if (!require(lavaan)) install.packages("lavaan")
## Loading required package: lavaan
## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.
library(lavaan)
#Step 1: Find path of data file and copy path (if using windows)
#Step 2: In the console below, type readClipboard()
#Step 3: Copy and paste R's path to the line below in quotes
#AUTOMATING PACKAGES NEEDED FOR ANALYSES--------------------------------------------------------------------
needed_packages = c("lavaan","semPlot")
for (i in 1:length(needed_packages)){
haspackage = require(needed_packages[i], character.only = TRUE)
if (haspackage==FALSE){
install.packages(needed_packages[i])
library(needed_packages[i], character.only = TRUE)
}
}
## Loading required package: semPlot
#FUNCTIONS FOR ANALYSES BELOW -------------------------------------------------------------------------------
data01 = read.csv(file = "gamblingdata.csv", na.strings="99")
#MODEL 01: Gambling GRI Single Factor Model ----------------------------------------------------------------
model01.syntax = "
GAMBLING =~ GRI1 + GRI3 + GRI5
"
model01.fit = sem(
model01.syntax,
data = data01,
estimator = "MLR",
mimic="Mplus"
)
summary(model01.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 0.000 0.000
## Degrees of freedom 0 0
##
## Model Test Baseline Model:
##
## Test statistic 480.988 199.641
## Degrees of freedom 3 3
## P-value 0.000 0.000
## Scaling correction factor 2.409
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.000 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5254.609 -5254.609
## Loglikelihood unrestricted model (H1) -5254.609 -5254.609
##
## Akaike (AIC) 10527.219 10527.219
## Bayesian (BIC) 10573.996 10573.996
## Sample-size adjusted Bayesian (SABIC) 10545.407 10545.407
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 NA
## 90 Percent confidence interval - lower 0.000 NA
## 90 Percent confidence interval - upper 0.000 NA
## P-value H_0: RMSEA <= 0.050 NA NA
## P-value H_0: RMSEA >= 0.080 NA 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 0.000
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 1.000 0.638 0.621
## GRI3 0.726 0.093 7.820 0.000 0.463 0.535
## GRI5 0.995 0.121 8.244 0.000 0.635 0.652
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 1.823 0.028 64.871 0.000 1.823 1.775
## .GRI3 1.548 0.024 65.365 0.000 1.548 1.788
## .GRI5 1.593 0.027 59.749 0.000 1.593 1.635
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.647 0.076 8.481 0.000 0.647 0.614
## .GRI3 0.535 0.047 11.449 0.000 0.535 0.714
## .GRI5 0.546 0.061 8.953 0.000 0.546 0.575
## GAMBLING 0.407 0.066 6.124 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.386
## GRI3 0.286
## GRI5 0.425
#display normalized residual covariances
residuals(model01.fit, type="normalized")
## $type
## [1] "normalized"
##
## $cov
## GRI1 GRI3 GRI5
## GRI1 0
## GRI3 0 0
## GRI5 0 0 0
##
## $mean
## GRI1 GRI3 GRI5
## 0 0 0
#plot path diagram with standardized coefficients
semPaths(model01.fit,intercepts = FALSE, residuals = TRUE, style="mx", layout="tree", rotation=1, what = "std",
optimizeLatRes=TRUE, whatLabels = "std", sizeLat = 5, sizeLat2=5, sizeMan=5, sizeMan2=5)
#model fitted values:
fitted.values(model01.fit)
## $cov
## GRI1 GRI3 GRI5
## GRI1 1.055
## GRI3 0.296 0.749
## GRI5 0.405 0.294 0.949
##
## $mean
## GRI1 GRI3 GRI5
## 1.823 1.548 1.593
#MODEL 02: Full Structural Equation Model ------------------------------------------------------------------
model02.syntax = "
GAMBLING =~ GRI1 + GRI3 + GRI5
GAMBLING ~ Student
"
model02.fit = sem(
model02.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus"
)
summary(model02.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 103.882 79.938
## Degrees of freedom 2 2
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.300
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 853.812 391.369
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.182
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.880 0.798
## Tucker-Lewis Index (TLI) 0.639 0.393
##
## Robust Comparative Fit Index (CFI) 0.880
## Robust Tucker-Lewis Index (TLI) 0.641
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5120.139 -5120.139
## Scaling correction factor 2.338
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5068.197 -5068.197
## Scaling correction factor 2.165
## for the MLR correction
##
## Akaike (AIC) 10260.277 10260.277
## Bayesian (BIC) 10312.251 10312.251
## Sample-size adjusted Bayesian (SABIC) 10280.486 10280.486
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.195 0.171
## 90 Percent confidence interval - lower 0.164 0.144
## 90 Percent confidence interval - upper 0.228 0.200
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.194
## 90 Percent confidence interval - lower 0.156
## 90 Percent confidence interval - upper 0.236
## 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 0.050 0.050
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 1.000 0.666 0.648
## GRI3 0.563 0.076 7.380 0.000 0.375 0.433
## GRI5 1.014 0.140 7.265 0.000 0.675 0.693
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING ~
## Student -1.162 0.140 -8.327 0.000 -1.745 -0.541
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 2.859 0.132 21.684 0.000 2.859 2.784
## .GRI3 2.131 0.078 27.395 0.000 2.131 2.462
## .GRI5 2.644 0.139 18.972 0.000 2.644 2.714
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.611 0.082 7.503 0.000 0.611 0.580
## .GRI3 0.609 0.047 13.048 0.000 0.609 0.813
## .GRI5 0.494 0.063 7.872 0.000 0.494 0.520
## .GAMBLING 0.313 0.051 6.138 0.000 0.707 0.707
##
## R-Square:
## Estimate
## GRI1 0.420
## GRI3 0.187
## GRI5 0.480
## GAMBLING 0.293
#display normalized residual covariances
residuals(model02.fit, type="normalized")
## $type
## [1] "normalized"
##
## $cov
## GRI1 GRI3 GRI5 Studnt
## GRI1 0.000
## GRI3 1.224 0.000
## GRI5 -1.052 1.172 0.000
## Student -1.145 4.653 -0.719 0.000
##
## $mean
## GRI1 GRI3 GRI5 Student
## 0 0 0 0
#display modification indices
modindices(model02.fit)
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 15 GRI1 ~~ GRI3 17.178 0.104 0.104 0.170 0.170
## 16 GRI1 ~~ GRI5 93.140 -0.477 -0.477 -0.868 -0.868
## 17 GRI3 ~~ GRI5 21.072 0.115 0.115 0.209 0.209
#MODEL Configural: Setting up invariance testing of GRI by student status ==========================
configural.syntax = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(SL1, NSL1)*GRI1 + c(SL3, NSL3)*GRI3 + c(SL5, NSL5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(SI1, NSI1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(SI5, NSI5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(SR3, NSR3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in both groups with label for each group
GAMBLING ~~ c(1, 1)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in both groups with label for each group
GAMBLING ~ c(0, 0)*1
#===================================================================================================
"
modelConfigural.fit = lavaan(
configural.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelConfigural.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 0.000 0.000
## Degrees of freedom 0 0
## Test statistic for each group:
## 1 0.000 0.000
## 0 0.000 0.000
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.000 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4919.375 -4919.375
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
##
## Akaike (AIC) 9874.750 9874.750
## Bayesian (BIC) 9968.304 9968.304
## Sample-size adjusted Bayesian (SABIC) 9911.126 9911.126
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 NA
## 90 Percent confidence interval - lower 0.000 NA
## 90 Percent confidence interval - upper 0.000 NA
## P-value H_0: RMSEA <= 0.050 NA NA
## P-value H_0: RMSEA >= 0.080 NA 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 0.000
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (SL1) 0.409 0.043 9.492 0.000 0.409 0.466
## GRI3 (SL3) 0.573 0.051 11.310 0.000 0.573 0.694
## GRI5 (SL5) 0.431 0.040 10.694 0.000 0.431 0.560
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SI1) 1.683 0.025 66.131 0.000 1.683 1.915
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.848
## .GRI5 (SI5) 1.456 0.022 65.314 0.000 1.456 1.892
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.604 0.070 8.680 0.000 0.604 0.783
## .GRI3 (SR3) 0.353 0.055 6.444 0.000 0.353 0.518
## .GRI5 (SR5) 0.406 0.046 8.841 0.000 0.406 0.687
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.217
## GRI3 0.482
## GRI5 0.313
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (NSL1) 1.013 0.215 4.710 0.000 1.013 0.736
## GRI3 (NSL3) 0.556 0.131 4.242 0.000 0.556 0.494
## GRI5 (NSL5) 0.817 0.203 4.033 0.000 0.817 0.521
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSI1) 2.979 0.115 25.967 0.000 2.979 2.164
## .GRI3 (NSI3) 1.729 0.094 18.435 0.000 1.729 1.536
## .GRI5 (NSI5) 2.729 0.131 20.875 0.000 2.729 1.740
## GAMBLIN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 0.868 0.406 2.138 0.033 0.868 0.458
## .GRI3 (NSR3) 0.957 0.201 4.757 0.000 0.957 0.756
## .GRI5 (NSR5) 1.794 0.308 5.834 0.000 1.794 0.729
## GAMBLIN 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.542
## GRI3 0.244
## GRI5 0.271
#MODEL Configural: Testing equality of loadings of GRI by student status ===========================
metric.syntax = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(SI1, NSI1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(SI5, NSI5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(SR3, NSR3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in both groups with label for each group
GAMBLING ~ c(0, 0)*1
#===================================================================================================
"
modelMetric.fit = lavaan(
metric.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelMetric.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
## Number of equality constraints 3
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 8.412 5.904
## Degrees of freedom 2 2
## P-value (Chi-square) 0.015 0.052
## Scaling correction factor 1.425
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 0.379 0.379
## 0 5.525 5.525
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.984 0.982
## Tucker-Lewis Index (TLI) 0.951 0.945
##
## Robust Comparative Fit Index (CFI) 0.986
## Robust Tucker-Lewis Index (TLI) 0.957
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4923.581 -4923.581
## Scaling correction factor 1.563
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9879.162 9879.162
## Bayesian (BIC) 9962.321 9962.321
## Sample-size adjusted Bayesian (SABIC) 9911.496 9911.496
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.069 0.054
## 90 Percent confidence interval - lower 0.026 0.013
## 90 Percent confidence interval - upper 0.120 0.098
## P-value H_0: RMSEA <= 0.050 0.198 0.366
## P-value H_0: RMSEA >= 0.080 0.421 0.188
##
## Robust RMSEA 0.065
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.128
## P-value H_0: Robust RMSEA <= 0.050 0.264
## P-value H_0: Robust RMSEA >= 0.080 0.409
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.014 0.014
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.427 0.041 10.492 0.000 0.427 0.484
## GRI3 (L3) 0.552 0.052 10.613 0.000 0.552 0.671
## GRI5 (L5) 0.440 0.039 11.332 0.000 0.440 0.571
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SI1) 1.683 0.025 66.131 0.000 1.683 1.908
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.854
## .GRI5 (SI5) 1.456 0.022 65.314 0.000 1.456 1.890
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.596 0.069 8.633 0.000 0.596 0.766
## .GRI3 (SR3) 0.373 0.054 6.961 0.000 0.373 0.550
## .GRI5 (SR5) 0.400 0.045 8.810 0.000 0.400 0.674
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.234
## GRI3 0.450
## GRI5 0.326
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.427 0.041 10.492 0.000 0.642 0.481
## GRI3 (L3) 0.552 0.052 10.613 0.000 0.831 0.720
## GRI5 (L5) 0.440 0.039 11.332 0.000 0.662 0.425
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSI1) 2.979 0.115 25.967 0.000 2.979 2.231
## .GRI3 (NSI3) 1.729 0.094 18.435 0.000 1.729 1.498
## .GRI5 (NSI5) 2.729 0.131 20.875 0.000 2.729 1.754
## GAMBLIN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 1.371 0.177 7.738 0.000 1.371 0.769
## .GRI3 (NSR3) 0.642 0.186 3.448 0.001 0.642 0.482
## .GRI5 (NSR5) 1.983 0.216 9.178 0.000 1.983 0.819
## GAMBLIN 2.264 0.558 4.057 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.231
## GRI3 0.518
## GRI5 0.181
# likelihood ratio test: all loadings tested at once:
anova(modelConfigural.fit, modelMetric.fit)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelConfigural.fit 0 9874.8 9968.3 0.0000
## modelMetric.fit 2 9879.2 9962.3 8.4121 5.9037 2 0.05224 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# looks like invariance--move to scalar
#MODEL Scalar: Testing equality of loadings of GRI by student status ===============================
scalar.syntax = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(I3, I3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(SR3, NSR3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in one group but not other for identification
GAMBLING ~ c(0, NA)*1
#===================================================================================================
"
modelScalar.fit = lavaan(
scalar.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelScalar.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 52 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 6
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 95.838 82.821
## Degrees of freedom 4 4
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.157
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 30.327 30.327
## 0 52.494 52.494
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.768 0.627
## Tucker-Lewis Index (TLI) 0.652 0.441
##
## Robust Comparative Fit Index (CFI) 0.769
## Robust Tucker-Lewis Index (TLI) 0.654
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4967.294 -4967.294
## Scaling correction factor 1.396
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9962.588 9962.588
## Bayesian (BIC) 10035.352 10035.352
## Sample-size adjusted Bayesian (SABIC) 9990.881 9990.881
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.185 0.172
## 90 Percent confidence interval - lower 0.154 0.143
## 90 Percent confidence interval - upper 0.218 0.203
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.184
## 90 Percent confidence interval - lower 0.148
## 90 Percent confidence interval - upper 0.222
## 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 0.066 0.066
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.488 0.043 11.233 0.000 0.488 0.543
## GRI3 (L3) 0.394 0.060 6.595 0.000 0.394 0.494
## GRI5 (L5) 0.496 0.043 11.593 0.000 0.496 0.638
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.698 0.027 63.246 0.000 1.698 1.890
## .GRI3 (I3) 1.500 0.023 66.196 0.000 1.500 1.882
## .GRI5 (I5) 1.461 0.023 64.354 0.000 1.461 1.878
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.569 0.076 7.513 0.000 0.569 0.705
## .GRI3 (SR3) 0.480 0.053 9.150 0.000 0.480 0.756
## .GRI5 (SR5) 0.359 0.051 7.000 0.000 0.359 0.593
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.295
## GRI3 0.244
## GRI5 0.407
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.488 0.043 11.233 0.000 0.797 0.580
## GRI3 (L3) 0.394 0.060 6.595 0.000 0.643 0.487
## GRI5 (L5) 0.496 0.043 11.593 0.000 0.810 0.517
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.698 0.027 63.246 0.000 1.698 1.235
## .GRI3 (I3) 1.500 0.023 66.196 0.000 1.500 1.137
## .GRI5 (I5) 1.461 0.023 64.354 0.000 1.461 0.932
## GAMBLING 2.066 0.316 6.539 0.000 1.266 1.266
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 1.254 0.275 4.559 0.000 1.254 0.664
## .GRI3 (NSR3) 1.329 0.205 6.493 0.000 1.329 0.763
## .GRI5 (NSR5) 1.800 0.284 6.338 0.000 1.800 0.733
## GAMBLIN 2.664 0.838 3.178 0.001 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.336
## GRI3 0.237
## GRI5 0.267
# likelihood ratio test: all loadings tested at once:
anova(modelMetric.fit, modelScalar.fit)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelMetric.fit 2 9879.2 9962.3 8.4121
## modelScalar.fit 4 9962.6 10035.4 95.8381 98.293 2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# modification indices inspection:
scalarMI1 = lavTestScore(modelScalar.fit)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to ordinary score
## test
#change label values
labelMap = data.frame(
lhs = modelScalar.fit@ParTable$plabel,
parameter = modelScalar.fit@ParTable$label
)
scalarMI1$uni = merge(x = scalarMI1$uni, y = labelMap, by = "lhs", all.x = TRUE)
# reorder by decreasing values of X2:
scalarMI1$uni = scalarMI1$uni[order(scalarMI1$uni$X2, decreasing = TRUE),]
#restrict to only means shown
scalarMI1$uni[grep(x = scalarMI1$uni$parameter, pattern = "I"),]
## lhs op rhs X2 df p.value parameter
## 5 .p5. == .p16. 73.73821 1 0.000000e+00 I3
## 4 .p4. == .p15. 24.03290 1 9.470376e-07 I1
## 6 .p6. == .p17. 10.75211 1 1.041604e-03 I5
# free parameter for I3 first:
scalar.syntax1 = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(SR3, NSR3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in one group but not other for identification
GAMBLING ~ c(0, NA)*1
#===================================================================================================
"
modelScalar.fit1 = lavaan(
scalar.syntax1,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelScalar.fit1, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 51 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 5
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 8.507 6.357
## Degrees of freedom 3 3
## P-value (Chi-square) 0.037 0.095
## Scaling correction factor 1.338
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 0.485 0.485
## 0 5.872 5.872
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.986 0.984
## Tucker-Lewis Index (TLI) 0.972 0.968
##
## Robust Comparative Fit Index (CFI) 0.989
## Robust Tucker-Lewis Index (TLI) 0.978
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4923.629 -4923.629
## Scaling correction factor 1.427
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9877.257 9877.257
## Bayesian (BIC) 9955.219 9955.219
## Sample-size adjusted Bayesian (SABIC) 9907.570 9907.570
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.052 0.041
## 90 Percent confidence interval - lower 0.012 0.000
## 90 Percent confidence interval - upper 0.096 0.080
## P-value H_0: RMSEA <= 0.050 0.390 0.592
## P-value H_0: RMSEA >= 0.080 0.164 0.048
##
## Robust RMSEA 0.047
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.100
## P-value H_0: Robust RMSEA <= 0.050 0.458
## P-value H_0: Robust RMSEA >= 0.080 0.174
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.015 0.015
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.431 0.035 12.217 0.000 0.431 0.488
## GRI3 (L3) 0.553 0.052 10.672 0.000 0.553 0.671
## GRI5 (L5) 0.436 0.034 12.784 0.000 0.436 0.567
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.460 0.000 1.684 1.907
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.854
## .GRI5 (I5) 1.455 0.022 66.384 0.000 1.455 1.892
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.594 0.068 8.670 0.000 0.594 0.762
## .GRI3 (SR3) 0.372 0.053 6.958 0.000 0.372 0.549
## .GRI5 (SR5) 0.402 0.045 8.914 0.000 0.402 0.679
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.238
## GRI3 0.451
## GRI5 0.321
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.431 0.035 12.217 0.000 0.648 0.485
## GRI3 (L3) 0.553 0.052 10.672 0.000 0.831 0.720
## GRI5 (L5) 0.436 0.034 12.784 0.000 0.655 0.422
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.460 0.000 1.684 1.259
## .GRI3 (NSI3) 0.087 0.223 0.390 0.697 0.087 0.075
## .GRI5 (I5) 1.455 0.022 66.384 0.000 1.455 0.936
## GAMBLIN 2.971 0.319 9.311 0.000 1.977 1.977
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 1.368 0.177 7.740 0.000 1.368 0.765
## .GRI3 (NSR3) 0.642 0.186 3.453 0.001 0.642 0.482
## .GRI5 (NSR5) 1.987 0.211 9.411 0.000 1.987 0.822
## GAMBLIN 2.260 0.556 4.066 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.235
## GRI3 0.518
## GRI5 0.178
# likelihood ratio test: all loadings tested at once:
anova(modelMetric.fit, modelScalar.fit1)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelMetric.fit 2 9879.2 9962.3 8.4121
## modelScalar.fit1 3 9877.3 9955.2 8.5070 0.081488 1 0.7753
# proceed to residual with GRI3 non-invariant for intercept and residual ============================
#MODEL Residual: Testing equality of residual variances of GRI by student status ====================
residual.syntax = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(R1, R1)*GRI1
GRI3 ~~ c(R3, R3)*GRI3
GRI5 ~~ c(R5, R5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in one group but not other for identification
GAMBLING ~ c(0, NA)*1
#===================================================================================================
"
modelResidual.fit = lavaan(
residual.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelResidual.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 8
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 209.808 321.542
## Degrees of freedom 6 6
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 0.653
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 96.675 96.675
## 0 224.867 224.867
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.485 0.000
## Tucker-Lewis Index (TLI) 0.485 -0.492
##
## Robust Comparative Fit Index (CFI) 0.486
## Robust Tucker-Lewis Index (TLI) 0.486
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5024.279 -5024.279
## Scaling correction factor 1.432
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 10072.558 10072.558
## Bayesian (BIC) 10134.927 10134.927
## Sample-size adjusted Bayesian (SABIC) 10096.808 10096.808
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.225 0.281
## 90 Percent confidence interval - lower 0.200 0.249
## 90 Percent confidence interval - upper 0.252 0.314
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.224
## 90 Percent confidence interval - lower 0.195
## 90 Percent confidence interval - upper 0.255
## 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 0.115 0.115
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.434 0.044 9.833 0.000 0.434 0.476
## GRI3 (L3) 0.378 0.066 5.703 0.000 0.378 0.457
## GRI5 (L5) 0.471 0.043 11.044 0.000 0.471 0.569
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.691 0.027 61.569 0.000 1.691 1.855
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.844
## .GRI5 (I5) 1.450 0.023 62.655 0.000 1.450 1.750
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (R1) 0.643 0.078 8.223 0.000 0.643 0.774
## .GRI3 (R3) 0.542 0.057 9.557 0.000 0.542 0.791
## .GRI5 (R5) 0.465 0.080 5.840 0.000 0.465 0.677
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.226
## GRI3 0.209
## GRI5 0.323
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.434 0.044 9.833 0.000 0.964 0.769
## GRI3 (L3) 0.378 0.066 5.703 0.000 0.840 0.752
## GRI5 (L5) 0.471 0.043 11.044 0.000 1.047 0.838
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.691 0.027 61.569 0.000 1.691 1.348
## .GRI3 (NSI3) 0.667 0.156 4.269 0.000 0.667 0.597
## .GRI5 (I5) 1.450 0.023 62.655 0.000 1.450 1.161
## GAMBLIN 2.811 0.301 9.329 0.000 1.265 1.265
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (R1) 0.643 0.078 8.223 0.000 0.643 0.409
## .GRI3 (R3) 0.542 0.057 9.557 0.000 0.542 0.434
## .GRI5 (R5) 0.465 0.080 5.840 0.000 0.465 0.298
## GAMBLING 4.939 1.218 4.054 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.591
## GRI3 0.566
## GRI5 0.702
# likelihood ratio test: all loadings tested at once:
anova(modelScalar.fit1, modelResidual.fit)
## Warning: lavaan->lav_test_diff_SatorraBentler2001():
## scaling factor is negative
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelScalar.fit1 3 9877.3 9955.2 8.507
## modelResidual.fit 6 10072.6 10134.9 209.808 3
# looks like a problem...investigate MIs
residualMI1 = lavTestScore(modelResidual.fit)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to ordinary score
## test
#change label values
labelMap = data.frame(
lhs = modelResidual.fit@ParTable$plabel,
parameter = modelResidual.fit@ParTable$label
)
residualMI1$uni = merge(x = residualMI1$uni, y = labelMap, by = "lhs", all.x = TRUE)
# reorder by decreasing values of X2:
residualMI1$uni = residualMI1$uni[order(residualMI1$uni$X2, decreasing = TRUE),]
#restrict to only means shown
residualMI1$uni[grep(x = residualMI1$uni$parameter, pattern = "R"),]
## lhs op rhs X2 df p.value parameter
## 8 .p9. == .p20. 283.19426 1 0.000000e+00 R5
## 7 .p8. == .p19. 63.41500 1 1.665335e-15 R3
## 6 .p7. == .p18. 60.25915 1 8.326673e-15 R1
# free parameter for R5 first:
residual.syntax1 = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(R1, R1)*GRI1
GRI3 ~~ c(R3, R3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in one group but not other for identification
GAMBLING ~ c(0, NA)*1
#===================================================================================================
"
modelResidual.fit1 = lavaan(
residual.syntax1,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelResidual.fit1, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 42 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 7
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 55.848 47.409
## Degrees of freedom 5 5
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.178
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 9.700 9.700
## 0 37.709 37.709
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.872 0.800
## Tucker-Lewis Index (TLI) 0.846 0.759
##
## Robust Comparative Fit Index (CFI) 0.875
## Robust Tucker-Lewis Index (TLI) 0.849
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4947.299 -4947.299
## Scaling correction factor 1.333
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9920.598 9920.598
## Bayesian (BIC) 9988.165 9988.165
## Sample-size adjusted Bayesian (SABIC) 9946.870 9946.870
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.123 0.113
## 90 Percent confidence interval - lower 0.095 0.087
## 90 Percent confidence interval - upper 0.154 0.141
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 0.994 0.980
##
## Robust RMSEA 0.121
## 90 Percent confidence interval - lower 0.089
## 90 Percent confidence interval - upper 0.156
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.982
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.064 0.064
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.449 0.037 12.223 0.000 0.449 0.488
## GRI3 (L3) 0.498 0.059 8.444 0.000 0.498 0.601
## GRI5 (L5) 0.451 0.035 12.835 0.000 0.451 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.026 66.010 0.000 1.684 1.829
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.842
## .GRI5 (I5) 1.455 0.022 66.365 0.000 1.455 1.899
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (R1) 0.646 0.075 8.653 0.000 0.646 0.762
## .GRI3 (R3) 0.438 0.060 7.325 0.000 0.438 0.638
## .GRI5 (SR5) 0.384 0.046 8.405 0.000 0.384 0.653
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.238
## GRI3 0.362
## GRI5 0.347
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.449 0.037 12.223 0.000 0.804 0.707
## GRI3 (L3) 0.498 0.059 8.444 0.000 0.892 0.803
## GRI5 (L5) 0.451 0.035 12.835 0.000 0.808 0.500
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.026 66.010 0.000 1.684 1.481
## .GRI3 (NSI3) 0.299 0.202 1.482 0.138 0.299 0.269
## .GRI5 (I5) 1.455 0.022 66.365 0.000 1.455 0.900
## GAMBLIN 2.871 0.318 9.041 0.000 1.603 1.603
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (R1) 0.646 0.075 8.653 0.000 0.646 0.500
## .GRI3 (R3) 0.438 0.060 7.325 0.000 0.438 0.355
## .GRI5 (NSR5) 1.958 0.241 8.110 0.000 1.958 0.750
## GAMBLIN 3.210 0.708 4.533 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.500
## GRI3 0.645
## GRI5 0.250
# likelihood ratio test: all loadings tested at once:
anova(modelScalar.fit1, modelResidual.fit1)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelScalar.fit1 3 9877.3 9955.2 8.507
## modelResidual.fit1 5 9920.6 9988.2 55.848 50.484 2 1.09e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# looks like a problem...investigate MIs
residualMI2 = lavTestScore(modelResidual.fit1)
## Warning: lavaan->lavTestScore():
## se is not `standard'; not implemented yet; falling back to ordinary score
## test
#change label values
labelMap = data.frame(
lhs = modelResidual.fit1@ParTable$plabel,
parameter = modelResidual.fit1@ParTable$label
)
residualMI2$uni = merge(x = residualMI2$uni, y = labelMap, by = "lhs", all.x = TRUE)
# reorder by decreasing values of X2:
residualMI2$uni = residualMI2$uni[order(residualMI2$uni$X2, decreasing = TRUE),]
#restrict to only means shown
residualMI2$uni[grep(x = residualMI2$uni$parameter, pattern = "R"),]
## lhs op rhs X2 df p.value parameter
## 6 .p7. == .p18. 57.12852 1 4.085621e-14 R1
## 7 .p8. == .p19. 26.69074 1 2.387628e-07 R3
# free parameter for R1:
residual.syntax2 = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(R3, R3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances all freely estimated in one group but not other for identification
GAMBLING ~~ c(1, NA)*GAMBLING
#===================================================================================================
#Factor means all freely estimated in one group but not other for identification
GAMBLING ~ c(0, NA)*1
#===================================================================================================
"
modelResidual.fit2 = lavaan(
residual.syntax2,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelResidual.fit2, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 6
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 12.651 10.087
## Degrees of freedom 4 4
## P-value (Chi-square) 0.013 0.039
## Scaling correction factor 1.254
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 0.213 0.213
## 0 9.874 9.874
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.978 0.971
## Tucker-Lewis Index (TLI) 0.967 0.957
##
## Robust Comparative Fit Index (CFI) 0.982
## Robust Tucker-Lewis Index (TLI) 0.972
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4925.701 -4925.701
## Scaling correction factor 1.377
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9879.402 9879.402
## Bayesian (BIC) 9952.166 9952.166
## Sample-size adjusted Bayesian (SABIC) 9907.694 9907.694
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.057 0.048
## 90 Percent confidence interval - lower 0.023 0.015
## 90 Percent confidence interval - upper 0.094 0.081
## P-value H_0: RMSEA <= 0.050 0.318 0.488
## P-value H_0: RMSEA >= 0.080 0.165 0.058
##
## Robust RMSEA 0.052
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.096
## P-value H_0: Robust RMSEA <= 0.050 0.402
## P-value H_0: Robust RMSEA >= 0.080 0.169
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.013 0.013
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.416 0.036 11.519 0.000 0.416 0.473
## GRI3 (L3) 0.571 0.050 11.353 0.000 0.571 0.688
## GRI5 (L5) 0.423 0.037 11.426 0.000 0.423 0.552
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.430 0.000 1.684 1.914
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.839
## .GRI5 (I5) 1.455 0.022 66.338 0.000 1.455 1.898
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.600 0.069 8.752 0.000 0.600 0.776
## .GRI3 (R3) 0.363 0.059 6.146 0.000 0.363 0.527
## .GRI5 (SR5) 0.409 0.046 8.914 0.000 0.409 0.695
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.224
## GRI3 0.473
## GRI5 0.305
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.416 0.036 11.519 0.000 0.673 0.487
## GRI3 (L3) 0.571 0.050 11.353 0.000 0.923 0.838
## GRI5 (L5) 0.423 0.037 11.426 0.000 0.685 0.427
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.430 0.000 1.684 1.219
## .GRI3 (NSI3) -0.024 0.234 -0.102 0.919 -0.024 -0.022
## .GRI5 (I5) 1.455 0.022 66.338 0.000 1.455 0.907
## GAMBLIN 3.071 0.362 8.490 0.000 1.898 1.898
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 1.454 0.164 8.877 0.000 1.454 0.762
## .GRI3 (R3) 0.363 0.059 6.146 0.000 0.363 0.298
## .GRI5 (NSR5) 2.106 0.239 8.813 0.000 2.106 0.818
## GAMBLIN 2.617 0.622 4.207 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.238
## GRI3 0.702
## GRI5 0.182
# likelihood ratio test: all loadings tested at once:
anova(modelScalar.fit1, modelResidual.fit2)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelScalar.fit1 3 9877.3 9955.2 8.507
## modelResidual.fit2 4 9879.4 9952.2 12.651 4.1339 1 0.04203 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# ignore and continue with structural model
#MODEL Structural: Testing equality of mean/variance of GRI by student status ======================
structural.syntax = "
#===================================================================================================
#Factor loadings all freely estimated in both groups with label for each group
GAMBLING =~ c(L1, L1)*GRI1 + c(L3, L3)*GRI3 + c(L5, L5)*GRI5
#===================================================================================================
#Item intercepts all freely estimated in both groups with label for each group
GRI1 ~ c(I1, I1)*1
GRI3 ~ c(SI3, NSI3)*1
GRI5 ~ c(I5, I5)*1
#===================================================================================================
#Redidual variances all freely estimated with label for each group
GRI1 ~~ c(SR1, NSR1)*GRI1
GRI3 ~~ c(R3, R3)*GRI3
GRI5 ~~ c(SR5, NSR5)*GRI5
#===================================================================================================
#Factor variances fixed to compare against previous model
GAMBLING ~~ c(1, 1)*GAMBLING
#===================================================================================================
#Factor means fixed to compare against previous model
GAMBLING ~ c(0,0)*1
#===================================================================================================
"
modelStructural.fit = lavaan(
structural.syntax,
data=data01,
estimator = "MLR",
mimic="Mplus",
group = "Student"
)
summary(modelStructural.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
## Number of equality constraints 6
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 207.431 178.319
## Degrees of freedom 6 6
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.163
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 8.456 8.456
## 0 169.863 169.863
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.491 0.185
## Tucker-Lewis Index (TLI) 0.491 0.185
##
## Robust Comparative Fit Index (CFI) 0.492
## Robust Tucker-Lewis Index (TLI) 0.492
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5023.091 -5023.091
## Scaling correction factor 1.420
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 10070.181 10070.181
## Bayesian (BIC) 10132.550 10132.550
## Sample-size adjusted Bayesian (SABIC) 10094.432 10094.432
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.224 0.207
## 90 Percent confidence interval - lower 0.199 0.184
## 90 Percent confidence interval - upper 0.251 0.232
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.223
## 90 Percent confidence interval - lower 0.194
## 90 Percent confidence interval - upper 0.254
## 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 0.104 0.104
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.442 0.043 10.267 0.000 0.442 0.496
## GRI3 (L3) 0.612 0.050 12.338 0.000 0.612 0.706
## GRI5 (L5) 0.453 0.040 11.270 0.000 0.453 0.582
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.728 0.028 61.209 0.000 1.728 1.940
## .GRI3 (SI3) 1.549 0.025 61.539 0.000 1.549 1.789
## .GRI5 (I5) 1.488 0.024 60.963 0.000 1.488 1.909
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.598 0.069 8.643 0.000 0.598 0.754
## .GRI3 (R3) 0.376 0.055 6.772 0.000 0.376 0.501
## .GRI5 (SR5) 0.402 0.045 8.907 0.000 0.402 0.662
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.246
## GRI3 0.499
## GRI5 0.338
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.442 0.043 10.267 0.000 0.442 0.253
## GRI3 (L3) 0.612 0.050 12.338 0.000 0.612 0.706
## GRI5 (L5) 0.453 0.040 11.270 0.000 0.453 0.238
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.728 0.028 61.209 0.000 1.728 0.991
## .GRI3 (NSI3) 1.535 0.090 17.023 0.000 1.535 1.773
## .GRI5 (I5) 1.488 0.024 60.963 0.000 1.488 0.780
## GAMBLIN 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 2.843 0.361 7.872 0.000 2.843 0.936
## .GRI3 (R3) 0.376 0.055 6.772 0.000 0.376 0.501
## .GRI5 (NSR5) 3.432 0.458 7.490 0.000 3.432 0.943
## GAMBLIN 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.064
## GRI3 0.499
## GRI5 0.057
# likelihood ratio test: all parameters tested at once:
anova(modelResidual.fit2, modelStructural.fit)
##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## modelResidual.fit2 4 9879.4 9952.2 12.651
## modelStructural.fit 6 10070.2 10132.6 207.431 198.51 2 < 2.2e-16
##
## modelResidual.fit2
## modelStructural.fit ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# conclusion: difference between students and non-students on GAMBLING factor ======================
summary(modelResidual.fit2, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
## Number of equality constraints 6
##
## Number of observations per group:
## 1 1192
## 0 144
## Number of missing patterns per group:
## 1 1
## 0 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 12.651 10.087
## Degrees of freedom 4 4
## P-value (Chi-square) 0.013 0.039
## Scaling correction factor 1.254
## Yuan-Bentler correction (Mplus variant)
## Test statistic for each group:
## 1 0.213 0.213
## 0 9.874 9.874
##
## Model Test Baseline Model:
##
## Test statistic 401.955 217.534
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.848
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.978 0.971
## Tucker-Lewis Index (TLI) 0.967 0.957
##
## Robust Comparative Fit Index (CFI) 0.982
## Robust Tucker-Lewis Index (TLI) 0.972
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4925.701 -4925.701
## Scaling correction factor 1.377
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4919.375 -4919.375
## Scaling correction factor 1.808
## for the MLR correction
##
## Akaike (AIC) 9879.402 9879.402
## Bayesian (BIC) 9952.166 9952.166
## Sample-size adjusted Bayesian (SABIC) 9907.694 9907.694
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.057 0.048
## 90 Percent confidence interval - lower 0.023 0.015
## 90 Percent confidence interval - upper 0.094 0.081
## P-value H_0: RMSEA <= 0.050 0.318 0.488
## P-value H_0: RMSEA >= 0.080 0.165 0.058
##
## Robust RMSEA 0.052
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.096
## P-value H_0: Robust RMSEA <= 0.050 0.402
## P-value H_0: Robust RMSEA >= 0.080 0.169
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.013 0.013
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
##
## Group 1 [1]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.416 0.036 11.519 0.000 0.416 0.473
## GRI3 (L3) 0.571 0.050 11.353 0.000 0.571 0.688
## GRI5 (L5) 0.423 0.037 11.426 0.000 0.423 0.552
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.430 0.000 1.684 1.914
## .GRI3 (SI3) 1.526 0.024 63.788 0.000 1.526 1.839
## .GRI5 (I5) 1.455 0.022 66.338 0.000 1.455 1.898
## GAMBLING 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (SR1) 0.600 0.069 8.752 0.000 0.600 0.776
## .GRI3 (R3) 0.363 0.059 6.146 0.000 0.363 0.527
## .GRI5 (SR5) 0.409 0.046 8.914 0.000 0.409 0.695
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.224
## GRI3 0.473
## GRI5 0.305
##
##
## Group 2 [0]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (L1) 0.416 0.036 11.519 0.000 0.673 0.487
## GRI3 (L3) 0.571 0.050 11.353 0.000 0.923 0.838
## GRI5 (L5) 0.423 0.037 11.426 0.000 0.685 0.427
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (I1) 1.684 0.025 66.430 0.000 1.684 1.219
## .GRI3 (NSI3) -0.024 0.234 -0.102 0.919 -0.024 -0.022
## .GRI5 (I5) 1.455 0.022 66.338 0.000 1.455 0.907
## GAMBLIN 3.071 0.362 8.490 0.000 1.898 1.898
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (NSR1) 1.454 0.164 8.877 0.000 1.454 0.762
## .GRI3 (R3) 0.363 0.059 6.146 0.000 0.363 0.298
## .GRI5 (NSR5) 2.106 0.239 8.813 0.000 2.106 0.818
## GAMBLIN 2.617 0.622 4.207 0.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.238
## GRI3 0.702
## GRI5 0.182
# comparison models:
#MODEL 03a: Structural Equation Model #2 -- prediction of GRI items by Student -------------------------------
model03a.syntax = "
GRI5 ~ Student
GRI3 ~ Student
GAMBLING =~ GRI1 + GRI3 + GRI5
GAMBLING ~ Student
"
model03a.fit = sem(model03a.syntax, data=data01, estimator = "MLR", mimic="Mplus", fixed.x=FALSE)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not
## appear to be positive definite! The smallest eigenvalue (= -6.261671e-20)
## is smaller than zero. This may be a symptom that the model is not
## identified.
summary(model03a.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 0.000 0.000
## Degrees of freedom 0 0
##
## Model Test Baseline Model:
##
## Test statistic 853.812 391.369
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.182
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.000 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5399.664 -5399.664
## Loglikelihood unrestricted model (H1) -5399.664 -5399.664
##
## Akaike (AIC) 10827.328 10827.328
## Bayesian (BIC) 10900.092 10900.092
## Sample-size adjusted Bayesian (SABIC) 10855.620 10855.620
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 NA
## 90 Percent confidence interval - lower 0.000 NA
## 90 Percent confidence interval - upper 0.000 NA
## P-value H_0: RMSEA <= 0.050 NA NA
## P-value H_0: RMSEA >= 0.080 NA 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 0.000
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 1.000 0.639 0.623
## GRI3 1.092 0.145 7.521 0.000 0.699 0.807
## GRI5 0.997 0.131 7.632 0.000 0.637 0.654
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GRI5 ~
## Student 0.018 0.208 0.088 0.930 0.018 0.006
## GRI3 ~
## Student 1.213 0.209 5.802 0.000 1.213 0.435
## GAMBLING ~
## Student -1.296 0.118 -11.031 0.000 -2.027 -0.629
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 2.979 0.115 25.967 0.000 2.979 2.901
## .GRI3 1.729 0.094 18.435 0.000 1.729 1.998
## .GRI5 2.729 0.131 20.875 0.000 2.729 2.801
## Student 0.892 0.008 105.162 0.000 0.892 2.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.646 0.069 9.365 0.000 0.646 0.612
## .GRI3 0.450 0.052 8.621 0.000 0.450 0.601
## .GRI5 0.548 0.052 10.537 0.000 0.548 0.577
## .GAMBLING 0.247 0.045 5.439 0.000 0.605 0.605
## Student 0.096 0.007 14.450 0.000 0.096 1.000
##
## R-Square:
## Estimate
## GRI1 0.388
## GRI3 0.399
## GRI5 0.423
## GAMBLING 0.395
#MODEL 03b: Structural Equation Model #2 -- NO prediction of GRI 3 by Student -------------------------------
model03b.syntax = "
GRI3 ~ Student
GAMBLING =~ GRI1 + GRI3 + GRI5
GAMBLING ~ 0*Student
"
model03b.fit = sem(model03b.syntax, data=data01, estimator = "MLR", mimic="Mplus", fixed.x=FALSE)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not
## appear to be positive definite! The smallest eigenvalue (= -1.223538e-19)
## is smaller than zero. This may be a symptom that the model is not
## identified.
summary(model03b.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 26 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 342.402 163.776
## Degrees of freedom 2 2
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 2.091
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 853.812 391.369
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.182
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.598 0.580
## Tucker-Lewis Index (TLI) -0.205 -0.259
##
## Robust Comparative Fit Index (CFI) 0.600
## Robust Tucker-Lewis Index (TLI) -0.200
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5570.865 -5570.865
## Scaling correction factor 2.167
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5399.664 -5399.664
## Scaling correction factor 2.156
## for the MLR correction
##
## Akaike (AIC) 11165.730 11165.730
## Bayesian (BIC) 11228.100 11228.100
## Sample-size adjusted Bayesian (SABIC) 11189.981 11189.981
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.357 0.246
## 90 Percent confidence interval - lower 0.326 0.224
## 90 Percent confidence interval - upper 0.389 0.268
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.354
## 90 Percent confidence interval - lower 0.298
## 90 Percent confidence interval - upper 0.415
## 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 0.165 0.165
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 1.000 0.639 0.622
## GRI3 0.857 0.097 8.800 0.000 0.548 0.611
## GRI5 0.993 0.106 9.357 0.000 0.635 0.651
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GRI3 ~
## Student 0.435 0.096 4.545 0.000 0.435 0.151
## GAMBLING ~
## Student 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 1.823 0.028 64.871 0.000 1.823 1.775
## .GRI3 1.160 0.087 13.329 0.000 1.160 1.295
## .GRI5 1.593 0.027 59.749 0.000 1.593 1.635
## Student 0.892 0.008 105.162 0.000 0.892 2.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.647 0.072 8.931 0.000 0.647 0.613
## .GRI3 0.485 0.048 10.064 0.000 0.485 0.604
## .GRI5 0.547 0.056 9.754 0.000 0.547 0.576
## .GAMBLING 0.408 0.062 6.582 0.000 1.000 1.000
## Student 0.096 0.007 14.450 0.000 0.096 1.000
##
## R-Square:
## Estimate
## GRI1 0.387
## GRI3 0.396
## GRI5 0.424
## GAMBLING -0.000
#MODEL 04a: Model 03b with Standardized Factor -------------------------------
model04a.syntax = "
GRI3 ~ Student
GAMBLING =~ GRI1 + GRI3 + GRI5
GAMBLING ~ 0*Student
"
model04a.fit = sem(model04a.syntax, data=data01, estimator = "MLR", mimic="Mplus", fixed.x=FALSE, std.lv = TRUE)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not
## appear to be positive definite! The smallest eigenvalue (= -2.261016e-19)
## is smaller than zero. This may be a symptom that the model is not
## identified.
summary(model04a.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 20 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 342.402 163.776
## Degrees of freedom 2 2
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 2.091
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 853.812 391.369
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.182
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.598 0.580
## Tucker-Lewis Index (TLI) -0.205 -0.259
##
## Robust Comparative Fit Index (CFI) 0.600
## Robust Tucker-Lewis Index (TLI) -0.200
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5570.865 -5570.865
## Scaling correction factor 2.167
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5399.664 -5399.664
## Scaling correction factor 2.156
## for the MLR correction
##
## Akaike (AIC) 11165.730 11165.730
## Bayesian (BIC) 11228.100 11228.100
## Sample-size adjusted Bayesian (SABIC) 11189.981 11189.981
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.357 0.246
## 90 Percent confidence interval - lower 0.326 0.224
## 90 Percent confidence interval - upper 0.389 0.268
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.354
## 90 Percent confidence interval - lower 0.298
## 90 Percent confidence interval - upper 0.415
## 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 0.165 0.165
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 0.639 0.049 13.164 0.000 0.639 0.622
## GRI3 0.548 0.047 11.544 0.000 0.548 0.611
## GRI5 0.635 0.049 12.869 0.000 0.635 0.651
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GRI3 ~
## Student 0.435 0.096 4.545 0.000 0.435 0.151
## GAMBLING ~
## Student 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 1.823 0.028 64.871 0.000 1.823 1.775
## .GRI3 1.160 0.087 13.329 0.000 1.160 1.295
## .GRI5 1.593 0.027 59.749 0.000 1.593 1.635
## Student 0.892 0.008 105.162 0.000 0.892 2.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.647 0.072 8.931 0.000 0.647 0.613
## .GRI3 0.485 0.048 10.064 0.000 0.485 0.604
## .GRI5 0.547 0.056 9.754 0.000 0.547 0.576
## .GAMBLING 1.000 1.000 1.000
## Student 0.096 0.007 14.450 0.000 0.096 1.000
##
## R-Square:
## Estimate
## GRI1 0.387
## GRI3 0.396
## GRI5 0.424
## GAMBLING 0.000
#MODEL 04b: Model 03a with Standardized Gambling Factor -------------------------------
model04b.syntax = "
GRI3 ~ Student
GAMBLING =~ GRI1 + GRI3 + GRI5
GAMBLING ~ Student
"
model04b.fit = sem(model04b.syntax, data=data01, estimator = "MLR", mimic="Mplus", fixed.x=FALSE, std.lv = TRUE)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not
## appear to be positive definite! The smallest eigenvalue (= -2.011605e-19)
## is smaller than zero. This may be a symptom that the model is not
## identified.
summary(model04b.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 37 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 0.014 0.008
## Degrees of freedom 1 1
## P-value (Chi-square) 0.906 0.929
## Scaling correction factor 1.765
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 853.812 391.369
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.182
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.007 1.015
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.012
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5399.671 -5399.671
## Scaling correction factor 2.186
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5399.664 -5399.664
## Scaling correction factor 2.156
## for the MLR correction
##
## Akaike (AIC) 10825.342 10825.342
## Bayesian (BIC) 10892.909 10892.909
## Sample-size adjusted Bayesian (SABIC) 10851.613 10851.613
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.031 0.000
## P-value H_0: RMSEA <= 0.050 0.982 0.999
## P-value H_0: RMSEA >= 0.080 0.001 0.000
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.030
## P-value H_0: Robust RMSEA <= 0.050 0.973
## P-value H_0: Robust RMSEA >= 0.080 0.006
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.001 0.001
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 0.500 0.039 12.897 0.000 0.641 0.624
## GRI3 0.543 0.049 11.135 0.000 0.697 0.805
## GRI5 0.494 0.039 12.712 0.000 0.633 0.649
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GRI3 ~
## Student 1.203 0.176 6.827 0.000 1.203 0.431
## GAMBLING ~
## Student -2.587 0.261 -9.909 0.000 -2.018 -0.626
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 2.976 0.111 26.768 0.000 2.976 2.898
## .GRI3 1.729 0.094 18.435 0.000 1.729 1.998
## .GRI5 2.732 0.123 22.176 0.000 2.732 2.804
## Student 0.892 0.008 105.162 0.000 0.892 2.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 0.644 0.067 9.603 0.000 0.644 0.611
## .GRI3 0.450 0.052 8.603 0.000 0.450 0.601
## .GRI5 0.549 0.049 11.105 0.000 0.549 0.578
## .GAMBLING 1.000 0.608 0.608
## Student 0.096 0.007 14.450 0.000 0.096 1.000
##
## R-Square:
## Estimate
## GRI1 0.389
## GRI3 0.399
## GRI5 0.422
## GAMBLING 0.392
#MODEL 05: ANALYSIS WITH SUM SCORE INSTEAD OF FACTOR ----------------------------
#creating sum score for GAMBLING 3-item Survey
data02 = data01
data02$GRI135sum = data02$GRI1 + data02$GRI3 + data02$GRI5
model05.syntax = "
GRI135sum ~ Student
"
model05.fit = sem(model05.syntax, data=data02, estimator = "MLR", mimic="Mplus", fixed.x=FALSE)
## Warning: lavaan->lav_model_vcov():
## The variance-covariance matrix of the estimated parameters (vcov) does not
## appear to be positive definite! The smallest eigenvalue (= -7.093836e-20)
## is smaller than zero. This may be a symptom that the model is not
## identified.
summary(model05.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 2 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 0.000 0.000
## Degrees of freedom 0 0
##
## Model Test Baseline Model:
##
## Test statistic 226.437 114.487
## Degrees of freedom 1 1
## P-value 0.000 0.000
## Scaling correction factor 1.978
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.000 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3153.864 -3153.864
## Loglikelihood unrestricted model (H1) -3153.864 -3153.864
##
## Akaike (AIC) 6317.728 6317.728
## Bayesian (BIC) 6343.715 6343.715
## Sample-size adjusted Bayesian (SABIC) 6327.832 6327.832
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 NA
## 90 Percent confidence interval - lower 0.000 NA
## 90 Percent confidence interval - upper 0.000 NA
## P-value H_0: RMSEA <= 0.050 NA NA
## P-value H_0: RMSEA >= 0.080 NA 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 0.000
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GRI135sum ~
## Student -2.773 0.260 -10.673 0.000 -2.773 -0.395
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI135sum 7.437 0.254 29.242 0.000 7.437 3.415
## Student 0.892 0.008 105.162 0.000 0.892 2.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI135sum 4.004 0.240 16.664 0.000 4.004 0.844
## Student 0.096 0.007 14.450 0.000 0.096 1.000
##
## R-Square:
## Estimate
## GRI135sum 0.156
#getting correct standardizedSolution value (nox as Student is a coded variable):
standardizedSolution(model05.fit, type="std.nox")[1,]
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 GRI135sum ~ Student -1.273 0.105 -12.106 0 -1.479 -1.067
#getting similar standardizedSolution values for model 03 (best fit--but with predictor of GRI3)
standardizedSolution(model03a.fit, type="std.nox")[5,]
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 5 GAMBLING =~ GRI5 0.654 0.063 10.435 0 0.531 0.777
#getting similar standardizedSolution values for model 02 (terrible fit, but similar in in that no predictor of GRI3 is part of model)
standardizedSolution(model02.fit, type="std.nox")[4,]
## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 4 GAMBLING ~ Student -1.745 0.135 -12.882 0 -2.011 -1.48
#Model 06: Calculation of Alpha Reliablity with Tau-Equivalent CFA Model -----------------------------
model06.syntax = "
GAMBLING =~ (loading)*GRI1 + (loading)*GRI3 + (loading)*GRI5
GRI1 ~~ (U1)*GRI1
GRI3 ~~ (U3)*GRI3
GRI5 ~~ (U5)*GRI5
GCalpha := (3*loading*loading)/( (3*loading*loading) + (U1 + U3 + U5))
"
model06.fit = sem(model06.syntax, data=data02, estimator = "MLR", mimic="Mplus", fixed.x=FALSE, std.lv = TRUE)
summary(model06.fit, fit.measures=TRUE, rsquare=TRUE, standardized=TRUE)
## lavaan 0.6-19 ended normally after 10 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
## Number of equality constraints 2
##
## Number of observations 1336
## Number of missing patterns 1
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 18.897 8.482
## Degrees of freedom 2 2
## P-value (Chi-square) 0.000 0.014
## Scaling correction factor 2.228
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 480.988 199.641
## Degrees of freedom 3 3
## P-value 0.000 0.000
## Scaling correction factor 2.409
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.965 0.967
## Tucker-Lewis Index (TLI) 0.947 0.951
##
## Robust Comparative Fit Index (CFI) 0.970
## Robust Tucker-Lewis Index (TLI) 0.954
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5264.058 -5264.058
## Scaling correction factor 1.741
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5254.609 -5254.609
## Scaling correction factor 2.236
## for the MLR correction
##
## Akaike (AIC) 10542.115 10542.115
## Bayesian (BIC) 10578.497 10578.497
## Sample-size adjusted Bayesian (SABIC) 10556.262 10556.262
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.080 0.049
## 90 Percent confidence interval - lower 0.049 0.028
## 90 Percent confidence interval - upper 0.114 0.073
## P-value H_0: RMSEA <= 0.050 0.053 0.475
## P-value H_0: RMSEA >= 0.080 0.537 0.015
##
## Robust RMSEA 0.074
## 90 Percent confidence interval - lower 0.028
## 90 Percent confidence interval - upper 0.128
## P-value H_0: Robust RMSEA <= 0.050 0.170
## P-value H_0: Robust RMSEA >= 0.080 0.485
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.040 0.040
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GAMBLING =~
## GRI1 (ldng) 0.567 0.027 20.821 0.000 0.567 0.560
## GRI3 (ldng) 0.567 0.027 20.821 0.000 0.567 0.638
## GRI5 (ldng) 0.567 0.027 20.821 0.000 0.567 0.589
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 1.823 0.028 64.871 0.000 1.823 1.801
## .GRI3 1.548 0.024 65.365 0.000 1.548 1.743
## .GRI5 1.593 0.027 59.749 0.000 1.593 1.656
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .GRI1 (U1) 0.703 0.063 11.116 0.000 0.703 0.686
## .GRI3 (U3) 0.468 0.043 10.903 0.000 0.468 0.593
## .GRI5 (U5) 0.603 0.054 11.148 0.000 0.603 0.653
## GAMBLING 1.000 1.000 1.000
##
## R-Square:
## Estimate
## GRI1 0.314
## GRI3 0.407
## GRI5 0.347
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## GCalpha 0.352 0.026 13.628 0.000 0.352 0.328