Chapter 8:
Phil Wood
2025-07-26
Figure 8.1 Factor with Unit Variance
Load Simulated Alcohol Data
<a href=“https://docs.google.com/document/d/1SZ44w8P1oq6C_kMhAdBE8WX9z14-u3NNKQDCVkNmNK4/edit?usp=sharing>
require(lavaan)## Loading required package: lavaan## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.AlcUseData <- read.table("singlegroupalc.txt", header = TRUE) ;
Fig8.1Model<-"
! regressions
AlcoholUse=~L1*alcf3mw1 + +NA*alcf3mw1 + L2*typqfrw1
AlcoholUse=~L3*typqsaw1
AlcoholUse=~L4*typqthw1
AlcoholUse=~L5*qpls5mw1
! residuals, variances and covariances
alcf3mw1 ~~ E1*alcf3mw1
typqfrw1 ~~ E2*typqfrw1
typqsaw1 ~~ E3*typqsaw1
typqthw1 ~~ E4*typqthw1
qpls5mw1 ~~ E5*qpls5mw1
AlcoholUse ~~ 1.0*AlcoholUse
! observed means
alcf3mw1~1;
typqfrw1~1;
typqsaw1~1;
typqthw1~1;
qpls5mw1~1;
"
Fig8.1Result<-lavaan(Fig8.1Model, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Fig8.1Result, fit.measures=TRUE,standardized=TRUE);## lavaan 0.6-19 ended normally after 16 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 107.700
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5465.449
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.981
## Tucker-Lewis Index (TLI) 0.962
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.962
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28205.240
## Loglikelihood unrestricted model (H1) -28151.390
##
## Akaike (AIC) 56440.480
## Bayesian (BIC) 56528.179
## Sample-size adjusted Bayesian (SABIC) 56480.520
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.090
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.870
##
## Robust RMSEA 0.090
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.105
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.870
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021
##
## 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
## AlcoholUse =~
## alcf3mw1 (L1) 2.360 0.052 45.124 0.000 2.360 0.789
## typqfrw1 (L2) 2.894 0.068 42.509 0.000 2.894 0.757
## typqsaw1 (L3) 3.209 0.074 43.206 0.000 3.209 0.766
## typqthw1 (L4) 1.585 0.053 29.821 0.000 1.585 0.576
## qpls5mw1 (L5) 0.886 0.019 45.923 0.000 0.886 0.801
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 3.968 0.059 67.051 0.000 3.968 1.326
## .typqfrw1 2.268 0.076 29.994 0.000 2.268 0.593
## .typqsaw1 2.654 0.083 32.051 0.000 2.654 0.634
## .typqthw1 1.077 0.054 19.783 0.000 1.077 0.391
## .qpls5mw1 0.666 0.022 30.428 0.000 0.666 0.602
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 (E1) 3.385 0.127 26.649 0.000 3.385 0.378
## .typqfrw1 (E2) 6.246 0.222 28.187 0.000 6.246 0.427
## .typqsaw1 (E3) 7.235 0.262 27.612 0.000 7.235 0.413
## .typqthw1 (E4) 5.071 0.154 32.974 0.000 5.071 0.669
## .qpls5mw1 (E5) 0.440 0.017 25.470 0.000 0.440 0.359
## AlcoholUs 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(Fig8.1result)
Single Factor with Unit Variance
Standardized Single Factor with Unit
Variance
Figure 8.3 Single Factor with Referent Indicator
Fig8.3model<-"
! regressions
AlcoholUse=~L1*alcf3mw1
AlcoholUse=~L4*typqfrw1
AlcoholUse=~1.0*typqsaw1
AlcoholUse=~L3*typqthw1
AlcoholUse=~L2*qpls5mw1
! residuals, variances and covariances
alcf3mw1 ~~ E1*alcf3mw1
typqfrw1 ~~ E2*typqfrw1
typqsaw1 ~~ E3*typqsaw1
typqthw1 ~~ E4*typqthw1
qpls5mw1 ~~ E5*qpls5mw1
AlcoholUse ~~ Vf*AlcoholUse
! observed means
alcf3mw1~1;
typqfrw1~1;
typqsaw1~1;
typqthw1~1;
qpls5mw1~1;
"
Figure8.3result<-lavaan(Fig8.3model, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Figure8.3result, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-19 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 107.700
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5465.449
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.981
## Tucker-Lewis Index (TLI) 0.962
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.962
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28205.240
## Loglikelihood unrestricted model (H1) -28151.390
##
## Akaike (AIC) 56440.480
## Bayesian (BIC) 56528.179
## Sample-size adjusted Bayesian (SABIC) 56480.520
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.090
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.870
##
## Robust RMSEA 0.090
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.105
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.870
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021
##
## 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
## AlcoholUse =~
## alcf3mw1 (L1) 0.735 0.019 39.258 0.000 2.360 0.789
## typqfrw1 (L4) 0.902 0.024 38.081 0.000 2.894 0.757
## typqsaw1 1.000 3.209 0.766
## typqthw1 (L3) 0.494 0.018 27.690 0.000 1.585 0.576
## qpls5mw1 (L2) 0.276 0.007 38.687 0.000 0.886 0.801
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 3.968 0.059 67.051 0.000 3.968 1.326
## .typqfrw1 2.268 0.076 29.994 0.000 2.268 0.593
## .typqsaw1 2.654 0.083 32.051 0.000 2.654 0.634
## .typqthw1 1.077 0.054 19.783 0.000 1.077 0.391
## .qpls5mw1 0.666 0.022 30.428 0.000 0.666 0.602
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 (E1) 3.385 0.127 26.649 0.000 3.385 0.378
## .typqfrw1 (E2) 6.246 0.222 28.187 0.000 6.246 0.427
## .typqsaw1 (E3) 7.235 0.262 27.612 0.000 7.235 0.413
## .typqthw1 (E4) 5.071 0.154 32.974 0.000 5.071 0.669
## .qpls5mw1 (E5) 0.440 0.017 25.470 0.000 0.440 0.359
## AlcoholUs (Vf) 10.296 0.477 21.603 0.000 1.000 1.000require(lavaangui)
#plot_lavaan(Figure8.3result)
Single Factor with Referent Indicator
- Single Factor with Effects Coding
Fig8.4Model <- "
# Latent factor loadings (all freely estimated)
AlcoholUse =~ L1*alcf3mw1 +
L2*qpls5mw1 +
L3*typqthw1 +
L4*typqfrw1 +
L5*typqsaw1
# Residual variances
alcf3mw1 ~~ E1*alcf3mw1
qpls5mw1 ~~ E2*qpls5mw1
typqthw1 ~~ E3*typqthw1
typqfrw1 ~~ E4*typqfrw1
typqsaw1 ~~ E5*typqsaw1
# Latent factor variance
AlcoholUse ~~ Vf*AlcoholUse
# Observed means (intercepts, all freely estimated)
alcf3mw1 ~ I1*1
qpls5mw1 ~ I2*1
typqthw1 ~ I3*1
typqfrw1 ~ I4*1
typqsaw1 ~ I5*1
AlcoholUse ~ Malc*1
# ---- Effects coding constraints ----
# Sum of loadings = 5 (number of indicators)
L1 ==5- L2 + L3 + L4 + L5
# Sum of intercepts = 0
I1 == -I2 - I3 - I4 - I5
"
Figure8.4result<-lavaan(Fig8.4Model, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Figure8.4result, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-19 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
## Number of equality constraints 2
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 107.700
## Degrees of freedom 5
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5465.449
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.981
## Tucker-Lewis Index (TLI) 0.962
##
## Robust Comparative Fit Index (CFI) 0.000
## Robust Tucker-Lewis Index (TLI) -7.046
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28205.240
## Loglikelihood unrestricted model (H1) -28151.390
##
## Akaike (AIC) 56440.480
## Bayesian (BIC) 56528.179
## Sample-size adjusted Bayesian (SABIC) 56480.520
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.090
## 90 Percent confidence interval - lower 0.075
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.870
##
## Robust RMSEA 1.310
## 90 Percent confidence interval - lower 1.296
## 90 Percent confidence interval - upper 1.325
## 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 0.021
##
## 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
## AlcoholUse =~
## alcf3mw1 (L1) 1.228 0.043 28.717 0.000 2.360 0.789
## qpls5mw1 (L2) 0.461 0.015 31.749 0.000 0.886 0.801
## typqthw1 (L3) 0.825 0.024 34.235 0.000 1.585 0.576
## typqfrw1 (L4) 1.507 0.031 48.069 0.000 2.894 0.757
## typqsaw1 (L5) 1.670 0.033 49.878 0.000 3.209 0.766
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3m1 (I1) 1.567 0.052 30.104 0.000 1.567 0.524
## .qpls5m1 (I2) -0.235 0.022 -10.784 0.000 -0.235 -0.213
## .typqth1 (I3) -0.535 0.060 -8.949 0.000 -0.535 -0.194
## .typqfr1 (I4) -0.676 0.063 -10.659 0.000 -0.676 -0.177
## .typqsw1 (I5) -0.610 0.066 -9.201 0.000 -0.610 -0.146
## AlchlUs (Malc) 1.954 0.056 35.059 0.000 1.017 1.017
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 (E1) 3.385 0.127 26.649 0.000 3.385 0.378
## .qpls5mw1 (E2) 0.440 0.017 25.470 0.000 0.440 0.359
## .typqthw1 (E3) 5.071 0.154 32.974 0.000 5.071 0.669
## .typqfrw1 (E4) 6.246 0.222 28.187 0.000 6.246 0.427
## .typqsaw1 (E5) 7.235 0.262 27.612 0.000 7.235 0.413
## AlcoholUs (Vf) 3.691 0.203 18.156 0.000 1.000 1.000
##
## Constraints:
## |Slack|
## L1 - (5-L2+L3+L4+L5) 7.313
## I1 - (-I2-I3-I4-I5) 0.490require(lavaangui)
#plot_lavaan(Figure8.4result)
Single Factor with Effects Coding
- Single Factor with Normalized Basis
``{r}
Fig8.5Model <- ” # Latent factor loadings (all freely estimated) AlcoholUse =~ L1alcf3mw1 + NAalcf3mw1 + start(.0.475)alcf3mw1 + L2qpls5mw1 + start(.482)qpls5mw1 + L3typqthw1 + start(.347)typqthw1 + L4typqfrw1 + start(.456)typqfrw1 + L5typqsaw1 + start(.462)*typqsaw1
# Residual variances alcf3mw1 ~~ E1alcf3mw1 qpls5mw1 ~~ E2qpls5mw1 typqthw1 ~~ E3typqthw1 typqfrw1 ~~ E4typqfrw1 typqsaw1 ~~ E5*typqsaw1
# Latent factor variance AlcoholUse ~~ Vf*AlcoholUse
# Observed means (intercepts, all freely estimated) alcf3mw1 ~ I11 qpls5mw1 ~ I21 typqthw1 ~ I31 typqfrw1 ~ I41 typqsaw1 ~ I51 AlcoholUse ~ 01 # —- Effects coding constraints —-
# Sum of squared loadings = 1 # or L1 == (1 - (L2L2) - (L3L3) - (L4L4) - (L5L5))##0.5 L1L1+L2L2+L3L3+L4L4+L5*L5==1 ” # (Transformed to z-scores so match discussion of exploratory factor analysis later) AlcUseDataZ <- as.data.frame(scale(AlcUseData)) Figure8.5result<-lavaan(Fig8.5Model, data=AlcUseDataZ, fixed.x=FALSE, missing=“FIML”) summary(Figure8.5result, standardized=TRUE, fit.measures=TRUE) require(lavaangui) #plot_lavaan(Figure8.5result)
* Correlated Two Factor Model
``` r
Fig8.6Model<-"
! regressions
LastWeekAlc=~L4*typqfrw1
LastWeekAlc=~L5*typqsaw1
LastWeekAlc=~L3*typqthw1
TypAlcUse=~L1*alcf3mw1
TypAlcUse=~L2*qpls5mw1
! residuals, variances and covariances
alcf3mw1 ~~ E1*alcf3mw1
typqfrw1 ~~ E2*typqfrw1
typqsaw1 ~~ E3*typqsaw1
typqthw1 ~~ E4*typqthw1
qpls5mw1 ~~ E5*qpls5mw1
LastWeekAlc ~~ 1.0*LastWeekAlc
TypAlcUse ~~ 1.0*TypAlcUse
TypAlcUse ~~ r*LastWeekAlc
! observed means
alcf3mw1~1;
typqfrw1~1;
typqsaw1~1;
typqthw1~1;
qpls5mw1~1;
"
Figure8.6result<-lavaan(Fig8.6Model, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Figure8.6result, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-19 ended normally after 21 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 96.646
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5465.449
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.983
## Tucker-Lewis Index (TLI) 0.958
##
## Robust Comparative Fit Index (CFI) 0.983
## Robust Tucker-Lewis Index (TLI) 0.958
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28199.713
## Loglikelihood unrestricted model (H1) -28151.390
##
## Akaike (AIC) 56431.426
## Bayesian (BIC) 56524.972
## Sample-size adjusted Bayesian (SABIC) 56474.135
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.095
## 90 Percent confidence interval - lower 0.079
## 90 Percent confidence interval - upper 0.112
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.942
##
## Robust RMSEA 0.095
## 90 Percent confidence interval - lower 0.079
## 90 Percent confidence interval - upper 0.112
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.942
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021
##
## 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
## LastWeekAlc =~
## typqfrw1 (L4) 2.933 0.069 42.624 0.000 2.933 0.767
## typqsaw1 (L5) 3.250 0.075 43.303 0.000 3.250 0.776
## typqthw1 (L3) 1.586 0.054 29.638 0.000 1.586 0.576
## TypAlcUse =~
## alcf3mw1 (L1) 2.386 0.053 45.127 0.000 2.386 0.798
## qpls5mw1 (L2) 0.895 0.019 45.954 0.000 0.895 0.809
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## LastWeekAlc ~~
## TypAlcUse (r) 0.967 0.010 94.379 0.000 0.967 0.967
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 3.968 0.059 67.051 0.000 3.968 1.326
## .typqfrw1 2.268 0.076 29.994 0.000 2.268 0.593
## .typqsaw1 2.654 0.083 32.051 0.000 2.654 0.634
## .typqthw1 1.077 0.054 19.783 0.000 1.077 0.391
## .qpls5mw1 0.666 0.022 30.428 0.000 0.666 0.602
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 (E1) 3.258 0.133 24.548 0.000 3.258 0.364
## .typqfrw1 (E2) 6.021 0.229 26.309 0.000 6.021 0.412
## .typqsaw1 (E3) 6.971 0.271 25.715 0.000 6.971 0.398
## .typqthw1 (E4) 5.069 0.155 32.712 0.000 5.069 0.668
## .qpls5mw1 (E5) 0.423 0.018 23.474 0.000 0.423 0.345
## LastWkAlc 1.000 1.000 1.000
## TypAlcUse 1.000 1.000 1.000require(lavaangui)
#plot_lavaan(Figure8.6result)
* Three
Indicator Factor Model
Fig8.7Model<-"
! regressions
LastWeekAlc=~L4*typqfrw1
LastWeekAlc=~L5*typqsaw1
LastWeekAlc=~L3*typqthw1
! residuals, variances and covariances
typqfrw1 ~~ E2*typqfrw1
typqsaw1 ~~ E3*typqsaw1
typqthw1 ~~ E4*typqthw1
LastWeekAlc ~~ 1.0*LastWeekAlc
! observed means
typqfrw1~1;
typqsaw1~1;
typqthw1~1;
"
Figure8.7result<-lavaan(Fig8.7Model, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Figure8.7result, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-19 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 1855.408
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -19638.607
## Loglikelihood unrestricted model (H1) -19638.607
##
## Akaike (AIC) 39295.214
## Bayesian (BIC) 39347.833
## Sample-size adjusted Bayesian (SABIC) 39319.237
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: Robust RMSEA <= 0.050 NA
## P-value H_0: Robust RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## 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
## LastWeekAlc =~
## typqfrw1 (L4) 3.037 0.084 36.207 0.000 3.037 0.794
## typqsaw1 (L5) 3.246 0.091 35.495 0.000 3.246 0.775
## typqthw1 (L3) 1.481 0.057 25.855 0.000 1.481 0.538
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .typqfrw1 2.268 0.076 29.994 0.000 2.268 0.593
## .typqsaw1 2.654 0.083 32.051 0.000 2.654 0.634
## .typqthw1 1.077 0.054 19.783 0.000 1.077 0.391
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .typqfrw1 (E2) 5.398 0.371 14.530 0.000 5.398 0.369
## .typqsaw1 (E3) 6.997 0.434 16.114 0.000 6.997 0.399
## .typqthw1 (E4) 5.392 0.171 31.530 0.000 5.392 0.711
## LastWkAlc 1.000 1.000 1.000require(lavaangui)
# plot_lavaan(Figure8.7result)
Three Indicator Factor Model
- Loss Function Plot
Load Predicted Loss Function Values
<a href=“https://docs.google.com/document/d/1fHcWHY9iRHhYrN3abCKXKfqEPbn-G7IkzxhCv9IaF4o/edit?usp=drive_link
x <- read.table("minimization.txt",header=TRUE)
library(lattice)
library(latticeExtra)## Warning: package 'latticeExtra' was built under R version 4.5.1library(akima)## Warning: package 'akima' was built under R version 4.5.1trellis.par.set("axis.line", list(col = "transparent"))
# Base wireframe
wf <- wireframe(
loss ~ l1 * l2, data = x,
xlab = expression(paste(lambda)),
ylab = expression(paste(lambda)),
scales = list(arrows = FALSE, cex = .45, col = "black", font = 6, shade = TRUE),
light.source = c(0, 20, 10),
colorkey = FALSE,
screen = list(z = -50, x = -50),
shade.colors = function(irr, ref, height, w = 0.4)
grey(w * irr + (1 - w) * (1 - (1 - ref)^0.4))
)
# Interpolate z value at (0.79, 0.54)
interp_surface <- with(x, interp(l1, l2, loss, duplicate = "mean"))## Warning in interp(l1, l2, loss, duplicate = "mean"): collinear points, trying
## to add some jitter to avoid colinearities!## Warning in interp(l1, l2, loss, duplicate = "mean"): success: collinearities
## reduced through jitterz_val <- interp_surface$z[
which.min(abs(interp_surface$x - 0.79)),
which.min(abs(interp_surface$y - 0.54))
]
# Add red dot (no text label or axis tick changes)
dot_layer <- cloud(
z_val ~ 0.79 * 0.54,
pch = 16, cex = 1.5, col = "red",
screen = list(z = -50, x = -50),
xlab = NULL, ylab = NULL, zlab = NULL
)
# Combine plot and dot
wf_annotated <- wf + as.layer(dot_layer)
library(svglite)
# Open SVG device (3x3 inches)
svglite("Figure8.8svg", width = 3, height = 3)
# Print your combined plot
print(wf_annotated)
# Close device
dev.off()## png
## 2
Three Indicator Factor Model
- Correlated Error Model
CorrErrmodel<-"
! regressions
LstWkAlcoholUse=~L1*alcf3mw1
LstWkAlcoholUse=~L2*typqfrw1
LstWkAlcoholUse=~L3*typqsaw1
LstWkAlcoholUse=~L4*typqthw1
LstWkAlcoholUse=~L5*qpls5mw1
e1=~sde1*alcf3mw1
e2=~sde2*qpls5mw1
! residuals, variances and covariances
typqfrw1 ~~ E2*typqfrw1
typqsaw1 ~~ E3*typqsaw1
typqthw1 ~~ E4*typqthw1
LstWkAlcoholUse ~~ 1.0*LstWkAlcoholUse
e1 ~~ 1.0*e1
e2 ~~ 1.0*e2
e2 ~~ r*e1
LstWkAlcoholUse ~~ 0.0*e1
LstWkAlcoholUse ~~ 0.0*e2
! observed means
alcf3mw1~1;
typqfrw1~1;
typqsaw1~1;
typqthw1~1;
qpls5mw1~1;
"
Figure8.9result<-lavaan(CorrErrmodel, data=AlcUseData, fixed.x=FALSE, missing="FIML")
summary(Figure8.9result, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-19 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 16
##
## Number of observations 2557
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 96.646
## Degrees of freedom 4
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5465.449
## Degrees of freedom 10
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.983
## Tucker-Lewis Index (TLI) 0.958
##
## Robust Comparative Fit Index (CFI) 0.983
## Robust Tucker-Lewis Index (TLI) 0.958
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -28199.713
## Loglikelihood unrestricted model (H1) -28151.390
##
## Akaike (AIC) 56431.426
## Bayesian (BIC) 56524.972
## Sample-size adjusted Bayesian (SABIC) 56474.135
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.095
## 90 Percent confidence interval - lower 0.079
## 90 Percent confidence interval - upper 0.112
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.942
##
## Robust RMSEA 0.095
## 90 Percent confidence interval - lower 0.079
## 90 Percent confidence interval - upper 0.112
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.942
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021
##
## 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
## LstWkAlcoholUse =~
## alcf3m1 (L1) 2.306 0.055 41.935 0.000 2.306 0.771
## typqfr1 (L2) 2.933 0.069 42.624 0.000 2.933 0.767
## typqsw1 (L3) 3.250 0.075 43.303 0.000 3.250 0.776
## typqth1 (L4) 1.586 0.054 29.638 0.000 1.586 0.576
## qpls5m1 (L5) 0.865 0.020 42.485 0.000 0.865 0.782
## e1 =~
## alcf3m1 (sde1) 1.906 0.039 48.631 0.000 1.906 0.637
## e2 =~
## qpls5m1 (sde2) 0.690 0.015 46.191 0.000 0.690 0.623
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## e1 ~~
## e2 (r) 0.107 0.030 3.527 0.000 0.107 0.107
## LstWkAlcoholUse ~~
## e1 0.000 0.000 0.000
## e2 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .alcf3mw1 3.968 0.059 67.051 0.000 3.968 1.326
## .typqfrw1 2.268 0.076 29.994 0.000 2.268 0.593
## .typqsaw1 2.654 0.083 32.051 0.000 2.654 0.634
## .typqthw1 1.077 0.054 19.783 0.000 1.077 0.391
## .qpls5mw1 0.666 0.022 30.428 0.000 0.666 0.602
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .typqfrw1 (E2) 6.021 0.229 26.309 0.000 6.021 0.412
## .typqsaw1 (E3) 6.971 0.271 25.715 0.000 6.971 0.398
## .typqthw1 (E4) 5.069 0.155 32.712 0.000 5.069 0.668
## LstWkAlcU 1.000 1.000 1.000
## e1 1.000 1.000 1.000
## e2 1.000 1.000 1.000
## .alcf3mw1 0.000 0.000 0.000
## .qpls5mw1 0.000 0.000 0.000require(lavaangui)
# plot_lavaan(Figure8.9result)
* Effect
of zero-values
library(ggplot2)##
## Attaching package: 'ggplot2'## The following object is masked from 'package:latticeExtra':
##
## layerlibrary(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(patchwork)
library(svglite)
# Load data
data <- read.table("singlegroupalcSIM.txt", header = TRUE)
# Composite predictor
data <- data %>%
mutate(AlcoholUse = rowMeans(select(., alcf3mw1, typqfrw1, typqsaw1, typqthw1, qpls5mw1), na.rm = TRUE))
# Split datasets
data_all <- data
data_filtered <- data %>% filter(typqsaw1 != 0)
# Function for square plot
make_plot <- function(df, title) {
ggplot(df, aes(x = AlcoholUse, y = typqsaw1)) +
geom_jitter(width = 0.1, height = 0.1, alpha = 0.5) +
geom_smooth(method = "lm", se = TRUE, color = "blue") +
geom_smooth(method = "loess", se = TRUE, color = "red", linetype = "dashed") +
scale_x_continuous(breaks = c(0, 2, 4, 6), limits = c(0, 6)) +
scale_y_continuous(breaks = c(0, 5, 10, 15, 20, 25), limits = c(0, 25)) +
labs(title = title, x = "AlcoholUse", y = "typqsaw1") +
theme_minimal(base_size = 14) +
coord_fixed(ratio = 1, clip = "on") +
theme(aspect.ratio=1,
plot.margin = margin(5, 5, 5, 5),
plot.title = element_text(hjust = 0.5)
)
}
# Create plots
p1 <- make_plot(data_all, "All Data")
p2 <- make_plot(data_filtered, "Excluding typqsaw1 = 0")
# Combine vertically
combined_plot <- p1 / p2 # Using patchwork
# Export combined plot as a single SVG (3" wide, 6" tall)
svglite("Figure8.10.svg", width = 6, height = 12)
print(combined_plot)## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 201 rows containing non-finite outside the scale range
## (`stat_smooth()`).## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 201 rows containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 1060 rows containing missing values or values outside the scale range
## (`geom_point()`).## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_smooth()`).## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 199 rows containing non-finite outside the scale range
## (`stat_smooth()`).## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 199 rows containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 199 rows containing missing values or values outside the scale range
## (`geom_point()`).dev.off()## png
## 2
Effect of Zero Reports