085   10.064    0.000    0.854    0.854
##     inc                 0.414    0.111    3.726    0.000    0.414    0.414
##     energy              0.494    0.118    4.188    0.000    0.494    0.494
##     urge                0.457    0.112    4.071    0.000    0.457    0.457
##   musclejointbone ~~                                                      
##     lookjr              0.511    0.086    5.945    0.000    0.511    0.511
##     soundjr             0.715    0.094    7.618    0.000    0.715    0.715
##     tactilejr           0.694    0.108    6.397    0.000    0.694    0.694
##     inc                 0.397    0.119    3.325    0.001    0.397    0.397
##     energy              0.622    0.106    5.865    0.000    0.622    0.622
##     urge                0.466    0.109    4.264    0.000    0.466    0.466
##   lookjr ~~                                                               
##     soundjr             0.663    0.067    9.894    0.000    0.663    0.663
##     tactilejr           0.627    0.072    8.676    0.000    0.627    0.627
##     inc                 0.432    0.077    5.642    0.000    0.432    0.432
##     energy              0.489    0.081    6.043    0.000    0.489    0.489
##     urge                0.467    0.071    6.545    0.000    0.467    0.467
##   soundjr ~~                                                              
##     tactilejr           0.852    0.074   11.497    0.000    0.852    0.852
##     inc                 0.452    0.104    4.339    0.000    0.452    0.452
##     energy              0.524    0.105    4.995    0.000    0.524    0.524
##     urge                0.614    0.093    6.606    0.000    0.614    0.614
##   tactilejr ~~                                                            
##     inc                 0.353    0.113    3.109    0.002    0.353    0.353
##     energy              0.523    0.110    4.755    0.000    0.523    0.523
##     urge                0.582    0.097    6.028    0.000    0.582    0.582
##   inc ~~                                                                  
##     energy              0.589    0.098    6.003    0.000    0.589    0.589
##     urge                0.439    0.097    4.528    0.000    0.439    0.439
##   energy ~~                                                               
##     urge                0.399    0.106    3.766    0.000    0.399    0.399
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tacphys           0.000                               0.000    0.000
##     musclejointbon    0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     soundjr           0.000                               0.000    0.000
##     tactilejr         0.000                               0.000    0.000
##     inc               0.000                               0.000    0.000
##     energy            0.000                               0.000    0.000
##     urge              0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.646                               0.646    0.646
##    .A1Q2              0.525                               0.525    0.525
##    .A1Q3              0.548                               0.548    0.548
##    .A2Q1              0.420                               0.420    0.420
##    .A2Q2              0.253                               0.253    0.253
##    .B1Q1              0.063                               0.063    0.063
##    .B1Q2              0.094                               0.094    0.094
##    .B1Q3              0.272                               0.272    0.272
##    .B2Q1              0.275                               0.275    0.275
##    .B2Q2              0.180                               0.180    0.180
##    .B3Q1              0.261                               0.261    0.261
##    .B3Q2              0.409                               0.409    0.409
##    .CQ1               0.190                               0.190    0.190
##    .DQ1               0.190                               0.190    0.190
##    .EQ1               0.190                               0.190    0.190
##     tacphys           1.000                               1.000    1.000
##     musclejointbon    1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     soundjr           1.000                               1.000    1.000
##     tactilejr         1.000                               1.000    1.000
##     inc               1.000                               1.000    1.000
##     energy            1.000                               1.000    1.000
##     urge              1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.8, ci=T, level = .90)
##                 lhs  op             rhs est.std    se      z pvalue ci.lower
## 1           tacphys  =~            A1Q1   0.595 0.069  8.592  0.000    0.481
## 2           tacphys  =~            A1Q2   0.690 0.077  8.904  0.000    0.562
## 3           tacphys  =~            A1Q3   0.673 0.073  9.221  0.000    0.553
## 4   musclejointbone  =~            A2Q1   0.761 0.072 10.622  0.000    0.644
## 5   musclejointbone  =~            A2Q2   0.864 0.071 12.208  0.000    0.748
## 6            lookjr  =~            B1Q1   0.968 0.025 38.202  0.000    0.926
## 7            lookjr  =~            B1Q2   0.952 0.023 42.025  0.000    0.915
## 8            lookjr  =~            B1Q3   0.853 0.032 26.274  0.000    0.800
## 9           soundjr  =~            B2Q1   0.851 0.051 16.608  0.000    0.767
## 10          soundjr  =~            B2Q2   0.906 0.048 18.734  0.000    0.826
## 11        tactilejr  =~            B3Q1   0.860 0.061 14.062  0.000    0.759
## 12        tactilejr  =~            B3Q2   0.769 0.063 12.192  0.000    0.665
## 13              inc  =~             CQ1   0.900 0.000     NA     NA    0.900
## 14           energy  =~             DQ1   0.900 0.000     NA     NA    0.900
## 15             urge  =~             EQ1   0.900 0.000     NA     NA    0.900
## 16             A1Q1   |              t1   0.843 0.064 13.122  0.000    0.737
## 17             A1Q2   |              t1   1.336 0.079 16.910  0.000    1.206
## 18             A1Q3   |              t1   1.254 0.076 16.548  0.000    1.130
## 19             A2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 20             A2Q2   |              t1   1.502 0.087 17.314  0.000    1.359
## 21             B1Q1   |              t1   0.297 0.057  5.196  0.000    0.203
## 22             B1Q2   |              t1   0.662 0.061 10.840  0.000    0.561
## 23             B1Q3   |              t1   0.895 0.065 13.692  0.000    0.787
## 24             B2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 25             B2Q2   |              t1   1.288 0.077 16.712  0.000    1.162
## 26             B3Q1   |              t1   1.349 0.080 16.956  0.000    1.218
## 27             B3Q2   |              t1   1.190 0.074 16.189  0.000    1.069
## 28              CQ1   |              t1   0.895 0.065 13.692  0.000    0.787
## 29              DQ1   |              t1   1.093 0.070 15.520  0.000    0.978
## 30              EQ1   |              t1   0.694 0.062 11.271  0.000    0.592
## 31             A1Q1  ~~            A1Q1   0.646 0.082  7.850  0.000    0.511
## 32             A1Q2  ~~            A1Q2   0.525 0.107  4.911  0.000    0.349
## 33             A1Q3  ~~            A1Q3   0.548 0.098  5.584  0.000    0.386
## 34             A2Q1  ~~            A2Q1   0.420 0.109  3.848  0.000    0.241
## 35             A2Q2  ~~            A2Q2   0.253 0.122  2.071  0.038    0.052
## 36             B1Q1  ~~            B1Q1   0.063 0.049  1.281  0.200   -0.018
## 37             B1Q2  ~~            B1Q2   0.094 0.043  2.183  0.029    0.023
## 38             B1Q3  ~~            B1Q3   0.272 0.055  4.906  0.000    0.181
## 39             B2Q1  ~~            B2Q1   0.275 0.087  3.157  0.002    0.132
## 40             B2Q2  ~~            B2Q2   0.180 0.088  2.056  0.040    0.036
## 41             B3Q1  ~~            B3Q1   0.261 0.105  2.483  0.013    0.088
## 42             B3Q2  ~~            B3Q2   0.409 0.097  4.213  0.000    0.249
## 43              CQ1  ~~             CQ1   0.190 0.000     NA     NA    0.190
## 44              DQ1  ~~             DQ1   0.190 0.000     NA     NA    0.190
## 45              EQ1  ~~             EQ1   0.190 0.000     NA     NA    0.190
## 46          tacphys  ~~         tacphys   1.000 0.000     NA     NA    1.000
## 47  musclejointbone  ~~ musclejointbone   1.000 0.000     NA     NA    1.000
## 48           lookjr  ~~          lookjr   1.000 0.000     NA     NA    1.000
## 49          soundjr  ~~         soundjr   1.000 0.000     NA     NA    1.000
## 50        tactilejr  ~~       tactilejr   1.000 0.000     NA     NA    1.000
## 51              inc  ~~             inc   1.000 0.000     NA     NA    1.000
## 52           energy  ~~          energy   1.000 0.000     NA     NA    1.000
## 53             urge  ~~            urge   1.000 0.000     NA     NA    1.000
## 54          tacphys  ~~ musclejointbone   0.863 0.104  8.293  0.000    0.692
## 55          tacphys  ~~          lookjr   0.747 0.072 10.405  0.000    0.629
## 56          tacphys  ~~         soundjr   0.753 0.101  7.468  0.000    0.587
## 57          tacphys  ~~       tactilejr   0.854 0.085 10.064  0.000    0.715
## 58          tacphys  ~~             inc   0.414 0.111  3.726  0.000    0.231
## 59          tacphys  ~~          energy   0.494 0.118  4.188  0.000    0.300
## 60          tacphys  ~~            urge   0.457 0.112  4.071  0.000    0.272
## 61  musclejointbone  ~~          lookjr   0.511 0.086  5.945  0.000    0.370
## 62  musclejointbone  ~~         soundjr   0.715 0.094  7.618  0.000    0.560
## 63  musclejointbone  ~~       tactilejr   0.694 0.108  6.397  0.000    0.515
## 64  musclejointbone  ~~             inc   0.397 0.119  3.325  0.001    0.200
## 65  musclejointbone  ~~          energy   0.622 0.106  5.865  0.000    0.448
## 66  musclejointbone  ~~            urge   0.466 0.109  4.264  0.000    0.286
## 67           lookjr  ~~         soundjr   0.663 0.067  9.894  0.000    0.553
## 68           lookjr  ~~       tactilejr   0.627 0.072  8.676  0.000    0.508
## 69           lookjr  ~~             inc   0.432 0.077  5.642  0.000    0.306
## 70           lookjr  ~~          energy   0.489 0.081  6.043  0.000    0.356
## 71           lookjr  ~~            urge   0.467 0.071  6.545  0.000    0.350
## 72          soundjr  ~~       tactilejr   0.852 0.074 11.497  0.000    0.730
## 73          soundjr  ~~             inc   0.452 0.104  4.339  0.000    0.280
## 74          soundjr  ~~          energy   0.524 0.105  4.995  0.000    0.351
## 75          soundjr  ~~            urge   0.614 0.093  6.606  0.000    0.461
## 76        tactilejr  ~~             inc   0.353 0.113  3.109  0.002    0.166
## 77        tactilejr  ~~          energy   0.523 0.110  4.755  0.000    0.342
## 78        tactilejr  ~~            urge   0.582 0.097  6.028  0.000    0.423
## 79              inc  ~~          energy   0.589 0.098  6.003  0.000    0.428
## 80              inc  ~~            urge   0.439 0.097  4.528  0.000    0.280
## 81           energy  ~~            urge   0.399 0.106  3.766  0.000    0.225
## 82             A1Q1 ~*~            A1Q1   1.000 0.000     NA     NA    1.000
## 83             A1Q2 ~*~            A1Q2   1.000 0.000     NA     NA    1.000
## 84             A1Q3 ~*~            A1Q3   1.000 0.000     NA     NA    1.000
## 85             A2Q1 ~*~            A2Q1   1.000 0.000     NA     NA    1.000
## 86             A2Q2 ~*~            A2Q2   1.000 0.000     NA     NA    1.000
## 87             B1Q1 ~*~            B1Q1   1.000 0.000     NA     NA    1.000
## 88             B1Q2 ~*~            B1Q2   1.000 0.000     NA     NA    1.000
## 89             B1Q3 ~*~            B1Q3   1.000 0.000     NA     NA    1.000
## 90             B2Q1 ~*~            B2Q1   1.000 0.000     NA     NA    1.000
## 91             B2Q2 ~*~            B2Q2   1.000 0.000     NA     NA    1.000
## 92             B3Q1 ~*~            B3Q1   1.000 0.000     NA     NA    1.000
## 93             B3Q2 ~*~            B3Q2   1.000 0.000     NA     NA    1.000
## 94              CQ1 ~*~             CQ1   1.000 0.000     NA     NA    1.000
## 95              DQ1 ~*~             DQ1   1.000 0.000     NA     NA    1.000
## 96              EQ1 ~*~             EQ1   1.000 0.000     NA     NA    1.000
## 97             A1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 98             A1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 99             A1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 100            A2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 101            A2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 102            B1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 103            B1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 104            B1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 105            B2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 106            B2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 107            B3Q1  ~1                   0.000 0.000     NA     NA    0.000
## 108            B3Q2  ~1                   0.000 0.000     NA     NA    0.000
## 109             CQ1  ~1                   0.000 0.000     NA     NA    0.000
## 110             DQ1  ~1                   0.000 0.000     NA     NA    0.000
## 111             EQ1  ~1                   0.000 0.000     NA     NA    0.000
## 112         tacphys  ~1                   0.000 0.000     NA     NA    0.000
## 113 musclejointbone  ~1                   0.000 0.000     NA     NA    0.000
## 114          lookjr  ~1                   0.000 0.000     NA     NA    0.000
## 115         soundjr  ~1                   0.000 0.000     NA     NA    0.000
## 116       tactilejr  ~1                   0.000 0.000     NA     NA    0.000
## 117             inc  ~1                   0.000 0.000     NA     NA    0.000
## 118          energy  ~1                   0.000 0.000     NA     NA    0.000
## 119            urge  ~1                   0.000 0.000     NA     NA    0.000
##     ci.upper
## 1      0.709
## 2      0.817
## 3      0.792
## 4      0.879
## 5      0.981
## 6      1.010
## 7      0.989
## 8      0.907
## 9      0.935
## 10     0.985
## 11     0.960
## 12     0.873
## 13     0.900
## 14     0.900
## 15     0.900
## 16     0.949
## 17     1.466
## 18     1.379
## 19     1.493
## 20     1.645
## 21     0.392
## 22     0.762
## 23     1.002
## 24     1.493
## 25     1.415
## 26     1.480
## 27     1.311
## 28     1.002
## 29     1.209
## 30     0.795
## 31     0.782
## 32     0.700
## 33     0.709
## 34     0.600
## 35     0.455
## 36     0.144
## 37     0.165
## 38     0.363
## 39     0.419
## 40     0.324
## 41     0.434
## 42     0.568
## 43     0.190
## 44     0.190
## 45     0.190
## 46     1.000
## 47     1.000
## 48     1.000
## 49     1.000
## 50     1.000
## 51     1.000
## 52     1.000
## 53     1.000
## 54     1.035
## 55     0.865
## 56     0.919
## 57     0.994
## 58     0.597
## 59     0.688
## 60     0.641
## 61     0.653
## 62     0.869
## 63     0.872
## 64     0.593
## 65     0.796
## 66     0.645
## 67     0.774
## 68     0.746
## 69     0.558
## 70     0.622
## 71     0.585
## 72     0.973
## 73     0.623
## 74     0.697
## 75     0.766
## 76     0.539
## 77     0.703
## 78     0.741
## 79     0.750
## 80     0.599
## 81     0.573
## 82     1.000
## 83     1.000
## 84     1.000
## 85     1.000
## 86     1.000
## 87     1.000
## 88     1.000
## 89     1.000
## 90     1.000
## 91     1.000
## 92     1.000
## 93     1.000
## 94     1.000
## 95     1.000
## 96     1.000
## 97     0.000
## 98     0.000
## 99     0.000
## 100    0.000
## 101    0.000
## 102    0.000
## 103    0.000
## 104    0.000
## 105    0.000
## 106    0.000
## 107    0.000
## 108    0.000
## 109    0.000
## 110    0.000
## 111    0.000
## 112    0.000
## 113    0.000
## 114    0.000
## 115    0.000
## 116    0.000
## 117    0.000
## 118    0.000
## 119    0.000

8 Factor CFA with Higher Order Factors

sps.cfa.8.h <- '
tacphys =~ A1Q1+ A1Q2+ A1Q3
musclejointbone =~ A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3
soundjr =~ B2Q1+ B2Q2
tactilejr =~ B3Q1+ B3Q2 
internal =~ .90*CQ1
energy =~ .90*DQ1
urge =~ .90*EQ1
fac1 =~ tacphys + musclejointbone
fac2 =~ lookjr + soundjr + tactilejr + internal
'

fit.sps.cfa.8.h <- cfa(sps.cfa.8.h, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) # Model does not converge

Alternative Models

6 Factor CFA

C, D, and E (the emotional/internally-focused items) are considered as loadings on a single factor instead of 3 separate factors

sps.cfa.6 <- '
tacphys =~ A1Q1+ A1Q2+ A1Q3
musclejointbone =~ A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3
soundjr =~ B2Q1+ B2Q2
tactilejr =~ B3Q1+ B3Q2 
internaljr =~ .9*CQ1
emo =~ DQ1 + EQ1
'
fit.sps.cfa.6<- cfa(sps.cfa.6, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.6, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 38 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        50
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                                59.382      93.892
##   Degrees of freedom                                70          70
##   P-value (Chi-square)                           0.813       0.030
##   Scaling correction factor                                  0.757
##   Shift parameter                                           15.410
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000       0.992
##   Tucker-Lewis Index (TLI)                       1.003       0.989
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000       0.026
##   90 Percent confidence interval - lower         0.000       0.009
##   90 Percent confidence interval - upper         0.017       0.039
##   P-value RMSEA <= 0.05                          1.000       0.999
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.063       0.063
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys =~                                                              
##     A1Q1                0.595    0.069    8.587    0.000    0.595    0.595
##     A1Q2                0.690    0.077    8.913    0.000    0.690    0.690
##     A1Q3                0.672    0.073    9.214    0.000    0.672    0.672
##   musclejointbone =~                                                      
##     A2Q1                0.761    0.072   10.613    0.000    0.761    0.761
##     A2Q2                0.864    0.071   12.145    0.000    0.864    0.864
##   lookjr =~                                                               
##     B1Q1                0.968    0.025   38.185    0.000    0.968    0.968
##     B1Q2                0.952    0.023   41.985    0.000    0.952    0.952
##     B1Q3                0.853    0.032   26.271    0.000    0.853    0.853
##   soundjr =~                                                              
##     B2Q1                0.851    0.051   16.584    0.000    0.851    0.851
##     B2Q2                0.906    0.048   18.775    0.000    0.906    0.906
##   tactilejr =~                                                            
##     B3Q1                0.860    0.061   14.037    0.000    0.860    0.860
##     B3Q2                0.769    0.063   12.177    0.000    0.769    0.769
##   internaljr =~                                                           
##     CQ1                 0.900                               0.900    0.900
##   emo =~                                                                  
##     DQ1                 0.581    0.090    6.487    0.000    0.581    0.581
##     EQ1                 0.556    0.085    6.545    0.000    0.556    0.556
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys ~~                                                              
##     musclejointbon      0.863    0.104    8.293    0.000    0.863    0.863
##     lookjr              0.747    0.072   10.405    0.000    0.747    0.747
##     soundjr             0.753    0.101    7.469    0.000    0.753    0.753
##     tactilejr           0.854    0.085   10.064    0.000    0.854    0.854
##     internaljr          0.414    0.111    3.726    0.000    0.414    0.414
##     emo                 0.752    0.156    4.829    0.000    0.752    0.752
##   musclejointbone ~~                                                      
##     lookjr              0.511    0.086    5.944    0.000    0.511    0.511
##     soundjr             0.714    0.094    7.621    0.000    0.714    0.714
##     tactilejr           0.694    0.108    6.397    0.000    0.694    0.694
##     internaljr          0.397    0.119    3.325    0.001    0.397    0.397
##     emo                 0.865    0.152    5.703    0.000    0.865    0.865
##   lookjr ~~                                                               
##     soundjr             0.663    0.067    9.894    0.000    0.663    0.663
##     tactilejr           0.627    0.072    8.676    0.000    0.627    0.627
##     internaljr          0.432    0.077    5.642    0.000    0.432    0.432
##     emo                 0.757    0.117    6.485    0.000    0.757    0.757
##   soundjr ~~                                                              
##     tactilejr           0.852    0.074   11.497    0.000    0.852    0.852
##     internaljr          0.452    0.104    4.339    0.000    0.452    0.452
##     emo                 0.911    0.141    6.478    0.000    0.911    0.911
##   tactilejr ~~                                                            
##     internaljr          0.353    0.113    3.109    0.002    0.353    0.353
##     emo                 0.881    0.145    6.074    0.000    0.881    0.881
##   internaljr ~~                                                           
##     emo                 0.815    0.134    6.084    0.000    0.815    0.815
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tacphys           0.000                               0.000    0.000
##     musclejointbon    0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     soundjr           0.000                               0.000    0.000
##     tactilejr         0.000                               0.000    0.000
##     internaljr        0.000                               0.000    0.000
##     emo               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.646                               0.646    0.646
##    .A1Q2              0.524                               0.524    0.524
##    .A1Q3              0.548                               0.548    0.548
##    .A2Q1              0.420                               0.420    0.420
##    .A2Q2              0.253                               0.253    0.253
##    .B1Q1              0.063                               0.063    0.063
##    .B1Q2              0.094                               0.094    0.094
##    .B1Q3              0.272                               0.272    0.272
##    .B2Q1              0.276                               0.276    0.276
##    .B2Q2              0.180                               0.180    0.180
##    .B3Q1              0.261                               0.261    0.261
##    .B3Q2              0.409                               0.409    0.409
##    .CQ1               0.190                               0.190    0.190
##    .DQ1               0.663                               0.663    0.663
##    .EQ1               0.691                               0.691    0.691
##     tacphys           1.000                               1.000    1.000
##     musclejointbon    1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     soundjr           1.000                               1.000    1.000
##     tactilejr         1.000                               1.000    1.000
##     internaljr        1.000                               1.000    1.000
##     emo               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.6, ci=T, level = .90)
##                 lhs  op             rhs est.std    se      z pvalue ci.lower
## 1           tacphys  =~            A1Q1   0.595 0.069  8.587  0.000    0.481
## 2           tacphys  =~            A1Q2   0.690 0.077  8.913  0.000    0.562
## 3           tacphys  =~            A1Q3   0.672 0.073  9.214  0.000    0.552
## 4   musclejointbone  =~            A2Q1   0.761 0.072 10.613  0.000    0.643
## 5   musclejointbone  =~            A2Q2   0.864 0.071 12.145  0.000    0.747
## 6            lookjr  =~            B1Q1   0.968 0.025 38.185  0.000    0.926
## 7            lookjr  =~            B1Q2   0.952 0.023 41.985  0.000    0.914
## 8            lookjr  =~            B1Q3   0.853 0.032 26.271  0.000    0.800
## 9           soundjr  =~            B2Q1   0.851 0.051 16.584  0.000    0.767
## 10          soundjr  =~            B2Q2   0.906 0.048 18.775  0.000    0.826
## 11        tactilejr  =~            B3Q1   0.860 0.061 14.037  0.000    0.759
## 12        tactilejr  =~            B3Q2   0.769 0.063 12.177  0.000    0.665
## 13       internaljr  =~             CQ1   0.900 0.000     NA     NA    0.900
## 14              emo  =~             DQ1   0.581 0.090  6.487  0.000    0.434
## 15              emo  =~             EQ1   0.556 0.085  6.545  0.000    0.416
## 16             A1Q1   |              t1   0.843 0.064 13.122  0.000    0.737
## 17             A1Q2   |              t1   1.336 0.079 16.910  0.000    1.206
## 18             A1Q3   |              t1   1.254 0.076 16.548  0.000    1.130
## 19             A2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 20             A2Q2   |              t1   1.502 0.087 17.314  0.000    1.359
## 21             B1Q1   |              t1   0.297 0.057  5.196  0.000    0.203
## 22             B1Q2   |              t1   0.662 0.061 10.840  0.000    0.561
## 23             B1Q3   |              t1   0.895 0.065 13.692  0.000    0.787
## 24             B2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 25             B2Q2   |              t1   1.288 0.077 16.712  0.000    1.162
## 26             B3Q1   |              t1   1.349 0.080 16.956  0.000    1.218
## 27             B3Q2   |              t1   1.190 0.074 16.189  0.000    1.069
## 28              CQ1   |              t1   0.895 0.065 13.692  0.000    0.787
## 29              DQ1   |              t1   1.093 0.070 15.520  0.000    0.978
## 30              EQ1   |              t1   0.694 0.062 11.271  0.000    0.592
## 31             A1Q1  ~~            A1Q1   0.646 0.082  7.847  0.000    0.511
## 32             A1Q2  ~~            A1Q2   0.524 0.107  4.912  0.000    0.349
## 33             A1Q3  ~~            A1Q3   0.548 0.098  5.582  0.000    0.386
## 34             A2Q1  ~~            A2Q1   0.420 0.109  3.847  0.000    0.241
## 35             A2Q2  ~~            A2Q2   0.253 0.123  2.058  0.040    0.051
## 36             B1Q1  ~~            B1Q1   0.063 0.049  1.280  0.201   -0.018
## 37             B1Q2  ~~            B1Q2   0.094 0.043  2.181  0.029    0.023
## 38             B1Q3  ~~            B1Q3   0.272 0.055  4.905  0.000    0.181
## 39             B2Q1  ~~            B2Q1   0.276 0.087  3.160  0.002    0.132
## 40             B2Q2  ~~            B2Q2   0.180 0.087  2.054  0.040    0.036
## 41             B3Q1  ~~            B3Q1   0.261 0.105  2.479  0.013    0.088
## 42             B3Q2  ~~            B3Q2   0.409 0.097  4.208  0.000    0.249
## 43              CQ1  ~~             CQ1   0.190 0.000     NA     NA    0.190
## 44              DQ1  ~~             DQ1   0.663 0.104  6.370  0.000    0.492
## 45              EQ1  ~~             EQ1   0.691 0.094  7.310  0.000    0.535
## 46          tacphys  ~~         tacphys   1.000 0.000     NA     NA    1.000
## 47  musclejointbone  ~~ musclejointbone   1.000 0.000     NA     NA    1.000
## 48           lookjr  ~~          lookjr   1.000 0.000     NA     NA    1.000
## 49          soundjr  ~~         soundjr   1.000 0.000     NA     NA    1.000
## 50        tactilejr  ~~       tactilejr   1.000 0.000     NA     NA    1.000
## 51       internaljr  ~~      internaljr   1.000 0.000     NA     NA    1.000
## 52              emo  ~~             emo   1.000 0.000     NA     NA    1.000
## 53          tacphys  ~~ musclejointbone   0.863 0.104  8.293  0.000    0.692
## 54          tacphys  ~~          lookjr   0.747 0.072 10.405  0.000    0.629
## 55          tacphys  ~~         soundjr   0.753 0.101  7.469  0.000    0.587
## 56          tacphys  ~~       tactilejr   0.854 0.085 10.064  0.000    0.715
## 57          tacphys  ~~      internaljr   0.414 0.111  3.726  0.000    0.231
## 58          tacphys  ~~             emo   0.752 0.156  4.829  0.000    0.496
## 59  musclejointbone  ~~          lookjr   0.511 0.086  5.944  0.000    0.370
## 60  musclejointbone  ~~         soundjr   0.714 0.094  7.621  0.000    0.560
## 61  musclejointbone  ~~       tactilejr   0.694 0.108  6.397  0.000    0.515
## 62  musclejointbone  ~~      internaljr   0.397 0.119  3.325  0.001    0.200
## 63  musclejointbone  ~~             emo   0.865 0.152  5.703  0.000    0.616
## 64           lookjr  ~~         soundjr   0.663 0.067  9.894  0.000    0.553
## 65           lookjr  ~~       tactilejr   0.627 0.072  8.676  0.000    0.508
## 66           lookjr  ~~      internaljr   0.432 0.077  5.642  0.000    0.306
## 67           lookjr  ~~             emo   0.757 0.117  6.485  0.000    0.565
## 68          soundjr  ~~       tactilejr   0.852 0.074 11.497  0.000    0.730
## 69          soundjr  ~~      internaljr   0.452 0.104  4.339  0.000    0.280
## 70          soundjr  ~~             emo   0.911 0.141  6.478  0.000    0.680
## 71        tactilejr  ~~      internaljr   0.353 0.113  3.109  0.002    0.166
## 72        tactilejr  ~~             emo   0.881 0.145  6.074  0.000    0.643
## 73       internaljr  ~~             emo   0.815 0.134  6.084  0.000    0.594
## 74             A1Q1 ~*~            A1Q1   1.000 0.000     NA     NA    1.000
## 75             A1Q2 ~*~            A1Q2   1.000 0.000     NA     NA    1.000
## 76             A1Q3 ~*~            A1Q3   1.000 0.000     NA     NA    1.000
## 77             A2Q1 ~*~            A2Q1   1.000 0.000     NA     NA    1.000
## 78             A2Q2 ~*~            A2Q2   1.000 0.000     NA     NA    1.000
## 79             B1Q1 ~*~            B1Q1   1.000 0.000     NA     NA    1.000
## 80             B1Q2 ~*~            B1Q2   1.000 0.000     NA     NA    1.000
## 81             B1Q3 ~*~            B1Q3   1.000 0.000     NA     NA    1.000
## 82             B2Q1 ~*~            B2Q1   1.000 0.000     NA     NA    1.000
## 83             B2Q2 ~*~            B2Q2   1.000 0.000     NA     NA    1.000
## 84             B3Q1 ~*~            B3Q1   1.000 0.000     NA     NA    1.000
## 85             B3Q2 ~*~            B3Q2   1.000 0.000     NA     NA    1.000
## 86              CQ1 ~*~             CQ1   1.000 0.000     NA     NA    1.000
## 87              DQ1 ~*~             DQ1   1.000 0.000     NA     NA    1.000
## 88              EQ1 ~*~             EQ1   1.000 0.000     NA     NA    1.000
## 89             A1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 90             A1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 91             A1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 92             A2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 93             A2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 94             B1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 95             B1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 96             B1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 97             B2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 98             B2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 99             B3Q1  ~1                   0.000 0.000     NA     NA    0.000
## 100            B3Q2  ~1                   0.000 0.000     NA     NA    0.000
## 101             CQ1  ~1                   0.000 0.000     NA     NA    0.000
## 102             DQ1  ~1                   0.000 0.000     NA     NA    0.000
## 103             EQ1  ~1                   0.000 0.000     NA     NA    0.000
## 104         tacphys  ~1                   0.000 0.000     NA     NA    0.000
## 105 musclejointbone  ~1                   0.000 0.000     NA     NA    0.000
## 106          lookjr  ~1                   0.000 0.000     NA     NA    0.000
## 107         soundjr  ~1                   0.000 0.000     NA     NA    0.000
## 108       tactilejr  ~1                   0.000 0.000     NA     NA    0.000
## 109      internaljr  ~1                   0.000 0.000     NA     NA    0.000
## 110             emo  ~1                   0.000 0.000     NA     NA    0.000
##     ci.upper
## 1      0.709
## 2      0.817
## 3      0.792
## 4      0.879
## 5      0.981
## 6      1.010
## 7      0.989
## 8      0.907
## 9      0.935
## 10     0.985
## 11     0.960
## 12     0.873
## 13     0.900
## 14     0.728
## 15     0.696
## 16     0.949
## 17     1.466
## 18     1.379
## 19     1.493
## 20     1.645
## 21     0.392
## 22     0.762
## 23     1.002
## 24     1.493
## 25     1.415
## 26     1.480
## 27     1.311
## 28     1.002
## 29     1.209
## 30     0.795
## 31     0.782
## 32     0.700
## 33     0.709
## 34     0.600
## 35     0.455
## 36     0.144
## 37     0.165
## 38     0.363
## 39     0.420
## 40     0.323
## 41     0.434
## 42     0.568
## 43     0.190
## 44     0.834
## 45     0.846
## 46     1.000
## 47     1.000
## 48     1.000
## 49     1.000
## 50     1.000
## 51     1.000
## 52     1.000
## 53     1.035
## 54     0.865
## 55     0.919
## 56     0.994
## 57     0.597
## 58     1.008
## 59     0.653
## 60     0.869
## 61     0.872
## 62     0.593
## 63     1.115
## 64     0.774
## 65     0.746
## 66     0.558
## 67     0.949
## 68     0.973
## 69     0.623
## 70     1.143
## 71     0.539
## 72     1.120
## 73     1.035
## 74     1.000
## 75     1.000
## 76     1.000
## 77     1.000
## 78     1.000
## 79     1.000
## 80     1.000
## 81     1.000
## 82     1.000
## 83     1.000
## 84     1.000
## 85     1.000
## 86     1.000
## 87     1.000
## 88     1.000
## 89     0.000
## 90     0.000
## 91     0.000
## 92     0.000
## 93     0.000
## 94     0.000
## 95     0.000
## 96     0.000
## 97     0.000
## 98     0.000
## 99     0.000
## 100    0.000
## 101    0.000
## 102    0.000
## 103    0.000
## 104    0.000
## 105    0.000
## 106    0.000
## 107    0.000
## 108    0.000
## 109    0.000
## 110    0.000
inspect(fit.sps.cfa.6, "cov.lv")
##                 tcphys mscljn lookjr sondjr tctljr intrnl emo  
## tacphys         1.000                                          
## musclejointbone 0.863  1.000                                   
## lookjr          0.747  0.511  1.000                            
## soundjr         0.753  0.714  0.663  1.000                     
## tactilejr       0.854  0.694  0.627  0.852  1.000              
## internaljr      0.414  0.397  0.432  0.452  0.353  1.000       
## emo             0.752  0.865  0.757  0.911  0.881  0.815  1.000

6 Factor CFA with Higher Order Factors

sps.cfa.6.h <- '
tacphys =~ A1Q1+ A1Q2+ A1Q3
musclejointbone =~ A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3
soundjr =~ B2Q1+ B2Q2
tactilejr =~ B3Q1+ B3Q2 
emo =~ CQ1 + DQ1 + EQ1
fac1 =~ tacphys + musclejointbone
fac2 =~ lookjr + soundjr + tactilejr + CQ1
'
fit.sps.cfa.6.h<- cfa(sps.cfa.6.h, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) # Model did not converge

5 Factor CFA

C, D, and E (the emotional/internally-focused items) are considered as loadings on a single factor instead of 3 separate factors. The tacphys and tactilejr items are considered as loading onto one “tactile” factor.

sps.cfa.5 <- '
tactile =~ A1Q1+ A1Q2+ A1Q3 + B3Q1+ B3Q2 
musclejointbone =~ A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3
soundjr =~ B2Q1+ B2Q2
emo =~ CQ1 + DQ1 + EQ1
'
fit.sps.cfa.5<- cfa(sps.cfa.5, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.5, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 25 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        40
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                                72.162     107.454
##   Degrees of freedom                                80          80
##   P-value (Chi-square)                           0.722       0.022
##   Scaling correction factor                                  0.813
##   Shift parameter                                           18.686
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000       0.991
##   Tucker-Lewis Index (TLI)                       1.002       0.988
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000       0.026
##   90 Percent confidence interval - lower         0.000       0.011
##   90 Percent confidence interval - upper         0.020       0.038
##   P-value RMSEA <= 0.05                          1.000       1.000
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.069       0.069
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tactile =~                                                              
##     A1Q1                0.582    0.067    8.740    0.000    0.582    0.582
##     A1Q2                0.673    0.070    9.634    0.000    0.673    0.673
##     A1Q3                0.657    0.067    9.804    0.000    0.657    0.657
##     B3Q1                0.805    0.055   14.655    0.000    0.805    0.805
##     B3Q2                0.721    0.059   12.139    0.000    0.721    0.721
##   musclejointbone =~                                                      
##     A2Q1                0.761    0.072   10.599    0.000    0.761    0.761
##     A2Q2                0.864    0.072   12.068    0.000    0.864    0.864
##   lookjr =~                                                               
##     B1Q1                0.968    0.025   38.203    0.000    0.968    0.968
##     B1Q2                0.952    0.023   41.814    0.000    0.952    0.952
##     B1Q3                0.854    0.032   26.313    0.000    0.854    0.854
##   soundjr =~                                                              
##     B2Q1                0.852    0.051   16.556    0.000    0.852    0.852
##     B2Q2                0.905    0.048   18.808    0.000    0.905    0.905
##   emo =~                                                                  
##     CQ1                 0.559    0.070    8.042    0.000    0.559    0.559
##     DQ1                 0.667    0.073    9.134    0.000    0.667    0.667
##     EQ1                 0.640    0.076    8.464    0.000    0.640    0.640
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tactile ~~                                                              
##     musclejointbon      0.817    0.091    8.969    0.000    0.817    0.817
##     lookjr              0.719    0.054   13.385    0.000    0.719    0.719
##     soundjr             0.851    0.068   12.509    0.000    0.851    0.851
##     emo                 0.721    0.088    8.185    0.000    0.721    0.721
##   musclejointbone ~~                                                      
##     lookjr              0.511    0.086    5.942    0.000    0.511    0.511
##     soundjr             0.715    0.094    7.622    0.000    0.715    0.715
##     emo                 0.726    0.104    7.000    0.000    0.726    0.726
##   lookjr ~~                                                               
##     soundjr             0.663    0.067    9.898    0.000    0.663    0.663
##     emo                 0.668    0.077    8.629    0.000    0.668    0.668
##   soundjr ~~                                                              
##     emo                 0.777    0.091    8.574    0.000    0.777    0.777
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tactile           0.000                               0.000    0.000
##     musclejointbon    0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     soundjr           0.000                               0.000    0.000
##     emo               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.662                               0.662    0.662
##    .A1Q2              0.547                               0.547    0.547
##    .A1Q3              0.569                               0.569    0.569
##    .B3Q1              0.352                               0.352    0.352
##    .B3Q2              0.480                               0.480    0.480
##    .A2Q1              0.420                               0.420    0.420
##    .A2Q2              0.253                               0.253    0.253
##    .B1Q1              0.063                               0.063    0.063
##    .B1Q2              0.094                               0.094    0.094
##    .B1Q3              0.271                               0.271    0.271
##    .B2Q1              0.275                               0.275    0.275
##    .B2Q2              0.181                               0.181    0.181
##    .CQ1               0.687                               0.687    0.687
##    .DQ1               0.555                               0.555    0.555
##    .EQ1               0.591                               0.591    0.591
##     tactile           1.000                               1.000    1.000
##     musclejointbon    1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     soundjr           1.000                               1.000    1.000
##     emo               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.5, ci=T, level = .90)
##                lhs  op             rhs est.std    se      z pvalue ci.lower
## 1          tactile  =~            A1Q1   0.582 0.067  8.740  0.000    0.472
## 2          tactile  =~            A1Q2   0.673 0.070  9.634  0.000    0.558
## 3          tactile  =~            A1Q3   0.657 0.067  9.804  0.000    0.546
## 4          tactile  =~            B3Q1   0.805 0.055 14.655  0.000    0.715
## 5          tactile  =~            B3Q2   0.721 0.059 12.139  0.000    0.623
## 6  musclejointbone  =~            A2Q1   0.761 0.072 10.599  0.000    0.643
## 7  musclejointbone  =~            A2Q2   0.864 0.072 12.068  0.000    0.746
## 8           lookjr  =~            B1Q1   0.968 0.025 38.203  0.000    0.926
## 9           lookjr  =~            B1Q2   0.952 0.023 41.814  0.000    0.914
## 10          lookjr  =~            B1Q3   0.854 0.032 26.313  0.000    0.800
## 11         soundjr  =~            B2Q1   0.852 0.051 16.556  0.000    0.767
## 12         soundjr  =~            B2Q2   0.905 0.048 18.808  0.000    0.826
## 13             emo  =~             CQ1   0.559 0.070  8.042  0.000    0.445
## 14             emo  =~             DQ1   0.667 0.073  9.134  0.000    0.547
## 15             emo  =~             EQ1   0.640 0.076  8.464  0.000    0.515
## 16            A1Q1   |              t1   0.843 0.064 13.122  0.000    0.737
## 17            A1Q2   |              t1   1.336 0.079 16.910  0.000    1.206
## 18            A1Q3   |              t1   1.254 0.076 16.548  0.000    1.130
## 19            B3Q1   |              t1   1.349 0.080 16.956  0.000    1.218
## 20            B3Q2   |              t1   1.190 0.074 16.189  0.000    1.069
## 21            A2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 22            A2Q2   |              t1   1.502 0.087 17.314  0.000    1.359
## 23            B1Q1   |              t1   0.297 0.057  5.196  0.000    0.203
## 24            B1Q2   |              t1   0.662 0.061 10.840  0.000    0.561
## 25            B1Q3   |              t1   0.895 0.065 13.692  0.000    0.787
## 26            B2Q1   |              t1   1.361 0.080 16.999  0.000    1.230
## 27            B2Q2   |              t1   1.288 0.077 16.712  0.000    1.162
## 28             CQ1   |              t1   0.895 0.065 13.692  0.000    0.787
## 29             DQ1   |              t1   1.093 0.070 15.520  0.000    0.978
## 30             EQ1   |              t1   0.694 0.062 11.271  0.000    0.592
## 31            A1Q1  ~~            A1Q1   0.662 0.077  8.549  0.000    0.534
## 32            A1Q2  ~~            A1Q2   0.547 0.094  5.809  0.000    0.392
## 33            A1Q3  ~~            A1Q3   0.569 0.088  6.470  0.000    0.424
## 34            B3Q1  ~~            B3Q1   0.352 0.088  3.977  0.000    0.206
## 35            B3Q2  ~~            B3Q2   0.480 0.086  5.602  0.000    0.339
## 36            A2Q1  ~~            A2Q1   0.420 0.109  3.843  0.000    0.240
## 37            A2Q2  ~~            A2Q2   0.253 0.124  2.045  0.041    0.049
## 38            B1Q1  ~~            B1Q1   0.063 0.049  1.280  0.201   -0.018
## 39            B1Q2  ~~            B1Q2   0.094 0.043  2.179  0.029    0.023
## 40            B1Q3  ~~            B1Q3   0.271 0.055  4.901  0.000    0.180
## 41            B2Q1  ~~            B2Q1   0.275 0.088  3.139  0.002    0.131
## 42            B2Q2  ~~            B2Q2   0.181 0.087  2.073  0.038    0.037
## 43             CQ1  ~~             CQ1   0.687 0.078  8.832  0.000    0.559
## 44             DQ1  ~~             DQ1   0.555 0.097  5.695  0.000    0.395
## 45             EQ1  ~~             EQ1   0.591 0.097  6.114  0.000    0.432
## 46         tactile  ~~         tactile   1.000 0.000     NA     NA    1.000
## 47 musclejointbone  ~~ musclejointbone   1.000 0.000     NA     NA    1.000
## 48          lookjr  ~~          lookjr   1.000 0.000     NA     NA    1.000
## 49         soundjr  ~~         soundjr   1.000 0.000     NA     NA    1.000
## 50             emo  ~~             emo   1.000 0.000     NA     NA    1.000
## 51         tactile  ~~ musclejointbone   0.817 0.091  8.969  0.000    0.667
## 52         tactile  ~~          lookjr   0.719 0.054 13.385  0.000    0.631
## 53         tactile  ~~         soundjr   0.851 0.068 12.509  0.000    0.739
## 54         tactile  ~~             emo   0.721 0.088  8.185  0.000    0.576
## 55 musclejointbone  ~~          lookjr   0.511 0.086  5.942  0.000    0.370
## 56 musclejointbone  ~~         soundjr   0.715 0.094  7.622  0.000    0.560
## 57 musclejointbone  ~~             emo   0.726 0.104  7.000  0.000    0.555
## 58          lookjr  ~~         soundjr   0.663 0.067  9.898  0.000    0.553
## 59          lookjr  ~~             emo   0.668 0.077  8.629  0.000    0.541
## 60         soundjr  ~~             emo   0.777 0.091  8.574  0.000    0.628
## 61            A1Q1 ~*~            A1Q1   1.000 0.000     NA     NA    1.000
## 62            A1Q2 ~*~            A1Q2   1.000 0.000     NA     NA    1.000
## 63            A1Q3 ~*~            A1Q3   1.000 0.000     NA     NA    1.000
## 64            B3Q1 ~*~            B3Q1   1.000 0.000     NA     NA    1.000
## 65            B3Q2 ~*~            B3Q2   1.000 0.000     NA     NA    1.000
## 66            A2Q1 ~*~            A2Q1   1.000 0.000     NA     NA    1.000
## 67            A2Q2 ~*~            A2Q2   1.000 0.000     NA     NA    1.000
## 68            B1Q1 ~*~            B1Q1   1.000 0.000     NA     NA    1.000
## 69            B1Q2 ~*~            B1Q2   1.000 0.000     NA     NA    1.000
## 70            B1Q3 ~*~            B1Q3   1.000 0.000     NA     NA    1.000
## 71            B2Q1 ~*~            B2Q1   1.000 0.000     NA     NA    1.000
## 72            B2Q2 ~*~            B2Q2   1.000 0.000     NA     NA    1.000
## 73             CQ1 ~*~             CQ1   1.000 0.000     NA     NA    1.000
## 74             DQ1 ~*~             DQ1   1.000 0.000     NA     NA    1.000
## 75             EQ1 ~*~             EQ1   1.000 0.000     NA     NA    1.000
## 76            A1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 77            A1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 78            A1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 79            B3Q1  ~1                   0.000 0.000     NA     NA    0.000
## 80            B3Q2  ~1                   0.000 0.000     NA     NA    0.000
## 81            A2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 82            A2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 83            B1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 84            B1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 85            B1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 86            B2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 87            B2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 88             CQ1  ~1                   0.000 0.000     NA     NA    0.000
## 89             DQ1  ~1                   0.000 0.000     NA     NA    0.000
## 90             EQ1  ~1                   0.000 0.000     NA     NA    0.000
## 91         tactile  ~1                   0.000 0.000     NA     NA    0.000
## 92 musclejointbone  ~1                   0.000 0.000     NA     NA    0.000
## 93          lookjr  ~1                   0.000 0.000     NA     NA    0.000
## 94         soundjr  ~1                   0.000 0.000     NA     NA    0.000
## 95             emo  ~1                   0.000 0.000     NA     NA    0.000
##    ci.upper
## 1     0.691
## 2     0.788
## 3     0.767
## 4     0.895
## 5     0.819
## 6     0.880
## 7     0.982
## 8     1.010
## 9     0.989
## 10    0.907
## 11    0.936
## 12    0.984
## 13    0.674
## 14    0.787
## 15    0.764
## 16    0.949
## 17    1.466
## 18    1.379
## 19    1.480
## 20    1.311
## 21    1.493
## 22    1.645
## 23    0.392
## 24    0.762
## 25    1.002
## 26    1.493
## 27    1.415
## 28    1.002
## 29    1.209
## 30    0.795
## 31    0.789
## 32    0.701
## 33    0.714
## 34    0.497
## 35    0.621
## 36    0.600
## 37    0.457
## 38    0.144
## 39    0.166
## 40    0.362
## 41    0.419
## 42    0.324
## 43    0.815
## 44    0.715
## 45    0.750
## 46    1.000
## 47    1.000
## 48    1.000
## 49    1.000
## 50    1.000
## 51    0.966
## 52    0.808
## 53    0.963
## 54    0.866
## 55    0.653
## 56    0.869
## 57    0.896
## 58    0.774
## 59    0.796
## 60    0.926
## 61    1.000
## 62    1.000
## 63    1.000
## 64    1.000
## 65    1.000
## 66    1.000
## 67    1.000
## 68    1.000
## 69    1.000
## 70    1.000
## 71    1.000
## 72    1.000
## 73    1.000
## 74    1.000
## 75    1.000
## 76    0.000
## 77    0.000
## 78    0.000
## 79    0.000
## 80    0.000
## 81    0.000
## 82    0.000
## 83    0.000
## 84    0.000
## 85    0.000
## 86    0.000
## 87    0.000
## 88    0.000
## 89    0.000
## 90    0.000
## 91    0.000
## 92    0.000
## 93    0.000
## 94    0.000
## 95    0.000

4 Factor CFA

Even though the USP-SPS lists the items according to 8 different groups of items, when we developed the USP-SPS we conceptualized 4 factor-models based on the literature. They were: a) Physical; b) Just-Right; c) Energy; d) Urge only

sps.cfa.4 <- '
phys =~ A1Q1+ A1Q2+ A1Q3 + A2Q1+ A2Q2
justright =~ B1Q1+ B1Q2+ B1Q3 + B2Q1+ B2Q2 + B3Q1+ B3Q2 + CQ1
energy =~ .90*DQ1
urge =~ .90*EQ1
'

fit.sps.cfa.4 <- cfa(sps.cfa.4, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1"))
summary(fit.sps.cfa.4, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 20 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        34
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                               172.764     209.034
##   Degrees of freedom                                86          86
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.929
##   Shift parameter                                           23.064
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.984       0.961
##   Tucker-Lewis Index (TLI)                       0.981       0.952
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.045       0.054
##   90 Percent confidence interval - lower         0.035       0.045
##   90 Percent confidence interval - upper         0.055       0.063
##   P-value RMSEA <= 0.05                          0.786       0.242
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.101       0.101
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   phys =~                                                               
##     A1Q1              0.607    0.068    8.974    0.000    0.607    0.607
##     A1Q2              0.701    0.076    9.263    0.000    0.701    0.701
##     A1Q3              0.685    0.068   10.100    0.000    0.685    0.685
##     A2Q1              0.681    0.068   10.021    0.000    0.681    0.681
##     A2Q2              0.773    0.069   11.225    0.000    0.773    0.773
##   justright =~                                                          
##     B1Q1              0.941    0.023   40.440    0.000    0.941    0.941
##     B1Q2              0.935    0.023   41.166    0.000    0.935    0.935
##     B1Q3              0.808    0.033   24.705    0.000    0.808    0.808
##     B2Q1              0.763    0.050   15.141    0.000    0.763    0.763
##     B2Q2              0.795    0.047   17.049    0.000    0.795    0.795
##     B3Q1              0.741    0.056   13.154    0.000    0.741    0.741
##     B3Q2              0.663    0.057   11.687    0.000    0.663    0.663
##     CQ1               0.460    0.063    7.328    0.000    0.460    0.460
##   energy =~                                                             
##     DQ1               0.900                               0.900    0.900
##   urge =~                                                               
##     EQ1               0.900                               0.900    0.900
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   phys ~~                                                               
##     justright         0.783    0.047   16.614    0.000    0.783    0.783
##     energy            0.582    0.094    6.170    0.000    0.582    0.582
##     urge              0.478    0.094    5.060    0.000    0.478    0.478
##   justright ~~                                                          
##     energy            0.572    0.072    7.981    0.000    0.572    0.572
##     urge              0.575    0.063    9.173    0.000    0.575    0.575
##   energy ~~                                                             
##     urge              0.399    0.106    3.766    0.000    0.399    0.399
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     phys              0.000                               0.000    0.000
##     justright         0.000                               0.000    0.000
##     energy            0.000                               0.000    0.000
##     urge              0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.632                               0.632    0.632
##    .A1Q2              0.509                               0.509    0.509
##    .A1Q3              0.531                               0.531    0.531
##    .A2Q1              0.536                               0.536    0.536
##    .A2Q2              0.402                               0.402    0.402
##    .B1Q1              0.115                               0.115    0.115
##    .B1Q2              0.126                               0.126    0.126
##    .B1Q3              0.347                               0.347    0.347
##    .B2Q1              0.417                               0.417    0.417
##    .B2Q2              0.368                               0.368    0.368
##    .B3Q1              0.451                               0.451    0.451
##    .B3Q2              0.561                               0.561    0.561
##    .CQ1               0.788                               0.788    0.788
##    .DQ1               0.190                               0.190    0.190
##    .EQ1               0.190                               0.190    0.190
##     phys              1.000                               1.000    1.000
##     justright         1.000                               1.000    1.000
##     energy            1.000                               1.000    1.000
##     urge              1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.4, ci=T, level = .90)
##          lhs  op       rhs est.std    se      z pvalue ci.lower ci.upper
## 1       phys  =~      A1Q1   0.607 0.068  8.974  0.000    0.495    0.718
## 2       phys  =~      A1Q2   0.701 0.076  9.263  0.000    0.577    0.825
## 3       phys  =~      A1Q3   0.685 0.068 10.100  0.000    0.573    0.797
## 4       phys  =~      A2Q1   0.681 0.068 10.021  0.000    0.569    0.793
## 5       phys  =~      A2Q2   0.773 0.069 11.225  0.000    0.660    0.886
## 6  justright  =~      B1Q1   0.941 0.023 40.440  0.000    0.903    0.979
## 7  justright  =~      B1Q2   0.935 0.023 41.166  0.000    0.898    0.972
## 8  justright  =~      B1Q3   0.808 0.033 24.705  0.000    0.754    0.862
## 9  justright  =~      B2Q1   0.763 0.050 15.141  0.000    0.680    0.846
## 10 justright  =~      B2Q2   0.795 0.047 17.049  0.000    0.718    0.871
## 11 justright  =~      B3Q1   0.741 0.056 13.154  0.000    0.649    0.834
## 12 justright  =~      B3Q2   0.663 0.057 11.687  0.000    0.570    0.756
## 13 justright  =~       CQ1   0.460 0.063  7.328  0.000    0.357    0.564
## 14    energy  =~       DQ1   0.900 0.000     NA     NA    0.900    0.900
## 15      urge  =~       EQ1   0.900 0.000     NA     NA    0.900    0.900
## 16      A1Q1   |        t1   0.843 0.064 13.122  0.000    0.737    0.949
## 17      A1Q2   |        t1   1.336 0.079 16.910  0.000    1.206    1.466
## 18      A1Q3   |        t1   1.254 0.076 16.548  0.000    1.130    1.379
## 19      A2Q1   |        t1   1.361 0.080 16.999  0.000    1.230    1.493
## 20      A2Q2   |        t1   1.502 0.087 17.314  0.000    1.359    1.645
## 21      B1Q1   |        t1   0.297 0.057  5.196  0.000    0.203    0.392
## 22      B1Q2   |        t1   0.662 0.061 10.840  0.000    0.561    0.762
## 23      B1Q3   |        t1   0.895 0.065 13.692  0.000    0.787    1.002
## 24      B2Q1   |        t1   1.361 0.080 16.999  0.000    1.230    1.493
## 25      B2Q2   |        t1   1.288 0.077 16.712  0.000    1.162    1.415
## 26      B3Q1   |        t1   1.349 0.080 16.956  0.000    1.218    1.480
## 27      B3Q2   |        t1   1.190 0.074 16.189  0.000    1.069    1.311
## 28       CQ1   |        t1   0.895 0.065 13.692  0.000    0.787    1.002
## 29       DQ1   |        t1   1.093 0.070 15.520  0.000    0.978    1.209
## 30       EQ1   |        t1   0.694 0.062 11.271  0.000    0.592    0.795
## 31      A1Q1  ~~      A1Q1   0.632 0.082  7.707  0.000    0.497    0.767
## 32      A1Q2  ~~      A1Q2   0.509 0.106  4.794  0.000    0.334    0.683
## 33      A1Q3  ~~      A1Q3   0.531 0.093  5.713  0.000    0.378    0.684
## 34      A2Q1  ~~      A2Q1   0.536 0.093  5.792  0.000    0.384    0.688
## 35      A2Q2  ~~      A2Q2   0.402 0.107  3.776  0.000    0.227    0.577
## 36      B1Q1  ~~      B1Q1   0.115 0.044  2.619  0.009    0.043    0.187
## 37      B1Q2  ~~      B1Q2   0.126 0.042  2.963  0.003    0.056    0.196
## 38      B1Q3  ~~      B1Q3   0.347 0.053  6.563  0.000    0.260    0.434
## 39      B2Q1  ~~      B2Q1   0.417 0.077  5.425  0.000    0.291    0.544
## 40      B2Q2  ~~      B2Q2   0.368 0.074  4.972  0.000    0.247    0.490
## 41      B3Q1  ~~      B3Q1   0.451 0.084  5.394  0.000    0.313    0.588
## 42      B3Q2  ~~      B3Q2   0.561 0.075  7.456  0.000    0.437    0.684
## 43       CQ1  ~~       CQ1   0.788 0.058 13.636  0.000    0.693    0.883
## 44       DQ1  ~~       DQ1   0.190 0.000     NA     NA    0.190    0.190
## 45       EQ1  ~~       EQ1   0.190 0.000     NA     NA    0.190    0.190
## 46      phys  ~~      phys   1.000 0.000     NA     NA    1.000    1.000
## 47 justright  ~~ justright   1.000 0.000     NA     NA    1.000    1.000
## 48    energy  ~~    energy   1.000 0.000     NA     NA    1.000    1.000
## 49      urge  ~~      urge   1.000 0.000     NA     NA    1.000    1.000
## 50      phys  ~~ justright   0.783 0.047 16.614  0.000    0.705    0.860
## 51      phys  ~~    energy   0.582 0.094  6.170  0.000    0.427    0.737
## 52      phys  ~~      urge   0.478 0.094  5.060  0.000    0.322    0.633
## 53 justright  ~~    energy   0.572 0.072  7.981  0.000    0.454    0.690
## 54 justright  ~~      urge   0.575 0.063  9.173  0.000    0.472    0.678
## 55    energy  ~~      urge   0.399 0.106  3.766  0.000    0.225    0.573
## 56      A1Q1 ~*~      A1Q1   1.000 0.000     NA     NA    1.000    1.000
## 57      A1Q2 ~*~      A1Q2   1.000 0.000     NA     NA    1.000    1.000
## 58      A1Q3 ~*~      A1Q3   1.000 0.000     NA     NA    1.000    1.000
## 59      A2Q1 ~*~      A2Q1   1.000 0.000     NA     NA    1.000    1.000
## 60      A2Q2 ~*~      A2Q2   1.000 0.000     NA     NA    1.000    1.000
## 61      B1Q1 ~*~      B1Q1   1.000 0.000     NA     NA    1.000    1.000
## 62      B1Q2 ~*~      B1Q2   1.000 0.000     NA     NA    1.000    1.000
## 63      B1Q3 ~*~      B1Q3   1.000 0.000     NA     NA    1.000    1.000
## 64      B2Q1 ~*~      B2Q1   1.000 0.000     NA     NA    1.000    1.000
## 65      B2Q2 ~*~      B2Q2   1.000 0.000     NA     NA    1.000    1.000
## 66      B3Q1 ~*~      B3Q1   1.000 0.000     NA     NA    1.000    1.000
## 67      B3Q2 ~*~      B3Q2   1.000 0.000     NA     NA    1.000    1.000
## 68       CQ1 ~*~       CQ1   1.000 0.000     NA     NA    1.000    1.000
## 69       DQ1 ~*~       DQ1   1.000 0.000     NA     NA    1.000    1.000
## 70       EQ1 ~*~       EQ1   1.000 0.000     NA     NA    1.000    1.000
## 71      A1Q1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 72      A1Q2  ~1             0.000 0.000     NA     NA    0.000    0.000
## 73      A1Q3  ~1             0.000 0.000     NA     NA    0.000    0.000
## 74      A2Q1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 75      A2Q2  ~1             0.000 0.000     NA     NA    0.000    0.000
## 76      B1Q1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 77      B1Q2  ~1             0.000 0.000     NA     NA    0.000    0.000
## 78      B1Q3  ~1             0.000 0.000     NA     NA    0.000    0.000
## 79      B2Q1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 80      B2Q2  ~1             0.000 0.000     NA     NA    0.000    0.000
## 81      B3Q1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 82      B3Q2  ~1             0.000 0.000     NA     NA    0.000    0.000
## 83       CQ1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 84       DQ1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 85       EQ1  ~1             0.000 0.000     NA     NA    0.000    0.000
## 86      phys  ~1             0.000 0.000     NA     NA    0.000    0.000
## 87 justright  ~1             0.000 0.000     NA     NA    0.000    0.000
## 88    energy  ~1             0.000 0.000     NA     NA    0.000    0.000
## 89      urge  ~1             0.000 0.000     NA     NA    0.000    0.000

3 Factor CFA

sps.cfa.3 <- '
tacphys =~ A1Q1+ A1Q2+ A1Q3 + A2Q1+ A2Q2
lookjr =~ B1Q1+ B1Q2+ B1Q3 + B2Q1+ B2Q2 + B3Q1+ B3Q2+ CQ1
emo =~ DQ1 + EQ1
'
fit.sps.cfa.3<- cfa(sps.cfa.3, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.3, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 22 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        33
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                               173.671     209.079
##   Degrees of freedom                                87          87
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.935
##   Shift parameter                                           23.337
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.984       0.961
##   Tucker-Lewis Index (TLI)                       0.981       0.953
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.045       0.053
##   90 Percent confidence interval - lower         0.035       0.044
##   90 Percent confidence interval - upper         0.055       0.063
##   P-value RMSEA <= 0.05                          0.801       0.271
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.101       0.101
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys =~                                                            
##     A1Q1              0.606    0.068    8.961    0.000    0.606    0.606
##     A1Q2              0.702    0.075    9.300    0.000    0.702    0.702
##     A1Q3              0.685    0.068   10.091    0.000    0.685    0.685
##     A2Q1              0.681    0.068   10.017    0.000    0.681    0.681
##     A2Q2              0.773    0.069   11.184    0.000    0.773    0.773
##   lookjr =~                                                             
##     B1Q1              0.941    0.023   40.441    0.000    0.941    0.941
##     B1Q2              0.935    0.023   41.129    0.000    0.935    0.935
##     B1Q3              0.808    0.033   24.700    0.000    0.808    0.808
##     B2Q1              0.763    0.050   15.121    0.000    0.763    0.763
##     B2Q2              0.795    0.047   17.050    0.000    0.795    0.795
##     B3Q1              0.741    0.056   13.147    0.000    0.741    0.741
##     B3Q2              0.663    0.057   11.684    0.000    0.663    0.663
##     CQ1               0.460    0.063    7.336    0.000    0.460    0.460
##   emo =~                                                                
##     DQ1               0.581    0.090    6.422    0.000    0.581    0.581
##     EQ1               0.556    0.086    6.498    0.000    0.556    0.556
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys ~~                                                            
##     lookjr            0.783    0.047   16.613    0.000    0.783    0.783
##     emo               0.837    0.133    6.312    0.000    0.837    0.837
##   lookjr ~~                                                             
##     emo               0.910    0.113    8.023    0.000    0.910    0.910
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tacphys           0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     emo               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.632                               0.632    0.632
##    .A1Q2              0.508                               0.508    0.508
##    .A1Q3              0.531                               0.531    0.531
##    .A2Q1              0.536                               0.536    0.536
##    .A2Q2              0.402                               0.402    0.402
##    .B1Q1              0.115                               0.115    0.115
##    .B1Q2              0.126                               0.126    0.126
##    .B1Q3              0.347                               0.347    0.347
##    .B2Q1              0.418                               0.418    0.418
##    .B2Q2              0.368                               0.368    0.368
##    .B3Q1              0.451                               0.451    0.451
##    .B3Q2              0.561                               0.561    0.561
##    .CQ1               0.788                               0.788    0.788
##    .DQ1               0.663                               0.663    0.663
##    .EQ1               0.690                               0.690    0.690
##     tacphys           1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     emo               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.3, ci=T, level = .90)
##        lhs  op     rhs est.std    se      z pvalue ci.lower ci.upper
## 1  tacphys  =~    A1Q1   0.606 0.068  8.961  0.000    0.495    0.718
## 2  tacphys  =~    A1Q2   0.702 0.075  9.300  0.000    0.578    0.826
## 3  tacphys  =~    A1Q3   0.685 0.068 10.091  0.000    0.573    0.796
## 4  tacphys  =~    A2Q1   0.681 0.068 10.017  0.000    0.569    0.793
## 5  tacphys  =~    A2Q2   0.773 0.069 11.184  0.000    0.659    0.887
## 6   lookjr  =~    B1Q1   0.941 0.023 40.441  0.000    0.903    0.979
## 7   lookjr  =~    B1Q2   0.935 0.023 41.129  0.000    0.898    0.972
## 8   lookjr  =~    B1Q3   0.808 0.033 24.700  0.000    0.754    0.862
## 9   lookjr  =~    B2Q1   0.763 0.050 15.121  0.000    0.680    0.846
## 10  lookjr  =~    B2Q2   0.795 0.047 17.050  0.000    0.718    0.871
## 11  lookjr  =~    B3Q1   0.741 0.056 13.147  0.000    0.648    0.834
## 12  lookjr  =~    B3Q2   0.663 0.057 11.684  0.000    0.570    0.756
## 13  lookjr  =~     CQ1   0.460 0.063  7.336  0.000    0.357    0.564
## 14     emo  =~     DQ1   0.581 0.090  6.422  0.000    0.432    0.729
## 15     emo  =~     EQ1   0.556 0.086  6.498  0.000    0.416    0.697
## 16    A1Q1   |      t1   0.843 0.064 13.122  0.000    0.737    0.949
## 17    A1Q2   |      t1   1.336 0.079 16.910  0.000    1.206    1.466
## 18    A1Q3   |      t1   1.254 0.076 16.548  0.000    1.130    1.379
## 19    A2Q1   |      t1   1.361 0.080 16.999  0.000    1.230    1.493
## 20    A2Q2   |      t1   1.502 0.087 17.314  0.000    1.359    1.645
## 21    B1Q1   |      t1   0.297 0.057  5.196  0.000    0.203    0.392
## 22    B1Q2   |      t1   0.662 0.061 10.840  0.000    0.561    0.762
## 23    B1Q3   |      t1   0.895 0.065 13.692  0.000    0.787    1.002
## 24    B2Q1   |      t1   1.361 0.080 16.999  0.000    1.230    1.493
## 25    B2Q2   |      t1   1.288 0.077 16.712  0.000    1.162    1.415
## 26    B3Q1   |      t1   1.349 0.080 16.956  0.000    1.218    1.480
## 27    B3Q2   |      t1   1.190 0.074 16.189  0.000    1.069    1.311
## 28     CQ1   |      t1   0.895 0.065 13.692  0.000    0.787    1.002
## 29     DQ1   |      t1   1.093 0.070 15.520  0.000    0.978    1.209
## 30     EQ1   |      t1   0.694 0.062 11.271  0.000    0.592    0.795
## 31    A1Q1  ~~    A1Q1   0.632 0.082  7.700  0.000    0.497    0.767
## 32    A1Q2  ~~    A1Q2   0.508 0.106  4.796  0.000    0.334    0.682
## 33    A1Q3  ~~    A1Q3   0.531 0.093  5.723  0.000    0.379    0.684
## 34    A2Q1  ~~    A2Q1   0.536 0.093  5.786  0.000    0.384    0.688
## 35    A2Q2  ~~    A2Q2   0.402 0.107  3.767  0.000    0.227    0.578
## 36    B1Q1  ~~    B1Q1   0.115 0.044  2.618  0.009    0.043    0.187
## 37    B1Q2  ~~    B1Q2   0.126 0.043  2.960  0.003    0.056    0.196
## 38    B1Q3  ~~    B1Q3   0.347 0.053  6.561  0.000    0.260    0.434
## 39    B2Q1  ~~    B2Q1   0.418 0.077  5.423  0.000    0.291    0.544
## 40    B2Q2  ~~    B2Q2   0.368 0.074  4.973  0.000    0.247    0.490
## 41    B3Q1  ~~    B3Q1   0.451 0.084  5.393  0.000    0.313    0.588
## 42    B3Q2  ~~    B3Q2   0.561 0.075  7.456  0.000    0.437    0.684
## 43     CQ1  ~~     CQ1   0.788 0.058 13.633  0.000    0.693    0.883
## 44     DQ1  ~~     DQ1   0.663 0.105  6.317  0.000    0.490    0.836
## 45     EQ1  ~~     EQ1   0.690 0.095  7.245  0.000    0.534    0.847
## 46 tacphys  ~~ tacphys   1.000 0.000     NA     NA    1.000    1.000
## 47  lookjr  ~~  lookjr   1.000 0.000     NA     NA    1.000    1.000
## 48     emo  ~~     emo   1.000 0.000     NA     NA    1.000    1.000
## 49 tacphys  ~~  lookjr   0.783 0.047 16.613  0.000    0.705    0.860
## 50 tacphys  ~~     emo   0.837 0.133  6.312  0.000    0.619    1.055
## 51  lookjr  ~~     emo   0.910 0.113  8.023  0.000    0.724    1.097
## 52    A1Q1 ~*~    A1Q1   1.000 0.000     NA     NA    1.000    1.000
## 53    A1Q2 ~*~    A1Q2   1.000 0.000     NA     NA    1.000    1.000
## 54    A1Q3 ~*~    A1Q3   1.000 0.000     NA     NA    1.000    1.000
## 55    A2Q1 ~*~    A2Q1   1.000 0.000     NA     NA    1.000    1.000
## 56    A2Q2 ~*~    A2Q2   1.000 0.000     NA     NA    1.000    1.000
## 57    B1Q1 ~*~    B1Q1   1.000 0.000     NA     NA    1.000    1.000
## 58    B1Q2 ~*~    B1Q2   1.000 0.000     NA     NA    1.000    1.000
## 59    B1Q3 ~*~    B1Q3   1.000 0.000     NA     NA    1.000    1.000
## 60    B2Q1 ~*~    B2Q1   1.000 0.000     NA     NA    1.000    1.000
## 61    B2Q2 ~*~    B2Q2   1.000 0.000     NA     NA    1.000    1.000
## 62    B3Q1 ~*~    B3Q1   1.000 0.000     NA     NA    1.000    1.000
## 63    B3Q2 ~*~    B3Q2   1.000 0.000     NA     NA    1.000    1.000
## 64     CQ1 ~*~     CQ1   1.000 0.000     NA     NA    1.000    1.000
## 65     DQ1 ~*~     DQ1   1.000 0.000     NA     NA    1.000    1.000
## 66     EQ1 ~*~     EQ1   1.000 0.000     NA     NA    1.000    1.000
## 67    A1Q1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 68    A1Q2  ~1           0.000 0.000     NA     NA    0.000    0.000
## 69    A1Q3  ~1           0.000 0.000     NA     NA    0.000    0.000
## 70    A2Q1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 71    A2Q2  ~1           0.000 0.000     NA     NA    0.000    0.000
## 72    B1Q1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 73    B1Q2  ~1           0.000 0.000     NA     NA    0.000    0.000
## 74    B1Q3  ~1           0.000 0.000     NA     NA    0.000    0.000
## 75    B2Q1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 76    B2Q2  ~1           0.000 0.000     NA     NA    0.000    0.000
## 77    B3Q1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 78    B3Q2  ~1           0.000 0.000     NA     NA    0.000    0.000
## 79     CQ1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 80     DQ1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 81     EQ1  ~1           0.000 0.000     NA     NA    0.000    0.000
## 82 tacphys  ~1           0.000 0.000     NA     NA    0.000    0.000
## 83  lookjr  ~1           0.000 0.000     NA     NA    0.000    0.000
## 84     emo  ~1           0.000 0.000     NA     NA    0.000    0.000

1-Factor CFA

sps.cfa.1 <- '
uspsps =~ A1Q1+ A1Q2+ A1Q3 + A2Q1+ A2Q2 + B1Q1+ B1Q2+ B1Q3 + B2Q1+ B2Q2 + B3Q1+ B3Q2 + CQ1 + DQ1 + EQ1
'
fit.sps.cfa.1<- cfa(sps.cfa.1, data=train.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.1, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 18 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        30
##                                                       
##                                                   Used       Total
##   Number of observations                           496         500
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                               198.368     232.485
##   Degrees of freedom                                90          90
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.955
##   Shift parameter                                           24.855
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              5539.417    3227.221
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.741
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.980       0.954
##   Tucker-Lewis Index (TLI)                       0.977       0.947
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.049       0.057
##   90 Percent confidence interval - lower         0.040       0.048
##   90 Percent confidence interval - upper         0.059       0.066
##   P-value RMSEA <= 0.05                          0.534       0.110
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.109       0.109
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   uspsps =~                                                             
##     A1Q1              0.528    0.058    9.073    0.000    0.528    0.528
##     A1Q2              0.611    0.068    8.994    0.000    0.611    0.611
##     A1Q3              0.593    0.061    9.789    0.000    0.593    0.593
##     A2Q1              0.593    0.066    8.968    0.000    0.593    0.593
##     A2Q2              0.672    0.064   10.572    0.000    0.672    0.672
##     B1Q1              0.936    0.023   40.230    0.000    0.936    0.936
##     B1Q2              0.932    0.023   40.872    0.000    0.932    0.932
##     B1Q3              0.801    0.033   24.214    0.000    0.801    0.801
##     B2Q1              0.753    0.050   14.961    0.000    0.753    0.753
##     B2Q2              0.785    0.047   16.743    0.000    0.785    0.785
##     B3Q1              0.732    0.055   13.206    0.000    0.732    0.732
##     B3Q2              0.654    0.056   11.603    0.000    0.654    0.654
##     CQ1               0.454    0.062    7.333    0.000    0.454    0.454
##     DQ1               0.542    0.063    8.594    0.000    0.542    0.542
##     EQ1               0.519    0.057    9.122    0.000    0.519    0.519
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     uspsps            0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.843    0.064   13.122    0.000    0.843    0.843
##     A1Q2|t1           1.336    0.079   16.910    0.000    1.336    1.336
##     A1Q3|t1           1.254    0.076   16.548    0.000    1.254    1.254
##     A2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     A2Q2|t1           1.502    0.087   17.314    0.000    1.502    1.502
##     B1Q1|t1           0.297    0.057    5.196    0.000    0.297    0.297
##     B1Q2|t1           0.662    0.061   10.840    0.000    0.662    0.662
##     B1Q3|t1           0.895    0.065   13.692    0.000    0.895    0.895
##     B2Q1|t1           1.361    0.080   16.999    0.000    1.361    1.361
##     B2Q2|t1           1.288    0.077   16.712    0.000    1.288    1.288
##     B3Q1|t1           1.349    0.080   16.956    0.000    1.349    1.349
##     B3Q2|t1           1.190    0.074   16.189    0.000    1.190    1.190
##     CQ1|t1            0.895    0.065   13.692    0.000    0.895    0.895
##     DQ1|t1            1.093    0.070   15.520    0.000    1.093    1.093
##     EQ1|t1            0.694    0.062   11.271    0.000    0.694    0.694
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.721                               0.721    0.721
##    .A1Q2              0.627                               0.627    0.627
##    .A1Q3              0.648                               0.648    0.648
##    .A2Q1              0.648                               0.648    0.648
##    .A2Q2              0.548                               0.548    0.548
##    .B1Q1              0.123                               0.123    0.123
##    .B1Q2              0.132                               0.132    0.132
##    .B1Q3              0.358                               0.358    0.358
##    .B2Q1              0.433                               0.433    0.433
##    .B2Q2              0.384                               0.384    0.384
##    .B3Q1              0.464                               0.464    0.464
##    .B3Q2              0.572                               0.572    0.572
##    .CQ1               0.794                               0.794    0.794
##    .DQ1               0.706                               0.706    0.706
##    .EQ1               0.730                               0.730    0.730
##     uspsps            1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.1, ci=T, level = .90)
##       lhs  op    rhs est.std    se      z pvalue ci.lower ci.upper
## 1  uspsps  =~   A1Q1   0.528 0.058  9.073  0.000    0.432    0.624
## 2  uspsps  =~   A1Q2   0.611 0.068  8.994  0.000    0.499    0.722
## 3  uspsps  =~   A1Q3   0.593 0.061  9.789  0.000    0.494    0.693
## 4  uspsps  =~   A2Q1   0.593 0.066  8.968  0.000    0.484    0.702
## 5  uspsps  =~   A2Q2   0.672 0.064 10.572  0.000    0.568    0.777
## 6  uspsps  =~   B1Q1   0.936 0.023 40.230  0.000    0.898    0.975
## 7  uspsps  =~   B1Q2   0.932 0.023 40.872  0.000    0.894    0.969
## 8  uspsps  =~   B1Q3   0.801 0.033 24.214  0.000    0.747    0.856
## 9  uspsps  =~   B2Q1   0.753 0.050 14.961  0.000    0.670    0.836
## 10 uspsps  =~   B2Q2   0.785 0.047 16.743  0.000    0.708    0.862
## 11 uspsps  =~   B3Q1   0.732 0.055 13.206  0.000    0.641    0.823
## 12 uspsps  =~   B3Q2   0.654 0.056 11.603  0.000    0.561    0.747
## 13 uspsps  =~    CQ1   0.454 0.062  7.333  0.000    0.352    0.556
## 14 uspsps  =~    DQ1   0.542 0.063  8.594  0.000    0.438    0.645
## 15 uspsps  =~    EQ1   0.519 0.057  9.122  0.000    0.426    0.613
## 16   A1Q1   |     t1   0.843 0.064 13.122  0.000    0.737    0.949
## 17   A1Q2   |     t1   1.336 0.079 16.910  0.000    1.206    1.466
## 18   A1Q3   |     t1   1.254 0.076 16.548  0.000    1.130    1.379
## 19   A2Q1   |     t1   1.361 0.080 16.999  0.000    1.230    1.493
## 20   A2Q2   |     t1   1.502 0.087 17.314  0.000    1.359    1.645
## 21   B1Q1   |     t1   0.297 0.057  5.196  0.000    0.203    0.392
## 22   B1Q2   |     t1   0.662 0.061 10.840  0.000    0.561    0.762
## 23   B1Q3   |     t1   0.895 0.065 13.692  0.000    0.787    1.002
## 24   B2Q1   |     t1   1.361 0.080 16.999  0.000    1.230    1.493
## 25   B2Q2   |     t1   1.288 0.077 16.712  0.000    1.162    1.415
## 26   B3Q1   |     t1   1.349 0.080 16.956  0.000    1.218    1.480
## 27   B3Q2   |     t1   1.190 0.074 16.189  0.000    1.069    1.311
## 28    CQ1   |     t1   0.895 0.065 13.692  0.000    0.787    1.002
## 29    DQ1   |     t1   1.093 0.070 15.520  0.000    0.978    1.209
## 30    EQ1   |     t1   0.694 0.062 11.271  0.000    0.592    0.795
## 31   A1Q1  ~~   A1Q1   0.721 0.061 11.738  0.000    0.620    0.822
## 32   A1Q2  ~~   A1Q2   0.627 0.083  7.558  0.000    0.491    0.763
## 33   A1Q3  ~~   A1Q3   0.648 0.072  9.016  0.000    0.530    0.766
## 34   A2Q1  ~~   A2Q1   0.648 0.078  8.264  0.000    0.519    0.777
## 35   A2Q2  ~~   A2Q2   0.548 0.086  6.404  0.000    0.407    0.689
## 36   B1Q1  ~~   B1Q1   0.123 0.044  2.828  0.005    0.052    0.195
## 37   B1Q2  ~~   B1Q2   0.132 0.042  3.116  0.002    0.062    0.202
## 38   B1Q3  ~~   B1Q3   0.358 0.053  6.757  0.000    0.271    0.445
## 39   B2Q1  ~~   B2Q1   0.433 0.076  5.705  0.000    0.308    0.557
## 40   B2Q2  ~~   B2Q2   0.384 0.074  5.225  0.000    0.263    0.505
## 41   B3Q1  ~~   B3Q1   0.464 0.081  5.727  0.000    0.331    0.598
## 42   B3Q2  ~~   B3Q2   0.572 0.074  7.768  0.000    0.451    0.694
## 43    CQ1  ~~    CQ1   0.794 0.056 14.092  0.000    0.701    0.886
## 44    DQ1  ~~    DQ1   0.706 0.068 10.344  0.000    0.594    0.819
## 45    EQ1  ~~    EQ1   0.730 0.059 12.363  0.000    0.633    0.828
## 46 uspsps  ~~ uspsps   1.000 0.000     NA     NA    1.000    1.000
## 47   A1Q1 ~*~   A1Q1   1.000 0.000     NA     NA    1.000    1.000
## 48   A1Q2 ~*~   A1Q2   1.000 0.000     NA     NA    1.000    1.000
## 49   A1Q3 ~*~   A1Q3   1.000 0.000     NA     NA    1.000    1.000
## 50   A2Q1 ~*~   A2Q1   1.000 0.000     NA     NA    1.000    1.000
## 51   A2Q2 ~*~   A2Q2   1.000 0.000     NA     NA    1.000    1.000
## 52   B1Q1 ~*~   B1Q1   1.000 0.000     NA     NA    1.000    1.000
## 53   B1Q2 ~*~   B1Q2   1.000 0.000     NA     NA    1.000    1.000
## 54   B1Q3 ~*~   B1Q3   1.000 0.000     NA     NA    1.000    1.000
## 55   B2Q1 ~*~   B2Q1   1.000 0.000     NA     NA    1.000    1.000
## 56   B2Q2 ~*~   B2Q2   1.000 0.000     NA     NA    1.000    1.000
## 57   B3Q1 ~*~   B3Q1   1.000 0.000     NA     NA    1.000    1.000
## 58   B3Q2 ~*~   B3Q2   1.000 0.000     NA     NA    1.000    1.000
## 59    CQ1 ~*~    CQ1   1.000 0.000     NA     NA    1.000    1.000
## 60    DQ1 ~*~    DQ1   1.000 0.000     NA     NA    1.000    1.000
## 61    EQ1 ~*~    EQ1   1.000 0.000     NA     NA    1.000    1.000
## 62   A1Q1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 63   A1Q2  ~1          0.000 0.000     NA     NA    0.000    0.000
## 64   A1Q3  ~1          0.000 0.000     NA     NA    0.000    0.000
## 65   A2Q1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 66   A2Q2  ~1          0.000 0.000     NA     NA    0.000    0.000
## 67   B1Q1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 68   B1Q2  ~1          0.000 0.000     NA     NA    0.000    0.000
## 69   B1Q3  ~1          0.000 0.000     NA     NA    0.000    0.000
## 70   B2Q1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 71   B2Q2  ~1          0.000 0.000     NA     NA    0.000    0.000
## 72   B3Q1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 73   B3Q2  ~1          0.000 0.000     NA     NA    0.000    0.000
## 74    CQ1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 75    DQ1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 76    EQ1  ~1          0.000 0.000     NA     NA    0.000    0.000
## 77 uspsps  ~1          0.000 0.000     NA     NA    0.000    0.000

Compare Fits for Models that Converged

for (mod in modnames) {
  fits[count,]$chisq <- fitMeasures(mod, c("chisq"))
  fits[count,]$df <- fitMeasures(mod, c("df"))
  fits[count,]$pvalue <- fitMeasures(mod, c("pvalue"))
  fits[count,]$cfi <- fitMeasures(mod, c("cfi"))
  fits[count,]$rmsea <- fitMeasures(mod, c("rmsea"))
  fits[count,]$srmr <- fitMeasures(mod, c("srmr"))
  count <- count + 1
}
library(kableExtra)
## 
## Attaching package: 'kableExtra'
## The following object is masked from 'package:dplyr':
## 
##     group_rows
fits %>% 
  kable(digits=3, bootstrap_options = "striped", font_size = 10) %>% 
  kable_styling()
Model chisq df pvalue cfi rmsea srmr
8 Factor Model 56.089 65 0.777 1.000 0.000 0.061
6 Factor Model 59.382 70 0.813 1.000 0.000 0.063
5 Factor Model 72.162 80 0.722 1.000 0.000 0.069
4 Factor Model 172.764 86 0.000 0.984 0.045 0.101
3 Factor Model 173.671 87 0.000 0.984 0.045 0.101
1 Factor Model 198.368 90 0.000 0.980 0.049 0.109

LRT Comparing 8-Factor and 6-Factor Models

anova(fit.sps.cfa.8, fit.sps.cfa.6)
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##               Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.sps.cfa.8 65         56.089                              
## fit.sps.cfa.6 70         59.382     3.8214       5     0.5754

LRT Comparing 6-Factor and 5-Factor Models

anova(fit.sps.cfa.6, fit.sps.cfa.5)
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##               Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.sps.cfa.6 70         59.382                              
## fit.sps.cfa.5 80         72.162     13.472      10     0.1985

Cross-Validation: Assess the two best-fitting models in Test Set of Sample

6 Factor CFA - Cross-Validation

C, D, and E (the emotional/internally-focused items) are considered as loadings on a single factor instead of 3 separate factors

fit.sps.cfa.6.test<- cfa(sps.cfa.6, data=test.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.6.test, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 35 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        50
##                                                       
##                                                   Used       Total
##   Number of observations                           497         501
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                                71.728      97.681
##   Degrees of freedom                                70          70
##   P-value (Chi-square)                           0.420       0.016
##   Scaling correction factor                                  0.871
##   Shift parameter                                           15.375
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              3548.794    2322.326
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.553
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.999       0.988
##   Tucker-Lewis Index (TLI)                       0.999       0.981
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.007       0.028
##   90 Percent confidence interval - lower         0.000       0.013
##   90 Percent confidence interval - upper         0.027       0.041
##   P-value RMSEA <= 0.05                          1.000       0.999
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.076       0.076
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys =~                                                              
##     A1Q1                0.633    0.061   10.394    0.000    0.633    0.633
##     A1Q2                0.793    0.071   11.244    0.000    0.793    0.793
##     A1Q3                0.632    0.068    9.252    0.000    0.632    0.632
##   musclejointbone =~                                                      
##     A2Q1                0.797    0.088    9.025    0.000    0.797    0.797
##     A2Q2                0.747    0.113    6.594    0.000    0.747    0.747
##   lookjr =~                                                               
##     B1Q1                0.995    0.032   30.811    0.000    0.995    0.995
##     B1Q2                0.847    0.033   25.934    0.000    0.847    0.847
##     B1Q3                0.820    0.035   23.240    0.000    0.820    0.820
##   soundjr =~                                                              
##     B2Q1                0.746    0.077    9.678    0.000    0.746    0.746
##     B2Q2                0.736    0.077    9.553    0.000    0.736    0.736
##   tactilejr =~                                                            
##     B3Q1                0.891    0.054   16.471    0.000    0.891    0.891
##     B3Q2                0.771    0.057   13.600    0.000    0.771    0.771
##   internaljr =~                                                           
##     CQ1                 0.900                               0.900    0.900
##   emo =~                                                                  
##     DQ1                 0.712    0.067   10.552    0.000    0.712    0.712
##     EQ1                 0.742    0.072   10.274    0.000    0.742    0.742
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys ~~                                                              
##     musclejointbon      0.665    0.112    5.954    0.000    0.665    0.665
##     lookjr              0.737    0.061   12.000    0.000    0.737    0.737
##     soundjr             0.633    0.116    5.444    0.000    0.633    0.633
##     tactilejr           0.845    0.085    9.941    0.000    0.845    0.845
##     internaljr          0.514    0.103    4.984    0.000    0.514    0.514
##     emo                 0.572    0.109    5.265    0.000    0.572    0.572
##   musclejointbone ~~                                                      
##     lookjr              0.364    0.091    3.987    0.000    0.364    0.364
##     soundjr             0.511    0.150    3.416    0.001    0.511    0.511
##     tactilejr           0.644    0.108    5.974    0.000    0.644    0.644
##     internaljr          0.267    0.139    1.920    0.055    0.267    0.267
##     emo                 0.447    0.112    3.980    0.000    0.447    0.447
##   lookjr ~~                                                               
##     soundjr             0.643    0.081    7.938    0.000    0.643    0.643
##     tactilejr           0.524    0.068    7.735    0.000    0.524    0.524
##     internaljr          0.428    0.073    5.850    0.000    0.428    0.428
##     emo                 0.539    0.076    7.088    0.000    0.539    0.539
##   soundjr ~~                                                              
##     tactilejr           0.761    0.097    7.871    0.000    0.761    0.761
##     internaljr          0.634    0.113    5.608    0.000    0.634    0.634
##     emo                 0.759    0.110    6.931    0.000    0.759    0.759
##   tactilejr ~~                                                            
##     internaljr          0.456    0.104    4.387    0.000    0.456    0.456
##     emo                 0.718    0.095    7.538    0.000    0.718    0.718
##   internaljr ~~                                                           
##     emo                 0.725    0.095    7.670    0.000    0.725    0.725
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tacphys           0.000                               0.000    0.000
##     musclejointbon    0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     soundjr           0.000                               0.000    0.000
##     tactilejr         0.000                               0.000    0.000
##     internaljr        0.000                               0.000    0.000
##     emo               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.728    0.062   11.729    0.000    0.728    0.728
##     A1Q2|t1           1.278    0.077   16.681    0.000    1.278    1.278
##     A1Q3|t1           1.245    0.075   16.514    0.000    1.245    1.245
##     A2Q1|t1           1.350    0.080   16.977    0.000    1.350    1.350
##     A2Q2|t1           1.703    0.099   17.250    0.000    1.703    1.703
##     B1Q1|t1           0.139    0.056    2.464    0.014    0.139    0.139
##     B1Q2|t1           0.457    0.058    7.812    0.000    0.457    0.457
##     B1Q3|t1           0.728    0.062   11.729    0.000    0.728    0.728
##     B2Q1|t1           1.337    0.079   16.931    0.000    1.337    1.337
##     B2Q2|t1           1.256    0.076   16.570    0.000    1.256    1.256
##     B3Q1|t1           1.212    0.074   16.336    0.000    1.212    1.212
##     B3Q2|t1           1.123    0.071   15.753    0.000    1.123    1.123
##     CQ1|t1            0.999    0.068   14.739    0.000    0.999    0.999
##     DQ1|t1            1.077    0.070   15.403    0.000    1.077    1.077
##     EQ1|t1            0.708    0.062   11.474    0.000    0.708    0.708
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.600                               0.600    0.600
##    .A1Q2              0.371                               0.371    0.371
##    .A1Q3              0.601                               0.601    0.601
##    .A2Q1              0.365                               0.365    0.365
##    .A2Q2              0.441                               0.441    0.441
##    .B1Q1              0.009                               0.009    0.009
##    .B1Q2              0.282                               0.282    0.282
##    .B1Q3              0.327                               0.327    0.327
##    .B2Q1              0.443                               0.443    0.443
##    .B2Q2              0.458                               0.458    0.458
##    .B3Q1              0.206                               0.206    0.206
##    .B3Q2              0.406                               0.406    0.406
##    .CQ1               0.190                               0.190    0.190
##    .DQ1               0.493                               0.493    0.493
##    .EQ1               0.450                               0.450    0.450
##     tacphys           1.000                               1.000    1.000
##     musclejointbon    1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     soundjr           1.000                               1.000    1.000
##     tactilejr         1.000                               1.000    1.000
##     internaljr        1.000                               1.000    1.000
##     emo               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.6.test, ci=T, level = .90)
##                 lhs  op             rhs est.std    se      z pvalue ci.lower
## 1           tacphys  =~            A1Q1   0.633 0.061 10.394  0.000    0.532
## 2           tacphys  =~            A1Q2   0.793 0.071 11.244  0.000    0.677
## 3           tacphys  =~            A1Q3   0.632 0.068  9.252  0.000    0.519
## 4   musclejointbone  =~            A2Q1   0.797 0.088  9.025  0.000    0.652
## 5   musclejointbone  =~            A2Q2   0.747 0.113  6.594  0.000    0.561
## 6            lookjr  =~            B1Q1   0.995 0.032 30.811  0.000    0.942
## 7            lookjr  =~            B1Q2   0.847 0.033 25.934  0.000    0.794
## 8            lookjr  =~            B1Q3   0.820 0.035 23.240  0.000    0.762
## 9           soundjr  =~            B2Q1   0.746 0.077  9.678  0.000    0.619
## 10          soundjr  =~            B2Q2   0.736 0.077  9.553  0.000    0.610
## 11        tactilejr  =~            B3Q1   0.891 0.054 16.471  0.000    0.802
## 12        tactilejr  =~            B3Q2   0.771 0.057 13.600  0.000    0.678
## 13       internaljr  =~             CQ1   0.900 0.000     NA     NA    0.900
## 14              emo  =~             DQ1   0.712 0.067 10.552  0.000    0.601
## 15              emo  =~             EQ1   0.742 0.072 10.274  0.000    0.623
## 16             A1Q1   |              t1   0.728 0.062 11.729  0.000    0.626
## 17             A1Q2   |              t1   1.278 0.077 16.681  0.000    1.152
## 18             A1Q3   |              t1   1.245 0.075 16.514  0.000    1.121
## 19             A2Q1   |              t1   1.350 0.080 16.977  0.000    1.219
## 20             A2Q2   |              t1   1.703 0.099 17.250  0.000    1.541
## 21             B1Q1   |              t1   0.139 0.056  2.464  0.014    0.046
## 22             B1Q2   |              t1   0.457 0.058  7.812  0.000    0.361
## 23             B1Q3   |              t1   0.728 0.062 11.729  0.000    0.626
## 24             B2Q1   |              t1   1.337 0.079 16.931  0.000    1.207
## 25             B2Q2   |              t1   1.256 0.076 16.570  0.000    1.131
## 26             B3Q1   |              t1   1.212 0.074 16.336  0.000    1.090
## 27             B3Q2   |              t1   1.123 0.071 15.753  0.000    1.005
## 28              CQ1   |              t1   0.999 0.068 14.739  0.000    0.887
## 29              DQ1   |              t1   1.077 0.070 15.403  0.000    0.962
## 30              EQ1   |              t1   0.708 0.062 11.474  0.000    0.607
## 31             A1Q1  ~~            A1Q1   0.600 0.077  7.793  0.000    0.473
## 32             A1Q2  ~~            A1Q2   0.371 0.112  3.313  0.001    0.187
## 33             A1Q3  ~~            A1Q3   0.601 0.086  6.973  0.000    0.459
## 34             A2Q1  ~~            A2Q1   0.365 0.141  2.595  0.009    0.134
## 35             A2Q2  ~~            A2Q2   0.441 0.169  2.604  0.009    0.163
## 36             B1Q1  ~~            B1Q1   0.009 0.064  0.140  0.889   -0.097
## 37             B1Q2  ~~            B1Q2   0.282 0.055  5.090  0.000    0.191
## 38             B1Q3  ~~            B1Q3   0.327 0.058  5.652  0.000    0.232
## 39             B2Q1  ~~            B2Q1   0.443 0.115  3.853  0.000    0.254
## 40             B2Q2  ~~            B2Q2   0.458 0.114  4.034  0.000    0.271
## 41             B3Q1  ~~            B3Q1   0.206 0.096  2.141  0.032    0.048
## 42             B3Q2  ~~            B3Q2   0.406 0.087  4.639  0.000    0.262
## 43              CQ1  ~~             CQ1   0.190 0.000     NA     NA    0.190
## 44              DQ1  ~~             DQ1   0.493 0.096  5.140  0.000    0.336
## 45              EQ1  ~~             EQ1   0.450 0.107  4.196  0.000    0.273
## 46          tacphys  ~~         tacphys   1.000 0.000     NA     NA    1.000
## 47  musclejointbone  ~~ musclejointbone   1.000 0.000     NA     NA    1.000
## 48           lookjr  ~~          lookjr   1.000 0.000     NA     NA    1.000
## 49          soundjr  ~~         soundjr   1.000 0.000     NA     NA    1.000
## 50        tactilejr  ~~       tactilejr   1.000 0.000     NA     NA    1.000
## 51       internaljr  ~~      internaljr   1.000 0.000     NA     NA    1.000
## 52              emo  ~~             emo   1.000 0.000     NA     NA    1.000
## 53          tacphys  ~~ musclejointbone   0.665 0.112  5.954  0.000    0.481
## 54          tacphys  ~~          lookjr   0.737 0.061 12.000  0.000    0.636
## 55          tacphys  ~~         soundjr   0.633 0.116  5.444  0.000    0.442
## 56          tacphys  ~~       tactilejr   0.845 0.085  9.941  0.000    0.705
## 57          tacphys  ~~      internaljr   0.514 0.103  4.984  0.000    0.345
## 58          tacphys  ~~             emo   0.572 0.109  5.265  0.000    0.393
## 59  musclejointbone  ~~          lookjr   0.364 0.091  3.987  0.000    0.214
## 60  musclejointbone  ~~         soundjr   0.511 0.150  3.416  0.001    0.265
## 61  musclejointbone  ~~       tactilejr   0.644 0.108  5.974  0.000    0.467
## 62  musclejointbone  ~~      internaljr   0.267 0.139  1.920  0.055    0.038
## 63  musclejointbone  ~~             emo   0.447 0.112  3.980  0.000    0.262
## 64           lookjr  ~~         soundjr   0.643 0.081  7.938  0.000    0.510
## 65           lookjr  ~~       tactilejr   0.524 0.068  7.735  0.000    0.413
## 66           lookjr  ~~      internaljr   0.428 0.073  5.850  0.000    0.307
## 67           lookjr  ~~             emo   0.539 0.076  7.088  0.000    0.414
## 68          soundjr  ~~       tactilejr   0.761 0.097  7.871  0.000    0.602
## 69          soundjr  ~~      internaljr   0.634 0.113  5.608  0.000    0.448
## 70          soundjr  ~~             emo   0.759 0.110  6.931  0.000    0.579
## 71        tactilejr  ~~      internaljr   0.456 0.104  4.387  0.000    0.285
## 72        tactilejr  ~~             emo   0.718 0.095  7.538  0.000    0.562
## 73       internaljr  ~~             emo   0.725 0.095  7.670  0.000    0.570
## 74             A1Q1 ~*~            A1Q1   1.000 0.000     NA     NA    1.000
## 75             A1Q2 ~*~            A1Q2   1.000 0.000     NA     NA    1.000
## 76             A1Q3 ~*~            A1Q3   1.000 0.000     NA     NA    1.000
## 77             A2Q1 ~*~            A2Q1   1.000 0.000     NA     NA    1.000
## 78             A2Q2 ~*~            A2Q2   1.000 0.000     NA     NA    1.000
## 79             B1Q1 ~*~            B1Q1   1.000 0.000     NA     NA    1.000
## 80             B1Q2 ~*~            B1Q2   1.000 0.000     NA     NA    1.000
## 81             B1Q3 ~*~            B1Q3   1.000 0.000     NA     NA    1.000
## 82             B2Q1 ~*~            B2Q1   1.000 0.000     NA     NA    1.000
## 83             B2Q2 ~*~            B2Q2   1.000 0.000     NA     NA    1.000
## 84             B3Q1 ~*~            B3Q1   1.000 0.000     NA     NA    1.000
## 85             B3Q2 ~*~            B3Q2   1.000 0.000     NA     NA    1.000
## 86              CQ1 ~*~             CQ1   1.000 0.000     NA     NA    1.000
## 87              DQ1 ~*~             DQ1   1.000 0.000     NA     NA    1.000
## 88              EQ1 ~*~             EQ1   1.000 0.000     NA     NA    1.000
## 89             A1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 90             A1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 91             A1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 92             A2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 93             A2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 94             B1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 95             B1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 96             B1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 97             B2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 98             B2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 99             B3Q1  ~1                   0.000 0.000     NA     NA    0.000
## 100            B3Q2  ~1                   0.000 0.000     NA     NA    0.000
## 101             CQ1  ~1                   0.000 0.000     NA     NA    0.000
## 102             DQ1  ~1                   0.000 0.000     NA     NA    0.000
## 103             EQ1  ~1                   0.000 0.000     NA     NA    0.000
## 104         tacphys  ~1                   0.000 0.000     NA     NA    0.000
## 105 musclejointbone  ~1                   0.000 0.000     NA     NA    0.000
## 106          lookjr  ~1                   0.000 0.000     NA     NA    0.000
## 107         soundjr  ~1                   0.000 0.000     NA     NA    0.000
## 108       tactilejr  ~1                   0.000 0.000     NA     NA    0.000
## 109      internaljr  ~1                   0.000 0.000     NA     NA    0.000
## 110             emo  ~1                   0.000 0.000     NA     NA    0.000
##     ci.upper
## 1      0.733
## 2      0.909
## 3      0.744
## 4      0.942
## 5      0.934
## 6      1.049
## 7      0.901
## 8      0.878
## 9      0.873
## 10     0.863
## 11     0.980
## 12     0.864
## 13     0.900
## 14     0.823
## 15     0.861
## 16     0.830
## 17     1.404
## 18     1.369
## 19     1.481
## 20     1.866
## 21     0.232
## 22     0.553
## 23     0.830
## 24     1.467
## 25     1.380
## 26     1.334
## 27     1.240
## 28     1.110
## 29     1.191
## 30     0.810
## 31     0.727
## 32     0.555
## 33     0.743
## 34     0.597
## 35     0.720
## 36     0.115
## 37     0.373
## 38     0.422
## 39     0.632
## 40     0.645
## 41     0.365
## 42     0.549
## 43     0.190
## 44     0.651
## 45     0.626
## 46     1.000
## 47     1.000
## 48     1.000
## 49     1.000
## 50     1.000
## 51     1.000
## 52     1.000
## 53     0.849
## 54     0.838
## 55     0.824
## 56     0.985
## 57     0.684
## 58     0.751
## 59     0.514
## 60     0.757
## 61     0.821
## 62     0.496
## 63     0.632
## 64     0.777
## 65     0.635
## 66     0.548
## 67     0.665
## 68     0.920
## 69     0.820
## 70     0.940
## 71     0.627
## 72     0.875
## 73     0.881
## 74     1.000
## 75     1.000
## 76     1.000
## 77     1.000
## 78     1.000
## 79     1.000
## 80     1.000
## 81     1.000
## 82     1.000
## 83     1.000
## 84     1.000
## 85     1.000
## 86     1.000
## 87     1.000
## 88     1.000
## 89     0.000
## 90     0.000
## 91     0.000
## 92     0.000
## 93     0.000
## 94     0.000
## 95     0.000
## 96     0.000
## 97     0.000
## 98     0.000
## 99     0.000
## 100    0.000
## 101    0.000
## 102    0.000
## 103    0.000
## 104    0.000
## 105    0.000
## 106    0.000
## 107    0.000
## 108    0.000
## 109    0.000
## 110    0.000
inspect(fit.sps.cfa.6.test, "cov.lv")
##                 tcphys mscljn lookjr sondjr tctljr intrnl emo  
## tacphys         1.000                                          
## musclejointbone 0.665  1.000                                   
## lookjr          0.737  0.364  1.000                            
## soundjr         0.633  0.511  0.643  1.000                     
## tactilejr       0.845  0.644  0.524  0.761  1.000              
## internaljr      0.514  0.267  0.428  0.634  0.456  1.000       
## emo             0.572  0.447  0.539  0.759  0.718  0.725  1.000

5 Factor CFA - Cross-Validation

fit.sps.cfa.5.test<- cfa(sps.cfa.5, data=test.dat, std.lv=T, ordered = c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2","B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2", "CQ1", "DQ1", "EQ1")) 
summary(fit.sps.cfa.5.test, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 27 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                        40
##                                                       
##                                                   Used       Total
##   Number of observations                           497         501
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                                89.524     115.506
##   Degrees of freedom                                80          80
##   P-value (Chi-square)                           0.219       0.006
##   Scaling correction factor                                  0.926
##   Shift parameter                                           18.846
##        simple second-order correction                             
## 
## Model Test Baseline Model:
## 
##   Test statistic                              3548.794    2322.326
##   Degrees of freedom                               105         105
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.553
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.997       0.984
##   Tucker-Lewis Index (TLI)                       0.996       0.979
##                                                                   
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.015       0.030
##   90 Percent confidence interval - lower         0.000       0.017
##   90 Percent confidence interval - upper         0.030       0.041
##   P-value RMSEA <= 0.05                          1.000       0.999
##                                                                   
##   Robust RMSEA                                                  NA
##   90 Percent confidence interval - lower                        NA
##   90 Percent confidence interval - upper                        NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.083       0.083
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tactile =~                                                              
##     A1Q1                0.620    0.060   10.314    0.000    0.620    0.620
##     A1Q2                0.774    0.057   13.621    0.000    0.774    0.774
##     A1Q3                0.619    0.066    9.399    0.000    0.619    0.619
##     B3Q1                0.821    0.049   16.651    0.000    0.821    0.821
##     B3Q2                0.720    0.055   13.069    0.000    0.720    0.720
##   musclejointbone =~                                                      
##     A2Q1                0.795    0.088    8.999    0.000    0.795    0.795
##     A2Q2                0.749    0.113    6.654    0.000    0.749    0.749
##   lookjr =~                                                               
##     B1Q1                0.997    0.033   30.633    0.000    0.997    0.997
##     B1Q2                0.847    0.033   25.748    0.000    0.847    0.847
##     B1Q3                0.819    0.036   22.914    0.000    0.819    0.819
##   soundjr =~                                                              
##     B2Q1                0.746    0.078    9.620    0.000    0.746    0.746
##     B2Q2                0.737    0.077    9.560    0.000    0.737    0.737
##   emo =~                                                                  
##     CQ1                 0.677    0.064   10.614    0.000    0.677    0.677
##     DQ1                 0.702    0.063   11.132    0.000    0.702    0.702
##     EQ1                 0.729    0.066   11.010    0.000    0.729    0.729
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tactile ~~                                                              
##     musclejointbon      0.687    0.091    7.536    0.000    0.687    0.687
##     lookjr              0.671    0.055   12.222    0.000    0.671    0.671
##     soundjr             0.738    0.090    8.198    0.000    0.738    0.738
##     emo                 0.688    0.077    8.953    0.000    0.688    0.688
##   musclejointbone ~~                                                      
##     lookjr              0.364    0.091    3.988    0.000    0.364    0.364
##     soundjr             0.511    0.150    3.418    0.001    0.511    0.511
##     emo                 0.427    0.107    4.006    0.000    0.427    0.427
##   lookjr ~~                                                               
##     soundjr             0.643    0.081    7.940    0.000    0.643    0.643
##     emo                 0.554    0.067    8.233    0.000    0.554    0.554
##   soundjr ~~                                                              
##     emo                 0.793    0.103    7.712    0.000    0.793    0.793
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.000                               0.000    0.000
##    .A1Q2              0.000                               0.000    0.000
##    .A1Q3              0.000                               0.000    0.000
##    .B3Q1              0.000                               0.000    0.000
##    .B3Q2              0.000                               0.000    0.000
##    .A2Q1              0.000                               0.000    0.000
##    .A2Q2              0.000                               0.000    0.000
##    .B1Q1              0.000                               0.000    0.000
##    .B1Q2              0.000                               0.000    0.000
##    .B1Q3              0.000                               0.000    0.000
##    .B2Q1              0.000                               0.000    0.000
##    .B2Q2              0.000                               0.000    0.000
##    .CQ1               0.000                               0.000    0.000
##    .DQ1               0.000                               0.000    0.000
##    .EQ1               0.000                               0.000    0.000
##     tactile           0.000                               0.000    0.000
##     musclejointbon    0.000                               0.000    0.000
##     lookjr            0.000                               0.000    0.000
##     soundjr           0.000                               0.000    0.000
##     emo               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1|t1           0.728    0.062   11.729    0.000    0.728    0.728
##     A1Q2|t1           1.278    0.077   16.681    0.000    1.278    1.278
##     A1Q3|t1           1.245    0.075   16.514    0.000    1.245    1.245
##     B3Q1|t1           1.212    0.074   16.336    0.000    1.212    1.212
##     B3Q2|t1           1.123    0.071   15.753    0.000    1.123    1.123
##     A2Q1|t1           1.350    0.080   16.977    0.000    1.350    1.350
##     A2Q2|t1           1.703    0.099   17.250    0.000    1.703    1.703
##     B1Q1|t1           0.139    0.056    2.464    0.014    0.139    0.139
##     B1Q2|t1           0.457    0.058    7.812    0.000    0.457    0.457
##     B1Q3|t1           0.728    0.062   11.729    0.000    0.728    0.728
##     B2Q1|t1           1.337    0.079   16.931    0.000    1.337    1.337
##     B2Q2|t1           1.256    0.076   16.570    0.000    1.256    1.256
##     CQ1|t1            0.999    0.068   14.739    0.000    0.999    0.999
##     DQ1|t1            1.077    0.070   15.403    0.000    1.077    1.077
##     EQ1|t1            0.708    0.062   11.474    0.000    0.708    0.708
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .A1Q1              0.616                               0.616    0.616
##    .A1Q2              0.400                               0.400    0.400
##    .A1Q3              0.617                               0.617    0.617
##    .B3Q1              0.325                               0.325    0.325
##    .B3Q2              0.482                               0.482    0.482
##    .A2Q1              0.367                               0.367    0.367
##    .A2Q2              0.440                               0.440    0.440
##    .B1Q1              0.007                               0.007    0.007
##    .B1Q2              0.282                               0.282    0.282
##    .B1Q3              0.329                               0.329    0.329
##    .B2Q1              0.444                               0.444    0.444
##    .B2Q2              0.457                               0.457    0.457
##    .CQ1               0.541                               0.541    0.541
##    .DQ1               0.508                               0.508    0.508
##    .EQ1               0.468                               0.468    0.468
##     tactile           1.000                               1.000    1.000
##     musclejointbon    1.000                               1.000    1.000
##     lookjr            1.000                               1.000    1.000
##     soundjr           1.000                               1.000    1.000
##     emo               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     A1Q1              1.000                               1.000    1.000
##     A1Q2              1.000                               1.000    1.000
##     A1Q3              1.000                               1.000    1.000
##     B3Q1              1.000                               1.000    1.000
##     B3Q2              1.000                               1.000    1.000
##     A2Q1              1.000                               1.000    1.000
##     A2Q2              1.000                               1.000    1.000
##     B1Q1              1.000                               1.000    1.000
##     B1Q2              1.000                               1.000    1.000
##     B1Q3              1.000                               1.000    1.000
##     B2Q1              1.000                               1.000    1.000
##     B2Q2              1.000                               1.000    1.000
##     CQ1               1.000                               1.000    1.000
##     DQ1               1.000                               1.000    1.000
##     EQ1               1.000                               1.000    1.000
standardizedSolution(fit.sps.cfa.5.test, ci=T, level = .90)
##                lhs  op             rhs est.std    se      z pvalue ci.lower
## 1          tactile  =~            A1Q1   0.620 0.060 10.314  0.000    0.521
## 2          tactile  =~            A1Q2   0.774 0.057 13.621  0.000    0.681
## 3          tactile  =~            A1Q3   0.619 0.066  9.399  0.000    0.511
## 4          tactile  =~            B3Q1   0.821 0.049 16.651  0.000    0.740
## 5          tactile  =~            B3Q2   0.720 0.055 13.069  0.000    0.629
## 6  musclejointbone  =~            A2Q1   0.795 0.088  8.999  0.000    0.650
## 7  musclejointbone  =~            A2Q2   0.749 0.113  6.654  0.000    0.564
## 8           lookjr  =~            B1Q1   0.997 0.033 30.633  0.000    0.943
## 9           lookjr  =~            B1Q2   0.847 0.033 25.748  0.000    0.793
## 10          lookjr  =~            B1Q3   0.819 0.036 22.914  0.000    0.760
## 11         soundjr  =~            B2Q1   0.746 0.078  9.620  0.000    0.618
## 12         soundjr  =~            B2Q2   0.737 0.077  9.560  0.000    0.610
## 13             emo  =~             CQ1   0.677 0.064 10.614  0.000    0.572
## 14             emo  =~             DQ1   0.702 0.063 11.132  0.000    0.598
## 15             emo  =~             EQ1   0.729 0.066 11.010  0.000    0.620
## 16            A1Q1   |              t1   0.728 0.062 11.729  0.000    0.626
## 17            A1Q2   |              t1   1.278 0.077 16.681  0.000    1.152
## 18            A1Q3   |              t1   1.245 0.075 16.514  0.000    1.121
## 19            B3Q1   |              t1   1.212 0.074 16.336  0.000    1.090
## 20            B3Q2   |              t1   1.123 0.071 15.753  0.000    1.005
## 21            A2Q1   |              t1   1.350 0.080 16.977  0.000    1.219
## 22            A2Q2   |              t1   1.703 0.099 17.250  0.000    1.541
## 23            B1Q1   |              t1   0.139 0.056  2.464  0.014    0.046
## 24            B1Q2   |              t1   0.457 0.058  7.812  0.000    0.361
## 25            B1Q3   |              t1   0.728 0.062 11.729  0.000    0.626
## 26            B2Q1   |              t1   1.337 0.079 16.931  0.000    1.207
## 27            B2Q2   |              t1   1.256 0.076 16.570  0.000    1.131
## 28             CQ1   |              t1   0.999 0.068 14.739  0.000    0.887
## 29             DQ1   |              t1   1.077 0.070 15.403  0.000    0.962
## 30             EQ1   |              t1   0.708 0.062 11.474  0.000    0.607
## 31            A1Q1  ~~            A1Q1   0.616 0.074  8.276  0.000    0.494
## 32            A1Q2  ~~            A1Q2   0.400 0.088  4.546  0.000    0.255
## 33            A1Q3  ~~            A1Q3   0.617 0.082  7.557  0.000    0.482
## 34            B3Q1  ~~            B3Q1   0.325 0.081  4.013  0.000    0.192
## 35            B3Q2  ~~            B3Q2   0.482 0.079  6.080  0.000    0.352
## 36            A2Q1  ~~            A2Q1   0.367 0.141  2.611  0.009    0.136
## 37            A2Q2  ~~            A2Q2   0.440 0.168  2.609  0.009    0.162
## 38            B1Q1  ~~            B1Q1   0.007 0.065  0.108  0.914   -0.100
## 39            B1Q2  ~~            B1Q2   0.282 0.056  5.062  0.000    0.191
## 40            B1Q3  ~~            B1Q3   0.329 0.059  5.625  0.000    0.233
## 41            B2Q1  ~~            B2Q1   0.444 0.116  3.838  0.000    0.254
## 42            B2Q2  ~~            B2Q2   0.457 0.114  4.028  0.000    0.271
## 43             CQ1  ~~             CQ1   0.541 0.086  6.260  0.000    0.399
## 44             DQ1  ~~             DQ1   0.508 0.088  5.744  0.000    0.362
## 45             EQ1  ~~             EQ1   0.468 0.097  4.849  0.000    0.309
## 46         tactile  ~~         tactile   1.000 0.000     NA     NA    1.000
## 47 musclejointbone  ~~ musclejointbone   1.000 0.000     NA     NA    1.000
## 48          lookjr  ~~          lookjr   1.000 0.000     NA     NA    1.000
## 49         soundjr  ~~         soundjr   1.000 0.000     NA     NA    1.000
## 50             emo  ~~             emo   1.000 0.000     NA     NA    1.000
## 51         tactile  ~~ musclejointbone   0.687 0.091  7.536  0.000    0.537
## 52         tactile  ~~          lookjr   0.671 0.055 12.222  0.000    0.581
## 53         tactile  ~~         soundjr   0.738 0.090  8.198  0.000    0.590
## 54         tactile  ~~             emo   0.688 0.077  8.953  0.000    0.561
## 55 musclejointbone  ~~          lookjr   0.364 0.091  3.988  0.000    0.214
## 56 musclejointbone  ~~         soundjr   0.511 0.150  3.418  0.001    0.265
## 57 musclejointbone  ~~             emo   0.427 0.107  4.006  0.000    0.251
## 58          lookjr  ~~         soundjr   0.643 0.081  7.940  0.000    0.510
## 59          lookjr  ~~             emo   0.554 0.067  8.233  0.000    0.443
## 60         soundjr  ~~             emo   0.793 0.103  7.712  0.000    0.624
## 61            A1Q1 ~*~            A1Q1   1.000 0.000     NA     NA    1.000
## 62            A1Q2 ~*~            A1Q2   1.000 0.000     NA     NA    1.000
## 63            A1Q3 ~*~            A1Q3   1.000 0.000     NA     NA    1.000
## 64            B3Q1 ~*~            B3Q1   1.000 0.000     NA     NA    1.000
## 65            B3Q2 ~*~            B3Q2   1.000 0.000     NA     NA    1.000
## 66            A2Q1 ~*~            A2Q1   1.000 0.000     NA     NA    1.000
## 67            A2Q2 ~*~            A2Q2   1.000 0.000     NA     NA    1.000
## 68            B1Q1 ~*~            B1Q1   1.000 0.000     NA     NA    1.000
## 69            B1Q2 ~*~            B1Q2   1.000 0.000     NA     NA    1.000
## 70            B1Q3 ~*~            B1Q3   1.000 0.000     NA     NA    1.000
## 71            B2Q1 ~*~            B2Q1   1.000 0.000     NA     NA    1.000
## 72            B2Q2 ~*~            B2Q2   1.000 0.000     NA     NA    1.000
## 73             CQ1 ~*~             CQ1   1.000 0.000     NA     NA    1.000
## 74             DQ1 ~*~             DQ1   1.000 0.000     NA     NA    1.000
## 75             EQ1 ~*~             EQ1   1.000 0.000     NA     NA    1.000
## 76            A1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 77            A1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 78            A1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 79            B3Q1  ~1                   0.000 0.000     NA     NA    0.000
## 80            B3Q2  ~1                   0.000 0.000     NA     NA    0.000
## 81            A2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 82            A2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 83            B1Q1  ~1                   0.000 0.000     NA     NA    0.000
## 84            B1Q2  ~1                   0.000 0.000     NA     NA    0.000
## 85            B1Q3  ~1                   0.000 0.000     NA     NA    0.000
## 86            B2Q1  ~1                   0.000 0.000     NA     NA    0.000
## 87            B2Q2  ~1                   0.000 0.000     NA     NA    0.000
## 88             CQ1  ~1                   0.000 0.000     NA     NA    0.000
## 89             DQ1  ~1                   0.000 0.000     NA     NA    0.000
## 90             EQ1  ~1                   0.000 0.000     NA     NA    0.000
## 91         tactile  ~1                   0.000 0.000     NA     NA    0.000
## 92 musclejointbone  ~1                   0.000 0.000     NA     NA    0.000
## 93          lookjr  ~1                   0.000 0.000     NA     NA    0.000
## 94         soundjr  ~1                   0.000 0.000     NA     NA    0.000
## 95             emo  ~1                   0.000 0.000     NA     NA    0.000
##    ci.upper
## 1     0.718
## 2     0.868
## 3     0.728
## 4     0.903
## 5     0.810
## 6     0.941
## 7     0.934
## 8     1.050
## 9     0.901
## 10    0.878
## 11    0.873
## 12    0.863
## 13    0.782
## 14    0.805
## 15    0.838
## 16    0.830
## 17    1.404
## 18    1.369
## 19    1.334
## 20    1.240
## 21    1.481
## 22    1.866
## 23    0.232
## 24    0.553
## 25    0.830
## 26    1.467
## 27    1.380
## 28    1.110
## 29    1.191
## 30    0.810
## 31    0.739
## 32    0.545
## 33    0.751
## 34    0.459
## 35    0.612
## 36    0.599
## 37    0.717
## 38    0.114
## 39    0.374
## 40    0.426
## 41    0.634
## 42    0.644
## 43    0.683
## 44    0.653
## 45    0.627
## 46    1.000
## 47    1.000
## 48    1.000
## 49    1.000
## 50    1.000
## 51    0.837
## 52    0.762
## 53    0.886
## 54    0.814
## 55    0.514
## 56    0.757
## 57    0.602
## 58    0.777
## 59    0.665
## 60    0.962
## 61    1.000
## 62    1.000
## 63    1.000
## 64    1.000
## 65    1.000
## 66    1.000
## 67    1.000
## 68    1.000
## 69    1.000
## 70    1.000
## 71    1.000
## 72    1.000
## 73    1.000
## 74    1.000
## 75    1.000
## 76    0.000
## 77    0.000
## 78    0.000
## 79    0.000
## 80    0.000
## 81    0.000
## 82    0.000
## 83    0.000
## 84    0.000
## 85    0.000
## 86    0.000
## 87    0.000
## 88    0.000
## 89    0.000
## 90    0.000
## 91    0.000
## 92    0.000
## 93    0.000
## 94    0.000
## 95    0.000

Compare Fits for Models that Converged

for (mod in modnames.test) {
  fits.test[count,]$chisq <- fitMeasures(mod, c("chisq"))
  fits.test[count,]$df <- fitMeasures(mod, c("df"))
  fits.test[count,]$pvalue <- fitMeasures(mod, c("pvalue"))
  fits.test[count,]$cfi <- fitMeasures(mod, c("cfi"))
  fits.test[count,]$rmsea <- fitMeasures(mod, c("rmsea"))
  fits.test[count,]$srmr <- fitMeasures(mod, c("srmr"))
  count <- count + 1
}
fits.test %>% 
  kable(digits=3, bootstrap_options = "striped", font_size = 10) %>% 
  kable_styling()
Model chisq df pvalue cfi rmsea srmr
6 Factor Model 71.728 70 0.420 0.999 0.007 0.076
5 Factor Model 89.524 80 0.219 0.997 0.015 0.083

LRT Comparing 6-Factor and 5-Factor Models

anova(fit.sps.cfa.6.test, fit.sps.cfa.5.test)
## Scaled Chi-Squared Difference Test (method = "satorra.2000")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                    Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)  
## fit.sps.cfa.6.test 70         71.728                                
## fit.sps.cfa.5.test 80         89.524     18.029      10    0.05448 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Create Composite Scores of USP-SPS Data

spsnames <- c("A1Q1", "A1Q2", "A1Q3", "A2Q1", "A2Q2", "B1Q1", "B1Q2", "B1Q3", "B2Q1", "B2Q2", "B3Q1", "B3Q2",  "CQ1", "DQ1", "EQ1")

ctoccsv.yn[,spsnames] = data.frame(sapply(ctoccsv.yn[,spsnames], as.integer))

ctoccsv.yn$tacphys=rowMeans(ctoccsv.yn[,c("A1Q1", "A1Q2", "A1Q3")], na.rm=TRUE)

ctoccsv.yn$musclejointbone=rowMeans(ctoccsv.yn[,c("A2Q1", "A2Q2")], na.rm=TRUE)

ctoccsv.yn$lookjr=rowMeans(ctoccsv.yn[,c("B1Q1", "B1Q2", "B1Q3")], na.rm=TRUE)

ctoccsv.yn$soundjr=rowMeans(ctoccsv.yn[,c("B2Q1", "B2Q2")], na.rm=TRUE)

ctoccsv.yn$tactilejr=rowMeans(ctoccsv.yn[,c("B3Q1", "B3Q2")], na.rm=TRUE)

ctoccsv.yn$emo=rowMeans(ctoccsv.yn[,c("CQ1", "DQ1", "EQ1")], na.rm=TRUE)

Multivariate Regression Model

Composites from 6-Factor CFA of USP-SPS + DYBOCS

sps.cfa.6.dy <- '
tacphys ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
musclejointbone ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
lookjr ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
soundjr ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
tactilejr ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
emo ~ TOTALAGR + TOTALSEX + TOTALCON + TOTALSIM + TOTALCOL + TOTALSIN
'
fit.sps.cfa.6.dy<- cfa(sps.cfa.6.dy, data=ctoccsv.yn, std.ov=T) 
summary(fit.sps.cfa.6.dy, fit.measures=T, standardized=T)
## lavaan 0.6-9 ended normally after 102 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        57
##                                                       
##                                                   Used       Total
##   Number of observations                           991        1001
##                                                                   
## Model Test User Model:
##                                                       
##   Test statistic                                 0.000
##   Degrees of freedom                                 0
## 
## Model Test Baseline Model:
## 
##   Test statistic                              1975.265
##   Degrees of freedom                                51
##   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)              94438.789
##   Loglikelihood unrestricted model (H1)     -17046.710
##                                                       
##   Akaike (AIC)                             -188763.579
##   Bayesian (BIC)                           -188484.352
##   Sample-size adjusted Bayesian (BIC)      -188665.386
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.000
##   P-value RMSEA <= 0.05                             NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   tacphys ~                                                              
##     TOTALAGR           0.010    0.007    1.374    0.170    0.010    0.048
##     TOTALSEX           0.009    0.007    1.359    0.174    0.009    0.045
##     TOTALCON           0.031    0.006    4.811    0.000    0.031    0.160
##     TOTALSIM           0.019    0.008    2.499    0.012    0.019    0.088
##     TOTALCOL           0.020    0.008    2.480    0.013    0.020    0.081
##     TOTALSIN           0.008    0.007    1.088    0.276    0.008    0.038
##   musclejointbone ~                                                      
##     TOTALAGR           0.003    0.007    0.368    0.713    0.003    0.013
##     TOTALSEX           0.015    0.007    2.122    0.034    0.015    0.073
##     TOTALCON          -0.013    0.007   -1.925    0.054   -0.013   -0.066
##     TOTALSIM           0.010    0.008    1.320    0.187    0.010    0.048
##     TOTALCOL           0.017    0.008    2.094    0.036    0.017    0.071
##     TOTALSIN           0.014    0.008    1.781    0.075    0.014    0.064
##   lookjr ~                                                               
##     TOTALAGR          -0.009    0.007   -1.376    0.169   -0.009   -0.046
##     TOTALSEX           0.006    0.007    0.879    0.379    0.006    0.028
##     TOTALCON           0.020    0.006    3.197    0.001    0.020    0.103
##     TOTALSIM           0.072    0.007    9.830    0.000    0.072    0.334
##     TOTALCOL           0.016    0.008    2.115    0.034    0.016    0.067
##     TOTALSIN          -0.006    0.007   -0.821    0.412   -0.006   -0.027
##   soundjr ~                                                              
##     TOTALAGR          -0.005    0.007   -0.685    0.493   -0.005   -0.024
##     TOTALSEX           0.014    0.007    2.008    0.045    0.014    0.068
##     TOTALCON          -0.005    0.007   -0.733    0.463   -0.005   -0.025
##     TOTALSIM           0.037    0.008    4.819    0.000    0.037    0.173
##     TOTALCOL           0.018    0.008    2.177    0.030    0.018    0.073
##     TOTALSIN           0.008    0.008    1.128    0.259    0.008    0.040
##   tactilejr ~                                                            
##     TOTALAGR           0.000    0.007    0.024    0.981    0.000    0.001
##     TOTALSEX           0.007    0.007    1.050    0.294    0.007    0.036
##     TOTALCON          -0.007    0.007   -1.042    0.297   -0.007   -0.036
##     TOTALSIM           0.027    0.008    3.507    0.000    0.027    0.127
##     TOTALCOL           0.022    0.008    2.627    0.009    0.022    0.088
##     TOTALSIN           0.013    0.008    1.679    0.093    0.013    0.060
##   emo ~                                                                  
##     TOTALAGR          -0.008    0.007   -1.098    0.272   -0.008   -0.039
##     TOTALSEX          -0.002    0.007   -0.222    0.824   -0.002   -0.008
##     TOTALCON          -0.005    0.007   -0.742    0.458   -0.005   -0.025
##     TOTALSIM           0.036    0.008    4.543    0.000    0.036    0.165
##     TOTALCOL           0.009    0.008    1.115    0.265    0.009    0.038
##     TOTALSIN           0.011    0.008    1.426    0.154    0.011    0.051
## 
## Covariances:
##                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .tacphys ~~                                                              
##    .musclejointbon      0.278    0.031    8.918    0.000    0.278    0.295
##    .lookjr              0.310    0.030   10.496    0.000    0.310    0.354
##    .soundjr             0.243    0.030    7.996    0.000    0.243    0.263
##    .tactilejr           0.321    0.031   10.259    0.000    0.321    0.345
##    .emo                 0.236    0.031    7.685    0.000    0.236    0.252
##  .musclejointbone ~~                                                      
##    .lookjr              0.165    0.029    5.649    0.000    0.165    0.182
##    .soundjr             0.231    0.031    7.385    0.000    0.231    0.241
##    .tactilejr           0.255    0.032    8.058    0.000    0.255    0.265
##    .emo                 0.202    0.031    6.435    0.000    0.202    0.209
##  .lookjr ~~                                                               
##    .soundjr             0.254    0.029    8.616    0.000    0.254    0.285
##    .tactilejr           0.239    0.030    8.085    0.000    0.239    0.266
##    .emo                 0.271    0.030    9.059    0.000    0.271    0.300
##  .soundjr ~~                                                              
##    .tactilejr           0.348    0.032   10.818    0.000    0.348    0.366
##    .emo                 0.308    0.032    9.659    0.000    0.308    0.322
##  .tactilejr ~~                                                            
##    .emo                 0.290    0.032    9.091    0.000    0.290    0.302
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .tacphys           0.909    0.041   22.260    0.000    0.909    0.910
##    .musclejointbon    0.972    0.044   22.260    0.000    0.972    0.973
##    .lookjr            0.844    0.038   22.260    0.000    0.844    0.845
##    .soundjr           0.944    0.042   22.260    0.000    0.944    0.945
##    .tactilejr         0.956    0.043   22.260    0.000    0.956    0.957
##    .emo               0.965    0.043   22.260    0.000    0.965    0.966
standardizedSolution(fit.sps.cfa.6.dy, ci=T, level = .90)
##                lhs op             rhs est.std    se      z pvalue ci.lower
## 1          tacphys  ~        TOTALAGR   0.048 0.035  1.375  0.169   -0.009
## 2          tacphys  ~        TOTALSEX   0.045 0.033  1.361  0.174   -0.009
## 3          tacphys  ~        TOTALCON   0.160 0.033  4.887  0.000    0.106
## 4          tacphys  ~        TOTALSIM   0.088 0.035  2.509  0.012    0.030
## 5          tacphys  ~        TOTALCOL   0.081 0.033  2.490  0.013    0.028
## 6          tacphys  ~        TOTALSIN   0.038 0.035  1.089  0.276   -0.019
## 7  musclejointbone  ~        TOTALAGR   0.013 0.036  0.368  0.713   -0.046
## 8  musclejointbone  ~        TOTALSEX   0.073 0.034  2.129  0.033    0.017
## 9  musclejointbone  ~        TOTALCON  -0.066 0.034 -1.930  0.054   -0.123
## 10 musclejointbone  ~        TOTALSIM   0.048 0.036  1.322  0.186   -0.012
## 11 musclejointbone  ~        TOTALCOL   0.071 0.034  2.100  0.036    0.015
## 12 musclejointbone  ~        TOTALSIN   0.064 0.036  1.785  0.074    0.005
## 13          lookjr  ~        TOTALAGR  -0.046 0.033 -1.377  0.168   -0.101
## 14          lookjr  ~        TOTALSEX   0.028 0.032  0.880  0.379   -0.025
## 15          lookjr  ~        TOTALCON   0.103 0.032  3.217  0.001    0.050
## 16          lookjr  ~        TOTALSIM   0.334 0.032 10.462  0.000    0.281
## 17          lookjr  ~        TOTALCOL   0.067 0.031  2.121  0.034    0.015
## 18          lookjr  ~        TOTALSIN  -0.027 0.033 -0.821  0.412   -0.082
## 19         soundjr  ~        TOTALAGR  -0.024 0.035 -0.685  0.493   -0.082
## 20         soundjr  ~        TOTALSEX   0.068 0.034  2.013  0.044    0.012
## 21         soundjr  ~        TOTALCON  -0.025 0.034 -0.733  0.463   -0.081
## 22         soundjr  ~        TOTALSIM   0.173 0.035  4.899  0.000    0.115
## 23         soundjr  ~        TOTALCOL   0.073 0.033  2.184  0.029    0.018
## 24         soundjr  ~        TOTALSIN   0.040 0.035  1.129  0.259   -0.018
## 25       tactilejr  ~        TOTALAGR   0.001 0.036  0.024  0.981   -0.058
## 26       tactilejr  ~        TOTALSEX   0.036 0.034  1.051  0.293   -0.020
## 27       tactilejr  ~        TOTALCON  -0.036 0.034 -1.043  0.297   -0.092
## 28       tactilejr  ~        TOTALSIM   0.127 0.036  3.538  0.000    0.068
## 29       tactilejr  ~        TOTALCOL   0.088 0.033  2.640  0.008    0.033
## 30       tactilejr  ~        TOTALSIN   0.060 0.035  1.683  0.092    0.001
## 31             emo  ~        TOTALAGR  -0.039 0.036 -1.099  0.272   -0.098
## 32             emo  ~        TOTALSEX  -0.008 0.034 -0.222  0.824   -0.064
## 33             emo  ~        TOTALCON  -0.025 0.034 -0.742  0.458   -0.082
## 34             emo  ~        TOTALSIM   0.165 0.036  4.612  0.000    0.106
## 35             emo  ~        TOTALCOL   0.038 0.034  1.116  0.264   -0.018
## 36             emo  ~        TOTALSIN   0.051 0.036  1.428  0.153   -0.008
## 37         tacphys ~~         tacphys   0.910 0.017 53.703  0.000    0.882
## 38 musclejointbone ~~ musclejointbone   0.973 0.010 96.669  0.000    0.957
## 39          lookjr ~~          lookjr   0.845 0.020 41.568  0.000    0.811
## 40         soundjr ~~         soundjr   0.945 0.014 68.132  0.000    0.922
## 41       tactilejr ~~       tactilejr   0.957 0.012 76.893  0.000    0.937
## 42             emo ~~             emo   0.966 0.011 85.651  0.000    0.947
## 43         tacphys ~~ musclejointbone   0.295 0.029 10.188  0.000    0.248
## 44         tacphys ~~          lookjr   0.354 0.028 12.724  0.000    0.308
## 45         tacphys ~~         soundjr   0.263 0.030  8.879  0.000    0.214
## 46         tacphys ~~       tactilejr   0.345 0.028 12.314  0.000    0.299
## 47         tacphys ~~             emo   0.252 0.030  8.461  0.000    0.203
## 48 musclejointbone ~~          lookjr   0.182 0.031  5.940  0.000    0.132
## 49 musclejointbone ~~         soundjr   0.241 0.030  8.067  0.000    0.192
## 50 musclejointbone ~~       tactilejr   0.265 0.030  8.964  0.000    0.216
## 51 musclejointbone ~~             emo   0.209 0.030  6.874  0.000    0.159
## 52          lookjr ~~         soundjr   0.285 0.029  9.747  0.000    0.237
## 53          lookjr ~~       tactilejr   0.266 0.030  9.001  0.000    0.217
## 54          lookjr ~~             emo   0.300 0.029 10.398  0.000    0.253
## 55         soundjr ~~       tactilejr   0.366 0.028 13.301  0.000    0.321
## 56         soundjr ~~             emo   0.322 0.028 11.325  0.000    0.276
## 57       tactilejr ~~             emo   0.302 0.029 10.446  0.000    0.254
## 58        TOTALAGR ~~        TOTALAGR   1.000 0.000     NA     NA    1.000
## 59        TOTALAGR ~~        TOTALSEX   0.386 0.000     NA     NA    0.386
## 60        TOTALAGR ~~        TOTALCON   0.185 0.000     NA     NA    0.185
## 61        TOTALAGR ~~        TOTALSIM   0.287 0.000     NA     NA    0.287
## 62        TOTALAGR ~~        TOTALCOL   0.234 0.000     NA     NA    0.234
## 63        TOTALAGR ~~        TOTALSIN   0.343 0.000     NA     NA    0.343
## 64        TOTALSEX ~~        TOTALSEX   1.000 0.000     NA     NA    1.000
## 65        TOTALSEX ~~        TOTALCON   0.147 0.000     NA     NA    0.147
## 66        TOTALSEX ~~        TOTALSIM   0.201 0.000     NA     NA    0.201
## 67        TOTALSEX ~~        TOTALCOL   0.171 0.000     NA     NA    0.171
## 68        TOTALSEX ~~        TOTALSIN   0.265 0.000     NA     NA    0.265
## 69        TOTALCON ~~        TOTALCON   1.000 0.000     NA     NA    1.000
## 70        TOTALCON ~~        TOTALSIM   0.362 0.000     NA     NA    0.362
## 71        TOTALCON ~~        TOTALCOL   0.244 0.000     NA     NA    0.244
## 72        TOTALCON ~~        TOTALSIN   0.282 0.000     NA     NA    0.282
## 73        TOTALSIM ~~        TOTALSIM   1.000 0.000     NA     NA    1.000
## 74        TOTALSIM ~~        TOTALCOL   0.310 0.000     NA     NA    0.310
## 75        TOTALSIM ~~        TOTALSIN   0.378 0.000     NA     NA    0.378
## 76        TOTALCOL ~~        TOTALCOL   1.000 0.000     NA     NA    1.000
## 77        TOTALCOL ~~        TOTALSIN   0.227 0.000     NA     NA    0.227
## 78        TOTALSIN ~~        TOTALSIN   1.000 0.000     NA     NA    1.000
##    ci.upper
## 1     0.105
## 2     0.100
## 3     0.214
## 4     0.146
## 5     0.135
## 6     0.095
## 7     0.072
## 8     0.130
## 9    -0.010
## 10    0.108
## 11    0.126
## 12    0.123
## 13    0.009
## 14    0.081
## 15    0.155
## 16    0.386
## 17    0.118
## 18    0.027
## 19    0.034
## 20    0.124
## 21    0.031
## 22    0.231
## 23    0.127
## 24    0.098
## 25    0.059
## 26    0.092
## 27    0.021
## 28    0.186
## 29    0.143
## 30    0.118
## 31    0.020
## 32    0.049
## 33    0.031
## 34    0.224
## 35    0.093
## 36    0.110
## 37    0.938
## 38    0.990
## 39    0.878
## 40    0.968
## 41    0.978
## 42    0.984
## 43    0.343
## 44    0.399
## 45    0.311
## 46    0.391
## 47    0.301
## 48    0.233
## 49    0.291
## 50    0.313
## 51    0.259
## 52    0.333
## 53    0.314
## 54    0.348
## 55    0.411
## 56    0.369
## 57    0.349
## 58    1.000
## 59    0.386
## 60    0.185
## 61    0.287
## 62    0.234
## 63    0.343
## 64    1.000
## 65    0.147
## 66    0.201
## 67    0.171
## 68    0.265
## 69    1.000
## 70    0.362
## 71    0.244
## 72    0.282
## 73    1.000
## 74    0.310
## 75    0.378
## 76    1.000
## 77    0.227
## 78    1.000