Chapter 12:
Phil Wood
2025-08-01
Figure 12.1 Orthogonal Factor Model of Alcohol Expectations
Load Simulated Alcohol Expectation Data
Path Diagram
Orthogonal Factor Model
R Program
require(lavaan)## Loading required package: lavaan## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.AlcExpect <- read.table("RFDSim.txt", header = TRUE) ;
head(AlcExpect)## rridaw0 rridbw0 rridcw0 rriddw0 rridew0 rridfw0 rridgw0 rridhw0
## 1 2.687040 2.105432 2.955291 2.820890 3.011609 1.3377554 0.5349941 0.4296285
## 2 2.415095 2.479291 2.404402 2.340840 2.564941 0.3607768 1.2527989 1.4869882
## 3 2.570646 3.143387 3.389949 2.972546 1.771171 4.6113733 4.0045561 3.5789757
## 4 2.078310 2.449843 1.911547 2.170200 3.104838 2.5728633 2.3151849 2.3457529
## 5 3.097760 2.887276 3.472790 3.071860 3.420305 2.2009355 1.5155192 3.0457780
## 6 4.277197 2.907983 3.549188 3.439084 2.629298 3.3831835 2.7476027 2.9028434
## rridiw0 rridjw0 rridkw0 rridlw0 rridmw0 rridnw0 rridow0 rridpw0
## 1 0.7943853 1.5222660 2.095139 2.355999 1.589406 1.784467 2.351270 1.0202452
## 2 1.2002544 0.9543229 2.650829 4.349754 1.303579 2.632062 2.787251 1.6073625
## 3 3.7166902 3.8827689 2.990634 2.715253 1.740789 1.804472 2.447188 3.0422424
## 4 0.7744396 2.0349575 1.867178 3.199668 1.734972 1.908805 2.693824 2.8287871
## 5 2.1533348 1.5777493 2.516460 2.515727 1.488641 1.918064 2.540850 0.8392062
## 6 3.1489301 2.7458411 2.286619 2.328228 2.020846 1.668394 4.285813 2.8689959
## rridqw0 rridrw0 rridsw0 rridtw0 rriduw0 rridvw0 rridww0
## 1 2.510164 2.971957 1.8797322 1.449552 1.476912 1.6832636 1.1923636
## 2 3.123877 3.128297 0.6928955 1.208093 1.399289 1.2096589 1.3229972
## 3 2.398190 3.197675 1.8309651 1.707260 2.016092 1.9380034 1.8090042
## 4 2.254861 2.735416 0.9300000 1.440608 1.652199 1.7063254 1.1159016
## 5 2.888308 3.513411 2.3369828 1.389949 1.055930 0.8787579 0.3784458
## 6 2.071705 3.520809 1.1979326 1.376556 1.625872 1.3022140 1.3423324Fig12.1Model<-"
! regressions
F1=~L1*rridaw0
F1=~L2*rridbw0
F1=~L3*rridcw0
F1=~L4*rriddw0
F1=~L5*rridew0
F2=~L6*rriduw0
F2=~L7*rridvw0
F2=~L8*rridtw0
F2=~L9*rridsw0
F2=~L10*rridww0
F3=~L11*rridqw0
F3=~L12*rridkw0
F3=~L13*rridpw0
F3=~L14*rridrw0
F3=~L15*rridow0
! residuals, variances and covariances
rridaw0 ~~ Ea*rridaw0
rridbw0 ~~ Eb*rridbw0
rridcw0 ~~ Ec*rridcw0
rriddw0 ~~ Ed*rriddw0
rridew0 ~~ Ee*rridew0
rriduw0 ~~ Eu*rriduw0
rridvw0 ~~ Ev*rridvw0
rridtw0 ~~ Et*rridtw0
rridsw0 ~~ Es*rridsw0
rridww0 ~~ Ew*rridww0
rridqw0 ~~ Eq*rridqw0
rridkw0 ~~ Ek*rridkw0
rridpw0 ~~ Ep*rridpw0
rridrw0 ~~ Er*rridrw0
rridow0 ~~ Eo*rridow0
F1 ~~ 1.0*F1
F2 ~~ 1.0*F2
F3 ~~ 1.0*F3
F1 ~~ 0.0*F2
F1 ~~ 0.0*F3
F2 ~~ 0.0*F3
! observed means
rridaw0~1;
rridbw0~1;
rridcw0~1;
rriddw0~1;
rridew0~1;
rriduw0~1;
rridvw0~1;
rridtw0~1;
rridsw0~1;
rridww0~1;
rridqw0~1;
rridkw0~1;
rridpw0~1;
rridrw0~1;
rridow0~1;
"
Fig12.1Result<-lavaan(Fig12.1Model, data=AlcExpect, fixed.x=FALSE, missing="FIML")
summary(Fig12.1Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 45
##
## Number of observations 2422
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 3345.089
## Degrees of freedom 90
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 27821.072
## Degrees of freedom 105
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.883
## Tucker-Lewis Index (TLI) 0.863
##
## Robust Comparative Fit Index (CFI) 0.883
## Robust Tucker-Lewis Index (TLI) 0.863
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -34225.575
## Loglikelihood unrestricted model (H1) -32553.030
##
## Akaike (AIC) 68541.150
## Bayesian (BIC) 68801.805
## Sample-size adjusted Bayesian (SABIC) 68658.830
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.122
## 90 Percent confidence interval - lower 0.119
## 90 Percent confidence interval - upper 0.126
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Robust RMSEA 0.122
## 90 Percent confidence interval - lower 0.119
## 90 Percent confidence interval - upper 0.126
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.244
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## rridaw0 (L1) 0.769 0.015 49.660 0.000 0.769 0.832
## rridbw0 (L2) 0.636 0.017 38.166 0.000 0.636 0.693
## rridcw0 (L3) 0.870 0.014 60.602 0.000 0.870 0.938
## rriddw0 (L4) 0.884 0.015 58.666 0.000 0.884 0.921
## rridew0 (L5) 0.580 0.016 35.726 0.000 0.580 0.658
## F2 =~
## rriduw0 (L6) 0.576 0.010 56.468 0.000 0.576 0.902
## rridvw0 (L7) 0.604 0.010 58.100 0.000 0.604 0.918
## rridtw0 (L8) 0.524 0.011 46.538 0.000 0.524 0.802
## rridsw0 (L9) 0.543 0.014 40.092 0.000 0.543 0.723
## rridww0 (L10) 0.624 0.014 45.705 0.000 0.624 0.790
## F3 =~
## rridqw0 (L11) 0.892 0.017 53.624 0.000 0.892 0.882
## rridkw0 (L12) 0.870 0.017 50.151 0.000 0.870 0.844
## rridpw0 (L13) 0.791 0.020 38.710 0.000 0.791 0.707
## rridrw0 (L14) 0.776 0.016 48.407 0.000 0.776 0.826
## rridow0 (L15) 0.791 0.018 43.243 0.000 0.791 0.766
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
## F2 ~~
## F3 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 3.023 0.019 160.998 0.000 3.023 3.271
## .rridbw0 2.935 0.019 157.441 0.000 2.935 3.199
## .rridcw0 3.067 0.019 162.812 0.000 3.067 3.308
## .rriddw0 2.995 0.020 153.421 0.000 2.995 3.117
## .rridew0 3.122 0.018 174.332 0.000 3.122 3.542
## .rriduw0 1.296 0.013 99.917 0.000 1.296 2.030
## .rridvw0 1.310 0.013 98.102 0.000 1.310 1.993
## .rridtw0 1.320 0.013 99.373 0.000 1.320 2.019
## .rridsw0 1.441 0.015 94.438 0.000 1.441 1.919
## .rridww0 1.469 0.016 91.442 0.000 1.469 1.858
## .rridqw0 2.767 0.021 134.527 0.000 2.767 2.734
## .rridkw0 2.881 0.021 137.706 0.000 2.881 2.798
## .rridpw0 2.187 0.023 96.154 0.000 2.187 1.954
## .rridrw0 3.098 0.019 162.275 0.000 3.098 3.297
## .rridow0 2.566 0.021 122.358 0.000 2.566 2.486
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 (Ea) 0.263 0.009 29.658 0.000 0.263 0.308
## .rridbw0 (Eb) 0.438 0.013 32.646 0.000 0.438 0.520
## .rridcw0 (Ec) 0.103 0.006 18.525 0.000 0.103 0.120
## .rriddw0 (Ed) 0.141 0.006 22.063 0.000 0.141 0.152
## .rridew0 (Ee) 0.440 0.013 33.084 0.000 0.440 0.567
## .rriduw0 (Eu) 0.076 0.003 23.693 0.000 0.076 0.186
## .rridvw0 (Ev) 0.068 0.003 20.561 0.000 0.068 0.156
## .rridtw0 (Et) 0.152 0.005 29.223 0.000 0.152 0.357
## .rridsw0 (Es) 0.269 0.009 31.396 0.000 0.269 0.477
## .rridww0 (Ew) 0.235 0.008 30.341 0.000 0.235 0.376
## .rridqw0 (Eq) 0.228 0.010 22.726 0.000 0.228 0.223
## .rridkw0 (Ek) 0.304 0.012 26.295 0.000 0.304 0.287
## .rridpw0 (Ep) 0.626 0.020 31.352 0.000 0.626 0.500
## .rridrw0 (Er) 0.281 0.010 27.304 0.000 0.281 0.318
## .rridow0 (Eo) 0.440 0.015 29.734 0.000 0.440 0.413
## F1 1.000 1.000 1.000
## F2 1.000 1.000 1.000
## F3 1.000 1.000 1.000require(lavaangui)## Loading required package: lavaangui## Warning: package 'lavaangui' was built under R version 4.5.1## This is lavaangui 0.2.5
## lavaangui is BETA software! Please report any bugs at https://github.com/karchjd/lavaangui/issues#plot_lavaan(Fig12.1Result)Figure 12.2 Correlated (a.k.a. Oblique) Factor Model of Alcohol Expectations
Path Diagram
Correlated (Oblique) Factor Model
R Program
require(lavaan)
Fig12.2Model<-"
! regressions
F1=~L1*rridaw0
F1=~L2*rridbw0
F1=~L3*rridcw0
F1=~L4*rriddw0
F1=~L5*rridew0
F2=~L6*rriduw0
F2=~L7*rridvw0
F2=~L8*rridtw0
F2=~L9*rridsw0
F2=~L10*rridww0
F3=~L11*rridqw0
F3=~L12*rridkw0
F3=~L13*rridpw0
F3=~L14*rridrw0
F3=~L15*rridow0
! residuals, variances and covariances
rridaw0 ~~ Ea*rridaw0
rridbw0 ~~ Eb*rridbw0
rridcw0 ~~ Ec*rridcw0
rriddw0 ~~ Ed*rriddw0
rridew0 ~~ Ee*rridew0
rriduw0 ~~ Eu*rriduw0
rridvw0 ~~ Ev*rridvw0
rridtw0 ~~ Et*rridtw0
rridsw0 ~~ Es*rridsw0
rridww0 ~~ Ew*rridww0
rridqw0 ~~ Eq*rridqw0
rridkw0 ~~ Ek*rridkw0
rridpw0 ~~ Ep*rridpw0
rridrw0 ~~ Er*rridrw0
rridow0 ~~ Eo*rridow0
F1 ~~ 1.0*F1
F2 ~~ 1.0*F2
F3 ~~ 1.0*F3
F1 ~~ r12*F2
F2 ~~ r23*F3
F1 ~~ r13*F3
! observed means
rridaw0~1;
rridbw0~1;
rridcw0~1;
rriddw0~1;
rridew0~1;
rriduw0~1;
rridvw0~1;
rridtw0~1;
rridsw0~1;
rridww0~1;
rridqw0~1;
rridkw0~1;
rridpw0~1;
rridrw0~1;
rridow0~1;
"
Fig12.2Result<-lavaan(Fig12.2Model, data=AlcExpect, fixed.x=FALSE, missing="FIML")
summary(Fig12.2Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 48
##
## Number of observations 2422
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 1453.821
## Degrees of freedom 87
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 27821.072
## Degrees of freedom 105
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.951
## Tucker-Lewis Index (TLI) 0.940
##
## Robust Comparative Fit Index (CFI) 0.951
## Robust Tucker-Lewis Index (TLI) 0.940
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -33279.941
## Loglikelihood unrestricted model (H1) -32553.030
##
## Akaike (AIC) 66655.882
## Bayesian (BIC) 66933.915
## Sample-size adjusted Bayesian (SABIC) 66781.408
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.077
## 90 Percent confidence interval - upper 0.084
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.601
##
## Robust RMSEA 0.081
## 90 Percent confidence interval - lower 0.077
## 90 Percent confidence interval - upper 0.084
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.601
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## rridaw0 (L1) 0.773 0.015 50.199 0.000 0.773 0.837
## rridbw0 (L2) 0.637 0.017 38.289 0.000 0.637 0.694
## rridcw0 (L3) 0.866 0.014 60.316 0.000 0.866 0.934
## rriddw0 (L4) 0.884 0.015 58.792 0.000 0.884 0.920
## rridew0 (L5) 0.585 0.016 36.193 0.000 0.585 0.664
## F2 =~
## rriduw0 (L6) 0.576 0.010 56.468 0.000 0.576 0.902
## rridvw0 (L7) 0.604 0.010 58.158 0.000 0.604 0.919
## rridtw0 (L8) 0.524 0.011 46.454 0.000 0.524 0.801
## rridsw0 (L9) 0.543 0.014 40.105 0.000 0.543 0.723
## rridww0 (L10) 0.625 0.014 45.752 0.000 0.625 0.790
## F3 =~
## rridqw0 (L11) 0.876 0.017 52.388 0.000 0.876 0.866
## rridkw0 (L12) 0.866 0.017 50.060 0.000 0.866 0.841
## rridpw0 (L13) 0.781 0.020 38.182 0.000 0.781 0.698
## rridrw0 (L14) 0.795 0.016 50.517 0.000 0.795 0.847
## rridow0 (L15) 0.798 0.018 44.030 0.000 0.798 0.773
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 (r12) 0.197 0.021 9.444 0.000 0.197 0.197
## F2 ~~
## F3 (r23) 0.194 0.021 9.094 0.000 0.194 0.194
## F1 ~~
## F3 (r13) 0.783 0.010 81.027 0.000 0.783 0.783
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 3.023 0.019 160.998 0.000 3.023 3.271
## .rridbw0 2.935 0.019 157.441 0.000 2.935 3.199
## .rridcw0 3.067 0.019 162.812 0.000 3.067 3.308
## .rriddw0 2.995 0.020 153.421 0.000 2.995 3.117
## .rridew0 3.122 0.018 174.332 0.000 3.122 3.542
## .rriduw0 1.296 0.013 99.917 0.000 1.296 2.030
## .rridvw0 1.310 0.013 98.102 0.000 1.310 1.993
## .rridtw0 1.320 0.013 99.373 0.000 1.320 2.019
## .rridsw0 1.441 0.015 94.437 0.000 1.441 1.919
## .rridww0 1.469 0.016 91.442 0.000 1.469 1.858
## .rridqw0 2.767 0.021 134.527 0.000 2.767 2.734
## .rridkw0 2.881 0.021 137.706 0.000 2.881 2.798
## .rridpw0 2.187 0.023 96.154 0.000 2.187 1.954
## .rridrw0 3.098 0.019 162.275 0.000 3.098 3.297
## .rridow0 2.566 0.021 122.359 0.000 2.566 2.486
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 (Ea) 0.256 0.009 29.730 0.000 0.256 0.299
## .rridbw0 (Eb) 0.437 0.013 32.755 0.000 0.437 0.519
## .rridcw0 (Ec) 0.110 0.005 20.825 0.000 0.110 0.128
## .rriddw0 (Ed) 0.141 0.006 23.325 0.000 0.141 0.153
## .rridew0 (Ee) 0.434 0.013 33.154 0.000 0.434 0.559
## .rriduw0 (Eu) 0.076 0.003 23.752 0.000 0.076 0.187
## .rridvw0 (Ev) 0.067 0.003 20.562 0.000 0.067 0.156
## .rridtw0 (Et) 0.153 0.005 29.317 0.000 0.153 0.358
## .rridsw0 (Es) 0.269 0.009 31.409 0.000 0.269 0.477
## .rridww0 (Ew) 0.234 0.008 30.347 0.000 0.234 0.375
## .rridqw0 (Eq) 0.256 0.010 25.433 0.000 0.256 0.250
## .rridkw0 (Ek) 0.310 0.011 27.409 0.000 0.310 0.293
## .rridpw0 (Ep) 0.642 0.020 31.807 0.000 0.642 0.513
## .rridrw0 (Er) 0.250 0.009 26.783 0.000 0.250 0.283
## .rridow0 (Eo) 0.429 0.014 30.197 0.000 0.429 0.403
## F1 1.000 1.000 1.000
## F2 1.000 1.000 1.000
## F3 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.2Result)Figure 12.3 BiFactor Model of Alcohol Expectations
Path Diagram
Bifactor Model
R Program
require(lavaan)
Fig12.3Model<-"
! regressions
F1=~L1*rridaw0
F1=~L2*rridbw0
F1=~L3*rridcw0
F1=~L4*rriddw0
F1=~L5*rridew0
F2=~L6*rriduw0
F2=~L7*rridvw0
F2=~L8*rridtw0
F2=~L9*rridsw0
F2=~L10*rridww0
F3=~L11*rridqw0
F3=~L12*rridkw0
F3=~L13*rridpw0
F3=~L14*rridrw0
F3=~L15*rridow0
General=~G1*rridcw0
General=~G2*rriddw0
General=~G3*rridaw0
General=~G4*rridbw0
General=~G5*rridew0
General=~G6*rriduw0
General=~G7*rridvw0
General=~G8*rridtw0
General=~G9*rridsw0
General=~G10*rridww0
General=~G11*rridqw0
General=~G12*rridkw0
General=~G13*rridpw0
General=~G14*rridrw0
General=~G15*rridow0
! residuals, variances and covariances
rridaw0 ~~ Ea*rridaw0
rridbw0 ~~ Eb*rridbw0
rridcw0 ~~ Ec*rridcw0
rriddw0 ~~ Ed*rriddw0
rridew0 ~~ Ee*rridew0
rriduw0 ~~ Eu*rriduw0
rridvw0 ~~ Ev*rridvw0
rridtw0 ~~ Et*rridtw0
rridsw0 ~~ Es*rridsw0
rridww0 ~~ Ew*rridww0
rridqw0 ~~ Eq*rridqw0
rridkw0 ~~ Ek*rridkw0
rridpw0 ~~ Ep*rridpw0
rridrw0 ~~ Er*rridrw0
rridow0 ~~ Eo*rridow0
F1 ~~ 1.0*F1
F2 ~~ 1.0*F2
F3 ~~ 1.0*F3
General ~~ 1.0*General
F1 ~~ 0.0*F2
F1 ~~ 0.0*F3
F1 ~~ 0.0*General
F2 ~~ 0.0*F3
F2 ~~ 0.0*General
F3 ~~ 0.0*General
! observed means
rridaw0~1;
rridbw0~1;
rridcw0~1;
rriddw0~1;
rridew0~1;
rriduw0~1;
rridvw0~1;
rridtw0~1;
rridsw0~1;
rridww0~1;
rridqw0~1;
rridkw0~1;
rridpw0~1;
rridrw0~1;
rridow0~1;
"
Fig12.3Result<-lavaan(Fig12.3Model, data=AlcExpect, fixed.x=FALSE, missing="FIML")
summary(Fig12.3Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 76 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 60
##
## Number of observations 2422
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 1216.891
## Degrees of freedom 75
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 27821.072
## Degrees of freedom 105
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.959
## Tucker-Lewis Index (TLI) 0.942
##
## Robust Comparative Fit Index (CFI) 0.959
## Robust Tucker-Lewis Index (TLI) 0.942
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -33161.476
## Loglikelihood unrestricted model (H1) -32553.030
##
## Akaike (AIC) 66442.952
## Bayesian (BIC) 66790.493
## Sample-size adjusted Bayesian (SABIC) 66599.859
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.083
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.388
##
## Robust RMSEA 0.079
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.083
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.388
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.036
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## rridaw0 (L1) 0.348 0.045 7.784 0.000 0.348 0.377
## rridbw0 (L2) 0.311 0.046 6.823 0.000 0.311 0.339
## rridcw0 (L3) 0.481 0.032 14.799 0.000 0.481 0.518
## rriddw0 (L4) 0.471 0.038 12.449 0.000 0.471 0.491
## rridew0 (L5) 0.221 0.038 5.814 0.000 0.221 0.250
## F2 =~
## rriduw0 (L6) 0.563 0.010 55.429 0.000 0.563 0.883
## rridvw0 (L7) 0.589 0.010 56.903 0.000 0.589 0.896
## rridtw0 (L8) 0.521 0.011 46.151 0.000 0.521 0.796
## rridsw0 (L9) 0.528 0.014 39.030 0.000 0.528 0.703
## rridww0 (L10) 0.607 0.014 44.419 0.000 0.607 0.768
## F3 =~
## rridqw0 (L11) 0.496 0.050 9.870 0.000 0.496 0.490
## rridkw0 (L12) 0.376 0.054 6.974 0.000 0.376 0.365
## rridpw0 (L13) 0.444 0.037 11.900 0.000 0.444 0.397
## rridrw0 (L14) 0.154 0.074 2.078 0.038 0.154 0.164
## rridow0 (L15) 0.257 0.052 4.931 0.000 0.257 0.249
## General =~
## rridcw0 (G1) 0.729 0.026 27.744 0.000 0.729 0.786
## rriddw0 (G2) 0.747 0.028 26.918 0.000 0.747 0.777
## rridaw0 (G3) 0.688 0.028 25.006 0.000 0.688 0.744
## rridbw0 (G4) 0.552 0.030 18.686 0.000 0.552 0.602
## rridew0 (G5) 0.545 0.023 24.002 0.000 0.545 0.619
## rriduw0 (G6) 0.118 0.015 8.143 0.000 0.118 0.186
## rridvw0 (G7) 0.130 0.015 8.678 0.000 0.130 0.198
## rridtw0 (G8) 0.075 0.015 5.019 0.000 0.075 0.115
## rridsw0 (G9) 0.132 0.017 7.959 0.000 0.132 0.176
## rridww0 (G10) 0.147 0.018 8.058 0.000 0.147 0.186
## rridqw0 (G11) 0.762 0.034 22.453 0.000 0.762 0.753
## rridkw0 (G12) 0.778 0.030 25.733 0.000 0.778 0.756
## rridpw0 (G13) 0.665 0.029 22.732 0.000 0.665 0.594
## rridrw0 (G14) 0.797 0.029 27.621 0.000 0.797 0.848
## rridow0 (G15) 0.750 0.026 29.099 0.000 0.750 0.726
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
## General 0.000 0.000 0.000
## F2 ~~
## F3 0.000 0.000 0.000
## General 0.000 0.000 0.000
## F3 ~~
## General 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 3.023 0.019 160.998 0.000 3.023 3.271
## .rridbw0 2.935 0.019 157.441 0.000 2.935 3.199
## .rridcw0 3.067 0.019 162.812 0.000 3.067 3.308
## .rriddw0 2.995 0.020 153.421 0.000 2.995 3.117
## .rridew0 3.122 0.018 174.332 0.000 3.122 3.542
## .rriduw0 1.296 0.013 99.917 0.000 1.296 2.030
## .rridvw0 1.310 0.013 98.102 0.000 1.310 1.993
## .rridtw0 1.320 0.013 99.373 0.000 1.320 2.019
## .rridsw0 1.441 0.015 94.437 0.000 1.441 1.919
## .rridww0 1.469 0.016 91.442 0.000 1.469 1.858
## .rridqw0 2.767 0.021 134.527 0.000 2.767 2.734
## .rridkw0 2.881 0.021 137.706 0.000 2.881 2.798
## .rridpw0 2.187 0.023 96.154 0.000 2.187 1.954
## .rridrw0 3.098 0.019 162.275 0.000 3.098 3.297
## .rridow0 2.566 0.021 122.358 0.000 2.566 2.486
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 (Ea) 0.259 0.009 30.391 0.000 0.259 0.304
## .rridbw0 (Eb) 0.440 0.013 32.915 0.000 0.440 0.522
## .rridcw0 (Ec) 0.097 0.007 14.813 0.000 0.097 0.113
## .rriddw0 (Ed) 0.143 0.007 20.707 0.000 0.143 0.155
## .rridew0 (Ee) 0.431 0.013 33.033 0.000 0.431 0.554
## .rriduw0 (Eu) 0.076 0.003 23.686 0.000 0.076 0.187
## .rridvw0 (Ev) 0.068 0.003 20.652 0.000 0.068 0.157
## .rridtw0 (Et) 0.151 0.005 28.912 0.000 0.151 0.353
## .rridsw0 (Es) 0.268 0.009 31.387 0.000 0.268 0.475
## .rridww0 (Ew) 0.234 0.008 30.378 0.000 0.234 0.375
## .rridqw0 (Eq) 0.198 0.016 12.574 0.000 0.198 0.193
## .rridkw0 (Ek) 0.313 0.012 26.847 0.000 0.313 0.295
## .rridpw0 (Ep) 0.613 0.024 26.048 0.000 0.613 0.489
## .rridrw0 (Er) 0.225 0.018 12.251 0.000 0.225 0.254
## .rridow0 (Eo) 0.437 0.014 30.745 0.000 0.437 0.411
## F1 1.000 1.000 1.000
## F2 1.000 1.000 1.000
## F3 1.000 1.000 1.000
## General 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.3Result)Figure 12.4 Hierarchical Factor Model
Path Diagram
Hierarchical Factor Model
R Program
require(lavaan)
Fig12.4Model<-"
! regressions
F1=~L1*rridaw0
F1=~L2*rridbw0
F1=~1.0*rridcw0
F1=~L4*rriddw0
F1=~L5*rridew0
F2=~1.0*rriduw0
F2=~L7*rridvw0
F2=~L8*rridtw0
F2=~L9*rridsw0
F2=~L10*rridww0
F3=~1.0*rridqw0
F3=~L12*rridkw0
F3=~L13*rridpw0
F3=~L14*rridrw0
F3=~L15*rridow0
G=~G1*F1
G=~G2*F2
G=~G3*F3
! residuals, variances and covariances
rridaw0 ~~ Ea*rridaw0
rridbw0 ~~ Eb*rridbw0
rridcw0 ~~ Ec*rridcw0
rriddw0 ~~ Ed*rriddw0
rridew0 ~~ Ee*rridew0
rriduw0 ~~ Eu*rriduw0
rridvw0 ~~ Ev*rridvw0
rridtw0 ~~ Et*rridtw0
rridsw0 ~~ Es*rridsw0
rridww0 ~~ Ew*rridww0
rridqw0 ~~ Eq*rridqw0
rridkw0 ~~ Ek*rridkw0
rridpw0 ~~ Ep*rridpw0
rridrw0 ~~ Er*rridrw0
rridow0 ~~ Eo*rridow0
F1 ~~ VF1*F1
F2 ~~ VF2*F2
F3 ~~ VF3*F3
G ~~ 1.0*G
F1 ~~ 0.0*F2
F1 ~~ 0.0*F3
F2 ~~ 0.0*F3
! observed means
rridaw0~1;
rridbw0~1;
rridcw0~1;
rriddw0~1;
rridew0~1;
rriduw0~1;
rridvw0~1;
rridtw0~1;
rridsw0~1;
rridww0~1;
rridqw0~1;
rridkw0~1;
rridpw0~1;
rridrw0~1;
rridow0~1;
"
Fig12.4Result<-lavaan(Fig12.4Model, data=AlcExpect, fixed.x=FALSE, missing="FIML")
summary(Fig12.4Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 48
##
## Number of observations 2422
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 1453.821
## Degrees of freedom 87
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 27821.072
## Degrees of freedom 105
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.951
## Tucker-Lewis Index (TLI) 0.940
##
## Robust Comparative Fit Index (CFI) 0.951
## Robust Tucker-Lewis Index (TLI) 0.940
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -33279.941
## Loglikelihood unrestricted model (H1) -32553.030
##
## Akaike (AIC) 66655.882
## Bayesian (BIC) 66933.915
## Sample-size adjusted Bayesian (SABIC) 66781.408
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.077
## 90 Percent confidence interval - upper 0.084
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.601
##
## Robust RMSEA 0.081
## 90 Percent confidence interval - lower 0.077
## 90 Percent confidence interval - upper 0.084
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.601
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## rridaw0 (L1) 0.893 0.015 61.458 0.000 0.773 0.837
## rridbw0 (L2) 0.735 0.017 42.803 0.000 0.637 0.694
## rridcw0 1.000 0.866 0.934
## rriddw0 (L4) 1.021 0.013 80.264 0.000 0.884 0.920
## rridew0 (L5) 0.676 0.017 39.701 0.000 0.585 0.664
## F2 =~
## rriduw0 1.000 0.576 0.902
## rridvw0 (L7) 1.049 0.015 70.884 0.000 0.604 0.919
## rridtw0 (L8) 0.910 0.017 52.068 0.000 0.524 0.801
## rridsw0 (L9) 0.943 0.022 43.422 0.000 0.543 0.723
## rridww0 (L10) 1.086 0.022 50.399 0.000 0.625 0.790
## F3 =~
## rridqw0 1.000 0.876 0.866
## rridkw0 (L12) 0.988 0.018 53.495 0.000 0.866 0.841
## rridpw0 (L13) 0.891 0.022 39.800 0.000 0.781 0.698
## rridrw0 (L14) 0.908 0.017 52.984 0.000 0.795 0.847
## rridow0 (L15) 0.910 0.020 45.740 0.000 0.798 0.773
## G =~
## F1 (G1) 0.773 0.035 22.152 0.000 0.893 0.893
## F2 (G2) 0.127 0.013 9.712 0.000 0.221 0.221
## F3 (G3) 0.769 0.036 21.594 0.000 0.877 0.877
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .F1 ~~
## .F2 0.000 0.000 0.000
## .F3 0.000 0.000 0.000
## .F2 ~~
## .F3 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 3.023 0.019 160.998 0.000 3.023 3.271
## .rridbw0 2.935 0.019 157.442 0.000 2.935 3.199
## .rridcw0 3.067 0.019 162.812 0.000 3.067 3.308
## .rriddw0 2.995 0.020 153.421 0.000 2.995 3.117
## .rridew0 3.122 0.018 174.332 0.000 3.122 3.542
## .rriduw0 1.296 0.013 99.917 0.000 1.296 2.030
## .rridvw0 1.310 0.013 98.102 0.000 1.310 1.993
## .rridtw0 1.320 0.013 99.373 0.000 1.320 2.019
## .rridsw0 1.441 0.015 94.438 0.000 1.441 1.919
## .rridww0 1.469 0.016 91.443 0.000 1.469 1.858
## .rridqw0 2.767 0.021 134.527 0.000 2.767 2.734
## .rridkw0 2.881 0.021 137.706 0.000 2.881 2.798
## .rridpw0 2.187 0.023 96.154 0.000 2.187 1.954
## .rridrw0 3.098 0.019 162.275 0.000 3.098 3.297
## .rridow0 2.566 0.021 122.358 0.000 2.566 2.486
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .rridaw0 (Ea) 0.256 0.009 29.730 0.000 0.256 0.299
## .rridbw0 (Eb) 0.437 0.013 32.755 0.000 0.437 0.519
## .rridcw0 (Ec) 0.110 0.005 20.825 0.000 0.110 0.128
## .rriddw0 (Ed) 0.141 0.006 23.325 0.000 0.141 0.153
## .rridew0 (Ee) 0.434 0.013 33.154 0.000 0.434 0.559
## .rriduw0 (Eu) 0.076 0.003 23.752 0.000 0.076 0.187
## .rridvw0 (Ev) 0.067 0.003 20.562 0.000 0.067 0.156
## .rridtw0 (Et) 0.153 0.005 29.317 0.000 0.153 0.358
## .rridsw0 (Es) 0.269 0.009 31.409 0.000 0.269 0.477
## .rridww0 (Ew) 0.234 0.008 30.347 0.000 0.234 0.375
## .rridqw0 (Eq) 0.256 0.010 25.433 0.000 0.256 0.250
## .rridkw0 (Ek) 0.310 0.011 27.409 0.000 0.310 0.293
## .rridpw0 (Ep) 0.642 0.020 31.807 0.000 0.642 0.513
## .rridrw0 (Er) 0.250 0.009 26.783 0.000 0.250 0.283
## .rridow0 (Eo) 0.429 0.014 30.197 0.000 0.429 0.403
## .F1 (VF1) 0.152 0.049 3.082 0.002 0.202 0.202
## .F2 (VF2) 0.315 0.011 27.962 0.000 0.951 0.951
## .F3 (VF3) 0.177 0.049 3.629 0.000 0.231 0.231
## G 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.4Result)Figure 12.5 Multi-Trait Multi-Method Model
Load MTMM Data
Path Diagram
Multi-Trait Multi-Method Model
R Program
require(lavaan)
MTMMData <- read.table("langermtmmsimulated.txt", header = TRUE) ;
head(MTMMData)## DSoc DGAD DSAD DPD ChSoc PaSoc ChGAD
## 1 0.6073740 -0.04574160 0.5724619 0.01820963 5.331529 16.285153 20.15238
## 2 0.2851913 -0.48379796 0.3141246 0.11417307 10.204388 9.967807 20.00466
## 3 -0.2550704 0.29333843 0.3291670 -0.26024833 15.677911 6.073015 17.81669
## 4 0.8230464 0.87144394 0.2126094 0.47227593 18.115698 13.964879 18.24485
## 5 1.1310499 0.06439362 0.2333899 0.33410893 16.408778 20.720852 14.93142
## 6 0.6128086 0.26980741 -0.1025633 0.11637706 15.234263 11.908552 10.11583
## PaGAD ChSAD PaSAD ChPD PaPD
## 1 16.29639 11.864066 13.754786 8.812848 12.82312
## 2 16.65290 11.294614 14.655742 12.923502 19.41736
## 3 15.74022 11.688042 7.216525 17.724105 12.87487
## 4 12.13322 2.229849 4.000555 16.011022 10.06640
## 5 18.12546 9.113720 8.096138 25.153023 15.16869
## 6 19.42117 5.402864 12.623651 16.751766 27.43542Fig12.5Model<-"
! regressions
SA=~T1*DSAD
SA=~T2*PaSAD
SA=~T3*ChSAD
PD=~T4*DPD
PD=~T5*PaPD
PD=~T6*ChPD
SP=~T7*DSoc
SP=~T8*PaSoc
SP=~T9*ChSoc
GA=~T10*DGAD
GA=~T11*PaGAD
GA=~T12*ChGAD
D=~M1*DSAD
D=~M2*DPD
D=~M3*DSoc
D=~M4*DGAD
P=~M5*PaSAD
P=~M6*PaPD
P=~M7*PaSoc
P=~M8*PaGAD
S=~M9*ChSAD
S=~M10*ChPD
S=~M11*ChSoc
S=~M12*ChGAD
! residuals, variances and covariances
DSAD ~~ E_DSAD*DSAD
PaSAD ~~ E_PaSAD*PaSAD
ChSAD ~~ E_ChSAD*ChSAD
DPD ~~ E_DPD*DPD
PaPD ~~ E_PaPD*PaPD
ChPD ~~ E_ChPD*ChPD
DSoc ~~ E_DSoc*DSoc
PaSoc ~~ E_PaSoc*PaSoc
ChSoc ~~ E_ChSoc*ChSoc
DGAD ~~ E_DGAD*DGAD
PaGAD ~~ E_PaGAD*PaGAD
ChGAD ~~ E_ChGAD*ChGAD
SA ~~ 1.0*SA
PD ~~ 1.0*PD
SP ~~ 1.0*SP
GA ~~ 1.0*GA
SA ~~ r12*PD
PD ~~ r23*SP
SP ~~ r34*GA
SA ~~ r13*SP
PD ~~ r24*GA
SA ~~ r14*GA
D ~~ 1.0*D
P ~~ 1.0*P
S ~~ 1.0*S
D ~~ RM12*P
P ~~ RM23*S
D ~~ RM13*S
SA ~~ 0.0*D
SA ~~ 0.0*P
SA ~~ 0.0*S
PD ~~ 0.0*D
PD ~~ 0.0*P
PD ~~ 0.0*S
SP ~~ 0.0*D
SP ~~ 0.0*P
SP ~~ 0.0*S
GA ~~ 0.0*D
GA ~~ 0.0*P
GA ~~ 0.0*S
! observed means
DSAD~1;
PaSAD~1;
ChSAD~1;
DPD~1;
PaPD~1;
ChPD~1;
DSoc~1;
PaSoc~1;
ChSoc~1;
DGAD~1;
PaGAD~1;
ChGAD~1;
"
Fig12.5Result<-lavaan(Fig12.5Model, data=MTMMData, fixed.x=FALSE, missing="FIML")
summary(Fig12.5Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 84 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 57
##
## Number of observations 174
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 33.674
## Degrees of freedom 33
## P-value (Chi-square) 0.435
##
## Model Test Baseline Model:
##
## Test statistic 568.394
## Degrees of freedom 66
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999
## Tucker-Lewis Index (TLI) 0.997
##
## Robust Comparative Fit Index (CFI) 0.999
## Robust Tucker-Lewis Index (TLI) 0.997
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4290.217
## Loglikelihood unrestricted model (H1) -4273.380
##
## Akaike (AIC) 8694.433
## Bayesian (BIC) 8874.500
## Sample-size adjusted Bayesian (SABIC) 8694.002
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.011
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.057
## P-value H_0: RMSEA <= 0.050 0.901
## P-value H_0: RMSEA >= 0.080 0.002
##
## Robust RMSEA 0.011
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.057
## P-value H_0: Robust RMSEA <= 0.050 0.901
## P-value H_0: Robust RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.035
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SA =~
## DSAD (T1) 0.162 0.029 5.669 0.000 0.162 0.464
## PaSAD (T2) 3.435 0.403 8.518 0.000 3.435 0.648
## ChSAD (T3) 4.198 0.395 10.617 0.000 4.198 0.841
## PD =~
## DPD (T4) 0.067 0.030 2.241 0.025 0.067 0.320
## PaPD (T5) 2.744 0.879 3.122 0.002 2.744 0.426
## ChPD (T6) 3.315 1.120 2.960 0.003 3.315 0.502
## SP =~
## DSoc (T7) 0.183 0.044 4.186 0.000 0.183 0.483
## PaSoc (T8) 2.837 0.827 3.430 0.001 2.837 0.489
## ChSoc (T9) 1.864 0.781 2.388 0.017 1.864 0.309
## GA =~
## DGAD (T10) -0.018 0.039 -0.446 0.656 -0.018 -0.039
## PaGAD (T11) 1.859 0.385 4.823 0.000 1.859 0.424
## ChGAD (T12) 2.435 0.448 5.430 0.000 2.435 0.541
## D =~
## DSAD (M1) 0.068 0.037 1.845 0.065 0.068 0.195
## DPD (M2) 0.067 0.025 2.659 0.008 0.067 0.319
## DSoc (M3) 0.145 0.053 2.727 0.006 0.145 0.381
## DGAD (M4) 0.197 0.061 3.249 0.001 0.197 0.438
## P =~
## PaSAD (M5) 3.199 0.355 8.999 0.000 3.199 0.603
## PaPD (M6) 3.920 0.588 6.671 0.000 3.920 0.608
## PaSoc (M7) 2.637 0.651 4.050 0.000 2.637 0.454
## PaGAD (M8) 2.991 0.362 8.271 0.000 2.991 0.682
## S =~
## ChSAD (M9) 2.048 0.497 4.123 0.000 2.048 0.411
## ChPD (M10) 4.684 0.754 6.216 0.000 4.684 0.709
## ChSoc (M11) 4.388 0.586 7.489 0.000 4.388 0.728
## ChGAD (M12) 1.735 0.445 3.896 0.000 1.735 0.386
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SA ~~
## PD (r12) 0.150 0.180 0.836 0.403 0.150 0.150
## PD ~~
## SP (r23) -0.127 0.390 -0.326 0.745 -0.127 -0.127
## SP ~~
## GA (r34) -0.416 0.315 -1.323 0.186 -0.416 -0.416
## SA ~~
## SP (r13) -0.125 0.194 -0.645 0.519 -0.125 -0.125
## PD ~~
## GA (r24) 0.085 0.255 0.333 0.739 0.085 0.085
## SA ~~
## GA (r14) 0.911 0.093 9.794 0.000 0.911 0.911
## D ~~
## P (RM12) 0.590 0.140 4.205 0.000 0.590 0.590
## P ~~
## S (RM23) 0.088 0.163 0.544 0.587 0.088 0.088
## D ~~
## S (RM13) 0.306 0.148 2.071 0.038 0.306 0.306
## SA ~~
## D 0.000 0.000 0.000
## P 0.000 0.000 0.000
## S 0.000 0.000 0.000
## PD ~~
## D 0.000 0.000 0.000
## P 0.000 0.000 0.000
## S 0.000 0.000 0.000
## SP ~~
## D 0.000 0.000 0.000
## P 0.000 0.000 0.000
## S 0.000 0.000 0.000
## GA ~~
## D 0.000 0.000 0.000
## P 0.000 0.000 0.000
## S 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .DSAD 0.140 0.026 5.290 0.000 0.140 0.401
## .PaSAD 10.510 0.402 26.149 0.000 10.510 1.982
## .ChSAD 9.560 0.378 25.272 0.000 9.560 1.916
## .DPD 0.050 0.016 3.150 0.002 0.050 0.239
## .PaPD 12.290 0.489 25.156 0.000 12.290 1.907
## .ChPD 13.520 0.501 26.994 0.000 13.520 2.046
## .DSoc 0.180 0.029 6.256 0.000 0.180 0.474
## .PaSoc 14.980 0.440 34.042 0.000 14.980 2.581
## .ChSoc 12.490 0.457 27.347 0.000 12.490 2.073
## .DGAD 0.290 0.034 8.526 0.000 0.290 0.646
## .PaGAD 15.770 0.332 47.448 0.000 15.770 3.597
## .ChGAD 16.260 0.341 47.702 0.000 16.260 3.616
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .DSAD (E_DSA) 0.091 0.011 8.490 0.000 0.091 0.747
## .PaSAD (E_PSA) 6.078 1.507 4.032 0.000 6.078 0.216
## .ChSAD (E_CSA) 3.080 1.828 1.685 0.092 3.080 0.124
## .DPD (E_DP) 0.035 0.005 6.843 0.000 0.035 0.796
## .PaPD (E_PP) 18.634 4.293 4.341 0.000 18.634 0.449
## .ChPD (E_CP) 10.718 5.743 1.866 0.062 10.718 0.246
## .DSoc (E_DSc) 0.090 0.020 4.582 0.000 0.090 0.622
## .PaSoc (E_PSc) 18.688 3.942 4.741 0.000 18.688 0.555
## .ChSoc (E_ChS) 13.565 4.662 2.910 0.004 13.565 0.374
## .DGAD (E_DG) 0.162 0.027 6.083 0.000 0.162 0.806
## .PaGAD (E_PG) 6.818 1.541 4.423 0.000 6.818 0.355
## .ChGAD (E_CG) 11.279 1.771 6.369 0.000 11.279 0.558
## SA 1.000 1.000 1.000
## PD 1.000 1.000 1.000
## SP 1.000 1.000 1.000
## GA 1.000 1.000 1.000
## D 1.000 1.000 1.000
## P 1.000 1.000 1.000
## S 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.5Result)State-Trait Model
Path Diagrams
Unstandardized Solution
Unstandardized State-Trait Model
Standardized Solution
Standardized State-Trait Model
R Program
BSISimData <- read.table("BSISim.txt", header = TRUE) ;
Fig12.6Model<-"
! regressions
Trait=~L1*BSIW1
Trait=~L2*BSIW2
Trait=~L3*BSIW3
Trait=~L4*BSIW4
Trait=~L5*BSIW5
Trait=~L6*BSIW6
Trait=~L7*BSIW7
Trait=~L8*BSIW8
BSIW2 ~ g1*BSIW1
BSIW3 ~ g2*BSIW2
BSIW4 ~ g3*BSIW3
BSIW5 ~ g4*BSIW4
BSIW6 ~ g5*BSIW5
BSIW7 ~ g6*BSIW6
BSIW8 ~ g7*BSIW7
! residuals, variances and covariances
BSIW1 ~~ E1*BSIW1
BSIW2 ~~ E2*BSIW2
BSIW3 ~~ E3*BSIW3
BSIW4 ~~ E4*BSIW4
BSIW5 ~~ E5*BSIW5
BSIW6 ~~ E6*BSIW6
BSIW7 ~~ E7*BSIW7
BSIW8 ~~ E8*BSIW8
Trait ~~ 1.0*Trait
! observed means
BSIW1~1;
BSIW2~1;
BSIW3~1;
BSIW4~1;
BSIW5~1;
BSIW6~1;
BSIW7~1;
BSIW8~1;
"
Fig12.6Result<-lavaan(Fig12.6Model, data=BSISimData, fixed.x=FALSE, missing="FIML")
summary(Fig12.6Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 50 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
##
## Number of observations 1191
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 39.105
## Degrees of freedom 13
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4328.000
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.994
## Tucker-Lewis Index (TLI) 0.987
##
## Robust Comparative Fit Index (CFI) 0.994
## Robust Tucker-Lewis Index (TLI) 0.987
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5729.907
## Loglikelihood unrestricted model (H1) -5710.355
##
## Akaike (AIC) 11521.814
## Bayesian (BIC) 11679.373
## Sample-size adjusted Bayesian (SABIC) 11580.906
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.041
## 90 Percent confidence interval - lower 0.027
## 90 Percent confidence interval - upper 0.056
## P-value H_0: RMSEA <= 0.050 0.825
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.041
## 90 Percent confidence interval - lower 0.027
## 90 Percent confidence interval - upper 0.056
## P-value H_0: Robust RMSEA <= 0.050 0.825
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.013
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Trait =~
## BSIW1 (L1) 0.353 0.017 20.508 0.000 0.353 0.587
## BSIW2 (L2) 0.283 0.018 15.415 0.000 0.283 0.519
## BSIW3 (L3) 0.364 0.022 16.429 0.000 0.364 0.651
## BSIW4 (L4) 0.402 0.028 14.380 0.000 0.402 0.735
## BSIW5 (L5) 0.413 0.028 14.805 0.000 0.413 0.760
## BSIW6 (L6) 0.309 0.024 12.875 0.000 0.309 0.595
## BSIW7 (L7) 0.304 0.025 12.101 0.000 0.304 0.531
## BSIW8 (L8) 0.302 0.020 15.062 0.000 0.302 0.558
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## BSIW2 ~
## BSIW1 (g1) 0.220 0.027 8.162 0.000 0.220 0.243
## BSIW3 ~
## BSIW2 (g2) 0.142 0.036 3.987 0.000 0.142 0.139
## BSIW4 ~
## BSIW3 (g3) 0.045 0.045 1.001 0.317 0.045 0.046
## BSIW5 ~
## BSIW4 (g4) -0.026 0.047 -0.559 0.576 -0.026 -0.027
## BSIW6 ~
## BSIW5 (g5) 0.148 0.040 3.676 0.000 0.148 0.155
## BSIW7 ~
## BSIW6 (g6) 0.206 0.044 4.667 0.000 0.206 0.187
## BSIW8 ~
## BSIW7 (g7) 0.188 0.032 5.856 0.000 0.188 0.199
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BSIW1 0.547 0.017 31.390 0.000 0.547 0.910
## .BSIW2 0.384 0.020 18.819 0.000 0.384 0.704
## .BSIW3 0.424 0.023 18.128 0.000 0.424 0.760
## .BSIW4 0.462 0.027 16.946 0.000 0.462 0.845
## .BSIW5 0.474 0.028 16.992 0.000 0.474 0.872
## .BSIW6 0.394 0.023 16.985 0.000 0.394 0.757
## .BSIW7 0.364 0.025 14.388 0.000 0.364 0.637
## .BSIW8 0.355 0.020 17.371 0.000 0.355 0.656
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BSIW1 (E1) 0.237 0.011 21.943 0.000 0.237 0.656
## .BSIW2 (E2) 0.155 0.007 21.497 0.000 0.155 0.523
## .BSIW3 (E3) 0.136 0.008 17.854 0.000 0.136 0.437
## .BSIW4 (E4) 0.122 0.008 15.137 0.000 0.122 0.407
## .BSIW5 (E5) 0.134 0.008 16.430 0.000 0.134 0.453
## .BSIW6 (E6) 0.131 0.007 19.565 0.000 0.131 0.486
## .BSIW7 (E7) 0.177 0.008 21.022 0.000 0.177 0.542
## .BSIW8 (E8) 0.147 0.007 21.310 0.000 0.147 0.501
## Trait 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.6Result)Random Intercept Model
Path Diagram
Random Intercept Model
R Code
Fig12.7Model<-"
! regressions
Trait=~L1*BSIW1
Trait=~L2*BSIW2
Trait=~L3*BSIW3
Trait=~L4*BSIW4
Trait=~L5*BSIW5
Trait=~L6*BSIW6
Trait=~L7*BSIW7
Trait=~L8*BSIW8
RI=~1.0*BSIW1
RI=~1.0*BSIW2
RI=~1.0*BSIW3
RI=~1.0*BSIW4
RI=~1.0*BSIW5
RI=~1.0*BSIW6
RI=~1.0*BSIW7
RI=~1.0*BSIW8
! residuals, variances and covariances
BSIW1 ~~ E1*BSIW1
BSIW2 ~~ E2*BSIW2
BSIW3 ~~ E3*BSIW3
BSIW4 ~~ E4*BSIW4
BSIW5 ~~ E5*BSIW5
BSIW6 ~~ E6*BSIW6
BSIW7 ~~ E7*BSIW7
BSIW8 ~~ E8*BSIW8
Trait ~~ 1.0*Trait
RI ~~ V_RI*RI
Trait ~~ 0.0*RI
! observed means
BSIW1~1;
BSIW2~1;
BSIW3~1;
BSIW4~1;
BSIW5~1;
BSIW6~1;
BSIW7~1;
BSIW8~1;
"
Fig12.7Result<-lavaan(Fig12.7Model, data=BSISimData, fixed.x=FALSE, missing="FIML")
summary(Fig12.7Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 72 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 25
##
## Number of observations 1191
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 56.786
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 4328.000
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991
## Tucker-Lewis Index (TLI) 0.987
##
## Robust Comparative Fit Index (CFI) 0.991
## Robust Tucker-Lewis Index (TLI) 0.987
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5738.748
## Loglikelihood unrestricted model (H1) -5710.355
##
## Akaike (AIC) 11527.496
## Bayesian (BIC) 11654.559
## Sample-size adjusted Bayesian (SABIC) 11575.150
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.041
## 90 Percent confidence interval - lower 0.029
## 90 Percent confidence interval - upper 0.053
## P-value H_0: RMSEA <= 0.050 0.882
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.041
## 90 Percent confidence interval - lower 0.029
## 90 Percent confidence interval - upper 0.053
## P-value H_0: Robust RMSEA <= 0.050 0.882
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Trait =~
## BSIW1 (L1) -0.167 0.027 -6.076 0.000 -0.167 -0.272
## BSIW2 (L2) -0.176 0.027 -6.410 0.000 -0.176 -0.321
## BSIW3 (L3) -0.055 0.025 -2.192 0.028 -0.055 -0.101
## BSIW4 (L4) -0.025 0.024 -1.015 0.310 -0.025 -0.046
## BSIW5 (L5) 0.079 0.024 3.246 0.001 0.079 0.146
## BSIW6 (L6) 0.108 0.023 4.642 0.000 0.108 0.205
## BSIW7 (L7) 0.151 0.026 5.707 0.000 0.151 0.265
## BSIW8 (L8) 0.090 0.024 3.745 0.000 0.090 0.163
## RI =~
## BSIW1 1.000 0.395 0.645
## BSIW2 1.000 0.395 0.722
## BSIW3 1.000 0.395 0.727
## BSIW4 1.000 0.395 0.734
## BSIW5 1.000 0.395 0.731
## BSIW6 1.000 0.395 0.748
## BSIW7 1.000 0.395 0.695
## BSIW8 1.000 0.395 0.717
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Trait ~~
## RI 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BSIW1 0.547 0.018 30.785 0.000 0.547 0.892
## .BSIW2 0.504 0.016 31.777 0.000 0.504 0.921
## .BSIW3 0.496 0.016 31.480 0.000 0.496 0.912
## .BSIW4 0.484 0.016 31.049 0.000 0.484 0.900
## .BSIW5 0.461 0.016 29.484 0.000 0.461 0.854
## .BSIW6 0.462 0.015 30.198 0.000 0.462 0.875
## .BSIW7 0.459 0.016 27.887 0.000 0.459 0.808
## .BSIW8 0.442 0.016 27.656 0.000 0.442 0.801
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BSIW1 (E1) 0.192 0.011 17.021 0.000 0.192 0.511
## .BSIW2 (E2) 0.113 0.010 11.720 0.000 0.113 0.376
## .BSIW3 (E3) 0.136 0.007 20.709 0.000 0.136 0.462
## .BSIW4 (E4) 0.133 0.006 21.305 0.000 0.133 0.459
## .BSIW5 (E5) 0.129 0.006 19.965 0.000 0.129 0.444
## .BSIW6 (E6) 0.111 0.006 17.629 0.000 0.111 0.398
## .BSIW7 (E7) 0.144 0.009 16.754 0.000 0.144 0.446
## .BSIW8 (E8) 0.140 0.007 19.825 0.000 0.140 0.460
## Trait 1.000 1.000 1.000
## RI (V_RI) 0.156 0.007 22.009 0.000 1.000 1.000require(lavaangui)
#plot_lavaan(Fig12.7Result)