library("psych")
library("lavaan")
## Warning: package 'lavaan' was built under R version 3.6.3
## This is lavaan 0.6-7
## lavaan is BETA software! Please report any bugs.
## 
## Attaching package: 'lavaan'
## The following object is masked from 'package:psych':
## 
##     cor2cov
library("lavaanPlot")
## Warning: package 'lavaanPlot' was built under R version 3.6.3
library("semTools")
## Warning: package 'semTools' was built under R version 3.6.3
## 
## ###############################################################################
## This is semTools 0.5-3
## All users of R (or SEM) are invited to submit functions or ideas for functions.
## ###############################################################################
## 
## Attaching package: 'semTools'
## The following object is masked from 'package:psych':
## 
##     skew
library("lmtest")
## Warning: package 'lmtest' was built under R version 3.6.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.6.3
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
lower <- '
1.0
-.57 1.0   
.65 -.42 1.0 
-.12 .45 -.10 1.0 
.82 -.53 .65 -.09 1.0 
-.41 .75 -.26 .53 -.39 1.0  
.62 -.39 .55 -.05 .79 -.25 1.0 
-.48 .68 -.31 .38 -.42 .77 -.24 1.0  

'
d <- getCov(lower,  names=c("M1T1", "M1T2", "M2T1", "M2T2", "M3T1", "M3T2", "M4T1", "M4T2"))
#### Widamen 3c - the CTCM target model ####
model <- ' T1  =~ M1T1 + M2T1 + M3T1 + M4T1 
           T2  =~ M1T2 + M2T2 + M3T2 + M4T2 
           M1  =~ M1T1 + M1T2 
           M2  =~ M2T1 + M2T2
           M3  =~ M3T1 + M3T2
           M4  =~ M4T1 + M4T2
           # traits and methods uncorrelated with one another
           T1~~0*M1
           T1~~0*M2
           T1~~0*M3
           T1~~0*M4
           T2~~0*M1
           T2~~0*M2
           T2~~0*M3
           T2~~0*M4
           
'




CTCM.out <- cfa(model, sample.cov = d, sample.nobs = 500, std.lv=TRUE)
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
lavaanPlot(model = CTCM.out)
summary(CTCM.out, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6-7 did NOT end normally after 10000 iterations
## ** WARNING ** Estimates below are most likely unreliable
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         31
##                                                       
##   Number of observations                           500
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                    NA
##   Degrees of freedom                                NA
## Warning in .local(object, ...): lavaan WARNING: fit measures not available if model did not converge
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 =~                                                                 
##     M1T1              0.001       NA                      0.001    0.001
##     M2T1              0.001       NA                      0.001    0.001
##     M3T1              0.001       NA                      0.001    0.001
##     M4T1              0.001       NA                      0.001    0.001
##   T2 =~                                                                 
##     M1T2              0.822       NA                      0.822    0.822
##     M2T2              0.529       NA                      0.529    0.530
##     M3T2              0.939       NA                      0.939    0.939
##     M4T2              0.821       NA                      0.821    0.820
##   M1 =~                                                                 
##     M1T1              0.840       NA                      0.840    0.839
##     M1T2             -0.122       NA                     -0.122   -0.122
##   M2 =~                                                                 
##     M2T1              0.608       NA                      0.608    0.609
##     M2T2              0.172       NA                      0.172    0.172
##   M3 =~                                                                 
##     M3T1              0.763       NA                      0.763    0.763
##     M3T2              0.114       NA                      0.114    0.114
##   M4 =~                                                                 
##     M4T1             18.413       NA                     18.413   18.412
##     M4T2              0.004       NA                      0.004    0.004
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 ~~                                                                 
##     M1                0.000                               0.000    0.000
##     M2                0.000                               0.000    0.000
##     M3                0.000                               0.000    0.000
##     M4                0.000                               0.000    0.000
##   T2 ~~                                                                 
##     M1                0.000                               0.000    0.000
##     M2                0.000                               0.000    0.000
##     M3                0.000                               0.000    0.000
##     M4                0.000                               0.000    0.000
##   T1 ~~                                                                 
##     T2             -415.943       NA                   -415.943 -415.943
##   M1 ~~                                                                 
##     M2                1.275       NA                      1.275    1.275
##     M3                1.284       NA                      1.284    1.284
##     M4                0.040       NA                      0.040    0.040
##   M2 ~~                                                                 
##     M3                1.404       NA                      1.404    1.404
##     M4                0.049       NA                      0.049    0.049
##   M3 ~~                                                                 
##     M4                0.056       NA                      0.056    0.056
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .M1T1              0.296       NA                      0.296    0.295
##    .M2T1              0.629       NA                      0.629    0.630
##    .M3T1              0.418       NA                      0.418    0.418
##    .M4T1           -338.039       NA                   -338.039 -337.991
##    .M1T2              0.310       NA                      0.310    0.309
##    .M2T2              0.689       NA                      0.689    0.690
##    .M3T2              0.106       NA                      0.106    0.106
##    .M4T2              0.328       NA                      0.328    0.327
##     T1                1.000                               1.000    1.000
##     T2                1.000                               1.000    1.000
##     M1                1.000                               1.000    1.000
##     M2                1.000                               1.000    1.000
##     M3                1.000                               1.000    1.000
##     M4                1.000                               1.000    1.000

CTCU model

modelCU <- ' T1  =~ M1T1 + M2T1 + M3T1 + M4T1  
           T2  =~ M1T2 + M2T2 + M3T2 + M4T2
           

  #Correlated uniqueness for methods factors
  M1T1 ~~ M1T2
  
  M2T1 ~~ M2T2
  
  M3T1 ~~ M3T2
  
  M4T1 ~~ M4T2
  
'



CTCU.out <- cfa(modelCU, sample.cov = d, sample.nobs = 500, std.lv=TRUE)
summary(CTCU.out, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6-7 ended normally after 31 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         21
##                                                       
##   Number of observations                           500
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                               178.869
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2701.140
##   Degrees of freedom                                28
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.939
##   Tucker-Lewis Index (TLI)                       0.886
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4410.615
##   Loglikelihood unrestricted model (H1)      -4321.180
##                                                       
##   Akaike (AIC)                                8863.229
##   Bayesian (BIC)                              8951.736
##   Sample-size adjusted Bayesian (BIC)         8885.081
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.148
##   90 Percent confidence interval - lower         0.129
##   90 Percent confidence interval - upper         0.168
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.077
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 =~                                                                 
##     M1T1              0.820    0.036   22.826    0.000    0.820    0.837
##     M2T1              0.687    0.040   17.154    0.000    0.687    0.685
##     M3T1              0.968    0.033   28.923    0.000    0.968    0.971
##     M4T1              0.806    0.038   21.431    0.000    0.806    0.803
##   T2 =~                                                                 
##     M1T2              0.816    0.037   22.042    0.000    0.816    0.827
##     M2T2              0.531    0.043   12.294    0.000    0.531    0.531
##     M3T2              0.912    0.036   25.455    0.000    0.912    0.913
##     M4T2              0.812    0.037   21.762    0.000    0.812    0.821
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .M1T1 ~~                                                               
##    .M1T2             -0.059    0.016   -3.600    0.000   -0.059   -0.198
##  .M2T1 ~~                                                               
##    .M2T2             -0.029    0.029   -1.010    0.312   -0.029   -0.047
##  .M3T1 ~~                                                               
##    .M3T2              0.006    0.012    0.525    0.599    0.006    0.066
##  .M4T1 ~~                                                               
##    .M4T2              0.067    0.018    3.656    0.000    0.067    0.197
##   T1 ~~                                                                 
##     T2               -0.511    0.037  -13.851    0.000   -0.511   -0.511
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .M1T1              0.286    0.022   13.061    0.000    0.286    0.299
##    .M2T1              0.535    0.036   15.031    0.000    0.535    0.531
##    .M3T1              0.056    0.017    3.398    0.001    0.056    0.057
##    .M4T1              0.359    0.026   13.847    0.000    0.359    0.356
##    .M1T2              0.306    0.026   11.947    0.000    0.306    0.315
##    .M2T2              0.716    0.047   15.190    0.000    0.716    0.718
##    .M3T2              0.165    0.023    7.316    0.000    0.165    0.166
##    .M4T2              0.319    0.026   12.093    0.000    0.319    0.326
##     T1                1.000                               1.000    1.000
##     T2                1.000                               1.000    1.000
(CTCU.fit <- fitMeasures(CTCU.out))
##                npar                fmin               chisq 
##              21.000               0.179             178.869 
##                  df              pvalue      baseline.chisq 
##              15.000               0.000            2701.140 
##         baseline.df     baseline.pvalue                 cfi 
##              28.000               0.000               0.939 
##                 tli                nnfi                 rfi 
##               0.886               0.886               0.876 
##                 nfi                pnfi                 ifi 
##               0.934               0.500               0.939 
##                 rni                logl   unrestricted.logl 
##               0.939           -4410.615           -4321.180 
##                 aic                 bic              ntotal 
##            8863.229            8951.736             500.000 
##                bic2               rmsea      rmsea.ci.lower 
##            8885.081               0.148               0.129 
##      rmsea.ci.upper        rmsea.pvalue                 rmr 
##               0.168               0.000               0.076 
##          rmr_nomean                srmr        srmr_bentler 
##               0.076               0.077               0.077 
## srmr_bentler_nomean                crmr         crmr_nomean 
##               0.077               0.084               0.084 
##          srmr_mplus   srmr_mplus_nomean               cn_05 
##               0.074               0.074              70.872 
##               cn_01                 gfi                agfi 
##              86.476               0.919               0.805 
##                pgfi                 mfi                ecvi 
##               0.383               0.849               0.442
(CTCU.pars <- inspect(CTCU.out,what="std"))
## $lambda
##         T1    T2
## M1T1 0.837 0.000
## M2T1 0.685 0.000
## M3T1 0.971 0.000
## M4T1 0.803 0.000
## M1T2 0.000 0.827
## M2T2 0.000 0.531
## M3T2 0.000 0.913
## M4T2 0.000 0.821
## 
## $theta
##      M1T1   M2T1   M3T1   M4T1   M1T2   M2T2   M3T2   M4T2  
## M1T1  0.299                                                 
## M2T1  0.000  0.531                                          
## M3T1  0.000  0.000  0.057                                   
## M4T1  0.000  0.000  0.000  0.356                            
## M1T2 -0.198  0.000  0.000  0.000  0.315                     
## M2T2  0.000 -0.047  0.000  0.000  0.000  0.718              
## M3T2  0.000  0.000  0.066  0.000  0.000  0.000  0.166       
## M4T2  0.000  0.000  0.000  0.197  0.000  0.000  0.000  0.326
## 
## $psi
##    T1     T2    
## T1  1.000       
## T2 -0.511  1.000
lavInspect(CTCU.out, "theta")
##      M1T1   M2T1   M3T1   M4T1   M1T2   M2T2   M3T2   M4T2  
## M1T1  0.286                                                 
## M2T1  0.000  0.535                                          
## M3T1  0.000  0.000  0.056                                   
## M4T1  0.000  0.000  0.000  0.359                            
## M1T2 -0.059  0.000  0.000  0.000  0.306                     
## M2T2  0.000 -0.029  0.000  0.000  0.000  0.716              
## M3T2  0.000  0.000  0.006  0.000  0.000  0.000  0.165       
## M4T2  0.000  0.000  0.000  0.067  0.000  0.000  0.000  0.319

CTCU model

modelCU <- ' T1  =~ M1T1 + M2T1 + M3T1 + M4T1  
           T2  =~ M1T2 + M2T2 + M3T2 + M4T2
           

  #Correlated uniqueness for methods factors
  M1T1 ~~ M1T2
  
  M2T1 ~~ M2T2
  
  M3T1 ~~ M3T2
  
  M4T1 ~~ M4T2
  
'

CTCU.out <- cfa(modelCU, sample.cov = d, sample.nobs = 500, std.lv=TRUE)
summary(CTCU.out, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6-7 ended normally after 31 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         21
##                                                       
##   Number of observations                           500
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                               178.869
##   Degrees of freedom                                15
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2701.140
##   Degrees of freedom                                28
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.939
##   Tucker-Lewis Index (TLI)                       0.886
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4410.615
##   Loglikelihood unrestricted model (H1)      -4321.180
##                                                       
##   Akaike (AIC)                                8863.229
##   Bayesian (BIC)                              8951.736
##   Sample-size adjusted Bayesian (BIC)         8885.081
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.148
##   90 Percent confidence interval - lower         0.129
##   90 Percent confidence interval - upper         0.168
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.077
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 =~                                                                 
##     M1T1              0.820    0.036   22.826    0.000    0.820    0.837
##     M2T1              0.687    0.040   17.154    0.000    0.687    0.685
##     M3T1              0.968    0.033   28.923    0.000    0.968    0.971
##     M4T1              0.806    0.038   21.431    0.000    0.806    0.803
##   T2 =~                                                                 
##     M1T2              0.816    0.037   22.042    0.000    0.816    0.827
##     M2T2              0.531    0.043   12.294    0.000    0.531    0.531
##     M3T2              0.912    0.036   25.455    0.000    0.912    0.913
##     M4T2              0.812    0.037   21.762    0.000    0.812    0.821
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .M1T1 ~~                                                               
##    .M1T2             -0.059    0.016   -3.600    0.000   -0.059   -0.198
##  .M2T1 ~~                                                               
##    .M2T2             -0.029    0.029   -1.010    0.312   -0.029   -0.047
##  .M3T1 ~~                                                               
##    .M3T2              0.006    0.012    0.525    0.599    0.006    0.066
##  .M4T1 ~~                                                               
##    .M4T2              0.067    0.018    3.656    0.000    0.067    0.197
##   T1 ~~                                                                 
##     T2               -0.511    0.037  -13.851    0.000   -0.511   -0.511
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .M1T1              0.286    0.022   13.061    0.000    0.286    0.299
##    .M2T1              0.535    0.036   15.031    0.000    0.535    0.531
##    .M3T1              0.056    0.017    3.398    0.001    0.056    0.057
##    .M4T1              0.359    0.026   13.847    0.000    0.359    0.356
##    .M1T2              0.306    0.026   11.947    0.000    0.306    0.315
##    .M2T2              0.716    0.047   15.190    0.000    0.716    0.718
##    .M3T2              0.165    0.023    7.316    0.000    0.165    0.166
##    .M4T2              0.319    0.026   12.093    0.000    0.319    0.326
##     T1                1.000                               1.000    1.000
##     T2                1.000                               1.000    1.000
(CTCU.fit <- fitMeasures(CTCU.out))
##                npar                fmin               chisq 
##              21.000               0.179             178.869 
##                  df              pvalue      baseline.chisq 
##              15.000               0.000            2701.140 
##         baseline.df     baseline.pvalue                 cfi 
##              28.000               0.000               0.939 
##                 tli                nnfi                 rfi 
##               0.886               0.886               0.876 
##                 nfi                pnfi                 ifi 
##               0.934               0.500               0.939 
##                 rni                logl   unrestricted.logl 
##               0.939           -4410.615           -4321.180 
##                 aic                 bic              ntotal 
##            8863.229            8951.736             500.000 
##                bic2               rmsea      rmsea.ci.lower 
##            8885.081               0.148               0.129 
##      rmsea.ci.upper        rmsea.pvalue                 rmr 
##               0.168               0.000               0.076 
##          rmr_nomean                srmr        srmr_bentler 
##               0.076               0.077               0.077 
## srmr_bentler_nomean                crmr         crmr_nomean 
##               0.077               0.084               0.084 
##          srmr_mplus   srmr_mplus_nomean               cn_05 
##               0.074               0.074              70.872 
##               cn_01                 gfi                agfi 
##              86.476               0.919               0.805 
##                pgfi                 mfi                ecvi 
##               0.383               0.849               0.442
(CTCU.pars <- inspect(CTCU.out,what="std"))
## $lambda
##         T1    T2
## M1T1 0.837 0.000
## M2T1 0.685 0.000
## M3T1 0.971 0.000
## M4T1 0.803 0.000
## M1T2 0.000 0.827
## M2T2 0.000 0.531
## M3T2 0.000 0.913
## M4T2 0.000 0.821
## 
## $theta
##      M1T1   M2T1   M3T1   M4T1   M1T2   M2T2   M3T2   M4T2  
## M1T1  0.299                                                 
## M2T1  0.000  0.531                                          
## M3T1  0.000  0.000  0.057                                   
## M4T1  0.000  0.000  0.000  0.356                            
## M1T2 -0.198  0.000  0.000  0.000  0.315                     
## M2T2  0.000 -0.047  0.000  0.000  0.000  0.718              
## M3T2  0.000  0.000  0.066  0.000  0.000  0.000  0.166       
## M4T2  0.000  0.000  0.000  0.197  0.000  0.000  0.000  0.326
## 
## $psi
##    T1     T2    
## T1  1.000       
## T2 -0.511  1.000
lavInspect(CTCU.out, "theta")
##      M1T1   M2T1   M3T1   M4T1   M1T2   M2T2   M3T2   M4T2  
## M1T1  0.286                                                 
## M2T1  0.000  0.535                                          
## M3T1  0.000  0.000  0.056                                   
## M4T1  0.000  0.000  0.000  0.359                            
## M1T2 -0.059  0.000  0.000  0.000  0.306                     
## M2T2  0.000 -0.029  0.000  0.000  0.000  0.716              
## M3T2  0.000  0.000  0.006  0.000  0.000  0.000  0.165       
## M4T2  0.000  0.000  0.000  0.067  0.000  0.000  0.000  0.319

CTCU model correlated traits

modelCT <- ' T1  =~ M1T1 + M2T1 + M3T1 + M4T1 
           T2  =~ M1T2 + M2T2 + M3T2 + M4T2 
           M1  =~ M1T1 + M1T2 
           M2  =~ M2T1 + M2T2
           M3  =~ M3T1 + M3T2
           M4  =~ M4T1 + M4T2
           # traits and methods uncorrelated with one another
           T1~~0*M1
           T1~~0*M2
           T1~~0*M3
           T1~~0*M4
           T2~~0*M1
           T2~~0*M2
           T2~~0*M3
           T2~~0*M4
           T1~~1*T2
           
'

T1CM.out <- cfa(modelCT, sample.cov = d, sample.nobs = 500, std.lv=TRUE)
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
## Warning in lav_model_estimate(lavmodel = lavmodel, lavpartable =
## lavpartable, : lavaan WARNING: the optimizer warns that a solution has NOT
## been found!
## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negative
## Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
##                 is not positive definite;
##                 use lavInspect(fit, "cov.lv") to investigate.
summary(T1CM.out, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6-7 ended normally after 194 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of free parameters                         30
##                                                       
##   Number of observations                           500
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                16.844
##   Degrees of freedom                                 6
##   P-value (Chi-square)                           0.010
## 
## Model Test Baseline Model:
## 
##   Test statistic                              2701.140
##   Degrees of freedom                                28
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.996
##   Tucker-Lewis Index (TLI)                       0.981
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -4329.602
##   Loglikelihood unrestricted model (H1)      -4321.180
##                                                       
##   Akaike (AIC)                                8719.204
##   Bayesian (BIC)                              8845.642
##   Sample-size adjusted Bayesian (BIC)         8750.420
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.060
##   90 Percent confidence interval - lower         0.027
##   90 Percent confidence interval - upper         0.095
##   P-value RMSEA <= 0.05                          0.268
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.013
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 =~                                                                 
##     M1T1              0.573    0.083    6.918    0.000    0.573    0.573
##     M2T1              0.391    0.078    4.990    0.000    0.391    0.391
##     M3T1              0.523    0.103    5.068    0.000    0.523    0.523
##     M4T1              0.404    0.090    4.484    0.000    0.404    0.404
##   T2 =~                                                                 
##     M1T2             -0.828    0.039  -21.180    0.000   -0.828   -0.829
##     M2T2             -0.519    0.050  -10.481    0.000   -0.519   -0.520
##     M3T2             -0.933    0.040  -23.273    0.000   -0.933   -0.934
##     M4T2             -0.820    0.038  -21.689    0.000   -0.820   -0.821
##   M1 =~                                                                 
##     M1T1             -0.701    0.072   -9.786    0.000   -0.701   -0.702
##     M1T2              0.135    0.094    1.435    0.151    0.135    0.135
##   M2 =~                                                                 
##     M2T1             -0.501    0.079   -6.328    0.000   -0.501   -0.502
##     M2T2             -0.206    0.073   -2.806    0.005   -0.206   -0.206
##   M3 =~                                                                 
##     M3T1             -0.653    0.071   -9.188    0.000   -0.653   -0.653
##     M3T2             -0.151    0.110   -1.381    0.167   -0.151   -0.151
##   M4 =~                                                                 
##     M4T1             -2.035    5.595   -0.364    0.716   -2.035   -2.037
##     M4T2             -0.045    0.156   -0.289    0.772   -0.045   -0.045
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   T1 ~~                                                                 
##     M1                0.000                               0.000    0.000
##     M2                0.000                               0.000    0.000
##     M3                0.000                               0.000    0.000
##     M4                0.000                               0.000    0.000
##   T2 ~~                                                                 
##     M1                0.000                               0.000    0.000
##     M2                0.000                               0.000    0.000
##     M3                0.000                               0.000    0.000
##     M4                0.000                               0.000    0.000
##   T1 ~~                                                                 
##     T2                1.000                               1.000    1.000
##   M1 ~~                                                                 
##     M2                1.210    0.218    5.546    0.000    1.210    1.210
##     M3                1.140    0.289    3.941    0.000    1.140    1.140
##     M4                0.273    0.708    0.385    0.700    0.273    0.273
##   M2 ~~                                                                 
##     M3                1.362    0.322    4.228    0.000    1.362    1.362
##     M4                0.386    1.027    0.376    0.707    0.386    0.386
##   M3 ~~                                                                 
##     M4                0.432    1.099    0.393    0.694    0.432    0.432
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .M1T1              0.178    0.096    1.854    0.064    0.178    0.178
##    .M2T1              0.594    0.083    7.150    0.000    0.594    0.595
##    .M3T1              0.299    0.174    1.714    0.087    0.299    0.299
##    .M4T1             -3.305   22.710   -0.146    0.884   -3.305   -3.312
##    .M1T2              0.294    0.023   12.685    0.000    0.294    0.295
##    .M2T2              0.686    0.047   14.649    0.000    0.686    0.687
##    .M3T2              0.104    0.025    4.194    0.000    0.104    0.104
##    .M4T2              0.324    0.026   12.218    0.000    0.324    0.324
##     T1                1.000                               1.000    1.000
##     T2                1.000                               1.000    1.000
##     M1                1.000                               1.000    1.000
##     M2                1.000                               1.000    1.000
##     M3                1.000                               1.000    1.000
##     M4                1.000                               1.000    1.000
(T1CM.fit <- fitMeasures(T1CM.out))
##                npar                fmin               chisq 
##              30.000               0.017              16.844 
##                  df              pvalue      baseline.chisq 
##               6.000               0.010            2701.140 
##         baseline.df     baseline.pvalue                 cfi 
##              28.000               0.000               0.996 
##                 tli                nnfi                 rfi 
##               0.981               0.981               0.971 
##                 nfi                pnfi                 ifi 
##               0.994               0.213               0.996 
##                 rni                logl   unrestricted.logl 
##               0.996           -4329.602           -4321.180 
##                 aic                 bic              ntotal 
##            8719.204            8845.642             500.000 
##                bic2               rmsea      rmsea.ci.lower 
##            8750.420               0.060               0.027 
##      rmsea.ci.upper        rmsea.pvalue                 rmr 
##               0.095               0.268               0.013 
##          rmr_nomean                srmr        srmr_bentler 
##               0.013               0.013               0.013 
## srmr_bentler_nomean                crmr         crmr_nomean 
##               0.013               0.015               0.015 
##          srmr_mplus   srmr_mplus_nomean               cn_05 
##               0.013               0.013             374.772 
##               cn_01                 gfi                agfi 
##             500.049               0.992               0.950 
##                pgfi                 mfi                ecvi 
##               0.165               0.989               0.154
(T1CM.pars <- inspect(T1CM.out,what="std"))
## $lambda
##         T1     T2     M1     M2     M3     M4
## M1T1 0.573  0.000 -0.702  0.000  0.000  0.000
## M2T1 0.391  0.000  0.000 -0.502  0.000  0.000
## M3T1 0.523  0.000  0.000  0.000 -0.653  0.000
## M4T1 0.404  0.000  0.000  0.000  0.000 -2.037
## M1T2 0.000 -0.829  0.135  0.000  0.000  0.000
## M2T2 0.000 -0.520  0.000 -0.206  0.000  0.000
## M3T2 0.000 -0.934  0.000  0.000 -0.151  0.000
## M4T2 0.000 -0.821  0.000  0.000  0.000 -0.045
## 
## $theta
##      M1T1   M2T1   M3T1   M4T1   M1T2   M2T2   M3T2   M4T2  
## M1T1  0.178                                                 
## M2T1  0.000  0.595                                          
## M3T1  0.000  0.000  0.299                                   
## M4T1  0.000  0.000  0.000 -3.312                            
## M1T2  0.000  0.000  0.000  0.000  0.295                     
## M2T2  0.000  0.000  0.000  0.000  0.000  0.687              
## M3T2  0.000  0.000  0.000  0.000  0.000  0.000  0.104       
## M4T2  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.324
## 
## $psi
##    T1    T2    M1    M2    M3    M4   
## T1 1.000                              
## T2 1.000 1.000                        
## M1 0.000 0.000 1.000                  
## M2 0.000 0.000 1.210 1.000            
## M3 0.000 0.000 1.140 1.362 1.000      
## M4 0.000 0.000 0.273 0.386 0.432 1.000
inspect(T1CM.out,what="std")$lambda
##         T1     T2     M1     M2     M3     M4
## M1T1 0.573  0.000 -0.702  0.000  0.000  0.000
## M2T1 0.391  0.000  0.000 -0.502  0.000  0.000
## M3T1 0.523  0.000  0.000  0.000 -0.653  0.000
## M4T1 0.404  0.000  0.000  0.000  0.000 -2.037
## M1T2 0.000 -0.829  0.135  0.000  0.000  0.000
## M2T2 0.000 -0.520  0.000 -0.206  0.000  0.000
## M3T2 0.000 -0.934  0.000  0.000 -0.151  0.000
## M4T2 0.000 -0.821  0.000  0.000  0.000 -0.045

Likelihood ratio test

lrtest(CTCU.out, T1CM.out)
## Likelihood ratio test
## 
## Model 1: CTCU.out
## Model 2: T1CM.out
##   #Df  LogLik Df  Chisq Pr(>Chisq)    
## 1  21 -4410.6                         
## 2  30 -4329.6  9 162.03  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1