Chapter 12:
Phil Wood
2025-08-01
Figure 12.1 Orthogonal Factor Model of Alcohol Expectations
Load Simulated Alcohol Expectation Data
<a href=“https://docs.google.com/document/d/17C7eM7Mc3pqBqe4eChuFqIIKSD7WVbhVoBfeUtA8fqM/edit?usp=sharing
Orthogonal Factor Model
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## This is lavaangui 0.2.4
## 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
Correlated (Oblique) Factor Model
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
Bifactor Model
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)Correlated Factor Model