Structural Equation Modeling | Exercise 3
1 What we are going to cover
- Ex.1 – Measurement equivalence
- Ex.2 – Multi-group mediation analysis
2 Data
The data set used throughout is the European Social Survey ESS4-2008 Edition 4.5 was released on 1 December 2018. We will restrict the analysis to the Belgian case. Each line in the data set represents a Belgian respondent. The full dataset an documentation can be found on the ESS website
Codebook:
gvslvol Standard of living for the old, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
gvslvue Standard of living for the unemployed, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
gvhlthc Health care for the sick, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
gvcldcr Child care services for working parents, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
gvjbevn Job for everyone, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
gvpdlwk Paid leave from work to care for sick family, governments’ responsibility (0 Not governments’ responsibility at all - 10 Entirely governments’ responsibility)
sbstrec Social benefits/services place too great strain on economy (1 Agree strongly - 5 Disagree strongly)
sbbsntx Social benefits/services cost businesses too much in taxes/charges (1 Agree strongly - 5 Disagree strongly)
sbprvpv Social benefits/services prevent widespread poverty (1 Agree strongly - 5 Disagree strongly)
sbeqsoc Social benefits/services lead to a more equal society (1 Agree strongly - 5 Disagree strongly)
sbcwkfm Social benefits/services make it easier to combine work and family (1 Agree strongly - 5 Disagree strongly)
sblazy Social benefits/services make people lazy (1 Agree strongly - 5 Disagree strongly)
sblwcoa Social benefits/services make people less willing care for one another (1 Agree strongly - 5 Disagree strongly)
sblwlka Social benefits/services make people less willing look after themselves/family (1 Agree strongly - 5 Disagree strongly)
In addition, we will use some other variables
agea Respondent’s age
eduyrs Years of full-time education completed
gndr Gender (1 Male, 2 Female)
hinctnta Household’s total net income, all sources (Deciles of the actual household income range in Belgium)
gincdif Government should reduce differences in income levels (1 Agree strongly - 5 Disagree strongly)
dfincac Large differences in income acceptable to reward talents and efforts (1 Agree strongly - 5 Disagree strongly)
smdfslv For fair society, differences in standard of living should be small (1 Agree strongly - 5 Disagree strongly)
3 Environment preparation
First, let’s load the necessary packages to load, manipulate, visualize and analyse the data.
# Uncomment this once if you need to install the packages on your system
### DATA MANIPULATION ###
# install.packages("haven") # data import from spss
# install.packages("dplyr") # data manipulation
# install.packages("psych") # descriptives
# install.packages("stringr") # string manipulation
# install.packages("purrr") # table manipulation
### MODELING ###
# install.packages("lavaan") # SEM modelling
### VISUALIZATION ###
# install.packages("tidySEM") # plotting SEM models
# Load the packages
### DATA MANIPULATION ###
library("haven")
library("dplyr")
library("psych")
library('stringr')
### MODELING ###
library("lavaan")
### VISUALIZATION ###
library("tidySEM")
library("purrr") 4 Ex.1 – Measurement equivalence
- Manually specify a configural invariance model for male and female
- Manually specify a configural invariance model where you estimate residual covariances for the manifest indicators
- Manually specify a metric invariance model for male and female
- Manually specify a scalar invariance model for male and female
- Explain differences in Degrees of Freedom for all the fitted models
- Add gvcldcr and see if the model reaches scalar invariance
- Request modification indices for the gvcldcr scalar model and interpret them (OPTIONAL)
Configural invariance model
ess_df <- haven::read_sav("https://github.com/albertostefanelli/SEM_labs/raw/master/data/ESS4_belgium.sav")
# lavaan requires the grouping variable to be a factor
# gender is coded as 1 Male, 2 Female
ess_df$gndr <- factor(ess_df$gndr,
levels = c("1", "2"), # levels
labels = c("Male", "Female")) # labels
model_ws_config <-'
# Factor loadings all freely estimated for each group (marker fixed to 1 by defult)
welf_supp =~ gvslvol + gvslvue + gvhlthc
# Item intercepts all freely estimated for each group
gvslvol ~ 1
gvslvue ~ 1
gvhlthc ~ 1
# Residual variances all freely estimated for each group
gvslvol ~~ gvslvol
gvslvue ~~ gvslvue
gvhlthc ~~ gvhlthc
# Factor mean (intercept) fixed to zero in each group
welf_supp ~ 0
'
fit_configural <- cfa(model_ws_config,
data = ess_df,
group = "gndr")
summary(fit_configural,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 51 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 18
Number of observations per group: Used Total
Male 861 864
Female 891 896
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Test statistic for each group:
Male 0.000
Female 0.000
Model Test Baseline Model:
Test statistic 1066.962
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9425.388
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 18886.776
Bayesian (BIC) 18985.209
Sample-size adjusted Bayesian (BIC) 18928.025
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 RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.215 0.802
gvslvue 0.657 0.067 9.780 0.000 0.799 0.399
gvhlthc 0.974 0.087 11.183 0.000 1.183 0.805
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.851 0.052 152.113 0.000 7.851 5.184
.gvslvue 6.005 0.068 88.020 0.000 6.005 3.000
.gvhlthc 8.057 0.050 160.839 0.000 8.057 5.481
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.817 0.130 6.271 0.000 0.817 0.356
.gvslvue 3.369 0.171 19.702 0.000 3.369 0.841
.gvhlthc 0.760 0.123 6.161 0.000 0.760 0.352
welf_supp 1.477 0.162 9.142 0.000 1.000 1.000
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.259 0.869
gvslvue 0.523 0.068 7.706 0.000 0.659 0.360
gvhlthc 0.801 0.090 8.906 0.000 1.008 0.685
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.892 0.049 162.542 0.000 7.892 5.445
.gvslvue 6.112 0.061 99.650 0.000 6.112 3.338
.gvhlthc 8.007 0.049 162.306 0.000 8.007 5.437
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.514 0.171 3.008 0.003 0.514 0.245
.gvslvue 2.918 0.146 20.011 0.000 2.918 0.870
.gvhlthc 1.151 0.121 9.480 0.000 1.151 0.531
welf_supp 1.586 0.195 8.141 0.000 1.000 1.000Configural invariance model with residual covariances
model_ws_config_cov <-'
# Factor loadings all freely estimated for each group (marker fixed to 1 by defult)
welf_supp =~ gvslvol + gvslvue + gvhlthc
# Item intercepts all freely estimated for each group
gvslvol ~ 1
gvslvue ~ 1
gvhlthc ~ 1
# Residual variances all freely estimated for each group
gvslvol ~~ gvslvol
gvslvue ~~ gvslvue
gvhlthc ~~ gvhlthc
# Residual covariance all freely estimated for each group
gvslvol ~~ gvslvue
gvslvol ~~ gvhlthc
gvslvue ~~ gvhlthc
# Factor mean (intercept) fixed to zero in each group
welf_supp ~ 0
'
fit_configural_cov <- cfa(model_ws_config_cov,
data = ess_df,
group = "gndr")
summary(fit_configural_cov,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 24
Number of observations per group: Used Total
Male 861 864
Female 891 896
Model Test User Model:
Test statistic NA
Degrees of freedom -6
P-value (Unknown) NA
Test statistic for each group:
Male NA
Female NA
User Model versus Baseline Model:
Comparative Fit Index (CFI) NA
Tucker-Lewis Index (TLI) NA
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9425.388
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 18898.776
Bayesian (BIC) 19030.020
Sample-size adjusted Bayesian (BIC) 18953.774
Root Mean Square Error of Approximation:
RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 0.966 0.638
gvslvue 0.920 NA 0.888 0.444
gvhlthc 1.058 NA 1.022 0.695
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol ~~
.gvslvue 0.113 NA 0.113 0.054
.gvhlthc 0.451 NA 0.451 0.366
.gvslvue ~~
.gvhlthc 0.037 NA 0.037 0.020
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.851 NA 7.851 5.184
.gvslvue 6.005 NA 6.005 3.000
.gvhlthc 8.057 NA 8.057 5.481
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 1.361 NA 1.361 0.593
.gvslvue 3.218 NA 3.218 0.803
.gvhlthc 1.116 NA 1.116 0.516
welf_supp 0.933 NA 1.000 1.000
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 0.934 0.644
gvslvue 0.780 NA 0.729 0.398
gvhlthc 0.993 NA 0.927 0.629
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol ~~
.gvslvue 0.150 NA 0.150 0.081
.gvhlthc 0.405 NA 0.405 0.319
.gvslvue ~~
.gvhlthc -0.010 NA -0.010 -0.005
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.892 NA 7.892 5.445
.gvslvue 6.112 NA 6.112 3.338
.gvhlthc 8.007 NA 8.007 5.437
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 1.229 NA 1.229 0.585
.gvslvue 2.821 NA 2.821 0.842
.gvhlthc 1.309 NA 1.309 0.604
welf_supp 0.872 NA 1.000 1.000Metric invariance model
model_ws_metric <-'
# Factor loadings set equal
welf_supp =~ c(L1,L1)*gvslvol + c(L2,L2)*gvslvue + c(L3,L3)*gvhlthc
# Item intercepts all freely estimated for each group
gvslvol ~ 1
gvslvue ~ 1
gvhlthc ~ 1
# Residual variances all freely estimated for each group
gvslvol ~~ gvslvol
gvslvue ~~ gvslvue
gvhlthc ~~ gvhlthc
# Factor mean (intercept) fixed to zero in each group
welf_supp ~ 0
'
fit_metric <- cfa(model_ws_metric,
data = ess_df,
group = "gndr")
summary(fit_metric,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 45 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 18
Number of equality constraints 2
Number of observations per group: Used Total
Male 861 864
Female 891 896
Model Test User Model:
Test statistic 2.555
Degrees of freedom 2
P-value (Chi-square) 0.279
Test statistic for each group:
Male 1.155
Female 1.400
Model Test Baseline Model:
Test statistic 1066.962
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.999
Tucker-Lewis Index (TLI) 0.998
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9426.665
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 18885.331
Bayesian (BIC) 18972.827
Sample-size adjusted Bayesian (BIC) 18921.997
Root Mean Square Error of Approximation:
RMSEA 0.018
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.072
P-value RMSEA <= 0.05 0.784
Standardized Root Mean Square Residual:
SRMR 0.012
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol (L1) 1.000 1.268 0.834
gvslvue (L2) 0.595 0.048 12.472 0.000 0.754 0.379
gvhlthc (L3) 0.897 0.062 14.381 0.000 1.138 0.776
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.851 0.052 151.451 0.000 7.851 5.161
.gvslvue 6.005 0.068 88.528 0.000 6.005 3.017
.gvhlthc 8.057 0.050 161.316 0.000 8.057 5.498
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.706 0.118 5.964 0.000 0.706 0.305
.gvslvue 3.392 0.170 19.924 0.000 3.392 0.856
.gvhlthc 0.853 0.100 8.522 0.000 0.853 0.397
welf_supp 1.608 0.148 10.875 0.000 1.000 1.000
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol (L1) 1.000 1.188 0.823
gvslvue (L2) 0.595 0.048 12.472 0.000 0.707 0.384
gvhlthc (L3) 0.897 0.062 14.381 0.000 1.066 0.721
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.892 0.048 163.261 0.000 7.892 5.469
.gvslvue 6.112 0.062 99.094 0.000 6.112 3.320
.gvhlthc 8.007 0.050 161.742 0.000 8.007 5.419
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.670 0.107 6.243 0.000 0.670 0.322
.gvslvue 2.890 0.144 20.073 0.000 2.890 0.853
.gvhlthc 1.047 0.097 10.821 0.000 1.047 0.480
welf_supp 1.412 0.131 10.815 0.000 1.000 1.000Scalar invariance model
model_ws_scalar <-'
# Factor loadings set equal
welf_supp =~ c(L1,L1)*gvslvol + c(L2,L2)*gvslvue + c(L3,L3)*gvhlthc
# Item intercepts set equal
gvslvol ~ c(I1,I1)*1
gvslvue ~ c(I2,I2)*1
gvhlthc ~ c(I3,I3)*1
# Redidual variances all freely estimated for each group
gvslvol ~~ gvslvol
gvslvue ~~ gvslvue
gvhlthc ~~ gvhlthc
# Factor mean (intercept) estimated in G2 and fixed to zero in G1
welf_supp ~ c(0,NA)*0
'
fit_scalar <- cfa(model_ws_scalar,
data = ess_df,
group = "gndr")
summary(fit_scalar,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 47 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 19
Number of equality constraints 5
Number of observations per group: Used Total
Male 861 864
Female 891 896
Model Test User Model:
Test statistic 6.199
Degrees of freedom 4
P-value (Chi-square) 0.185
Test statistic for each group:
Male 3.053
Female 3.145
Model Test Baseline Model:
Test statistic 1066.962
Degrees of freedom 6
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.998
Tucker-Lewis Index (TLI) 0.997
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9428.487
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 18884.975
Bayesian (BIC) 18961.534
Sample-size adjusted Bayesian (BIC) 18917.057
Root Mean Square Error of Approximation:
RMSEA 0.025
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.061
P-value RMSEA <= 0.05 0.850
Standardized Root Mean Square Residual:
SRMR 0.017
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol (L1) 1.000 1.270 0.835
gvslvue (L2) 0.594 0.048 12.441 0.000 0.754 0.379
gvhlthc (L3) 0.894 0.062 14.356 0.000 1.135 0.775
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol (I1) 7.865 0.050 156.652 0.000 7.865 5.171
.gvslvue (I2) 6.059 0.050 120.178 0.000 6.059 3.043
.gvhlthc (I3) 8.028 0.047 171.303 0.000 8.028 5.478
welf_supp 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.700 0.119 5.893 0.000 0.700 0.303
.gvslvue 3.396 0.170 19.924 0.000 3.396 0.856
.gvhlthc 0.859 0.100 8.594 0.000 0.859 0.400
welf_supp 1.614 0.148 10.873 0.000 1.000 1.000
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol (L1) 1.000 1.190 0.825
gvslvue (L2) 0.594 0.048 12.441 0.000 0.707 0.384
gvhlthc (L3) 0.894 0.062 14.356 0.000 1.064 0.720
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol (I1) 7.865 0.050 156.652 0.000 7.865 5.450
.gvslvue (I2) 6.059 0.050 120.178 0.000 6.059 3.290
.gvhlthc (I3) 8.028 0.047 171.303 0.000 8.028 5.432
welf_supp 0.014 0.066 0.207 0.836 0.012 0.012
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.666 0.108 6.173 0.000 0.666 0.320
.gvslvue 2.893 0.144 20.074 0.000 2.893 0.853
.gvhlthc 1.053 0.097 10.888 0.000 1.053 0.482
welf_supp 1.417 0.131 10.812 0.000 1.000 1.000Scalar invariance model with the addition of gvcldcr
model_ws_gvcldcr <- '
welf_supp =~ gvslvol + gvslvue + gvhlthc + gvcldcr
'
fit_conf_gvcldcr <- cfa(model_ws_gvcldcr,
data = ess_df,
group = "gndr"
)
fit_metric_gvcldcr <- cfa(model_ws_gvcldcr,
data = ess_df,
group = "gndr",
group.equal = c("loadings")
)
fit_scalar_gvcldcr <- cfa(model_ws_gvcldcr,
data = ess_df,
group = "gndr",
group.equal = c("loadings",
"intercepts")
)
# Let's compare the nested model using the anova function
table_anova <- list(anova(fit_conf_gvcldcr, fit_metric_gvcldcr),
anova(fit_metric_gvcldcr, fit_scalar_gvcldcr)) %>%
reduce(rbind) %>%
.[-c(3),]
table_anovaChi-Squared Difference Test
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
fit_conf_gvcldcr 4 25344 25475 21.641
fit_metric_gvcldcr 7 25340 25455 23.436 1.795 3 0.6160263
fit_scalar_gvcldcr 10 25353 25452 42.889 19.453 3 0.0002203 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lavTestScore(fit_scalar_gvcldcr)$test
total score test:
test X2 df p.value
1 score 21.248 7 0.003
$uni
univariate score tests:
lhs op rhs X2 df p.value
1 .p2. == .p16. 0.064 1 0.801
2 .p3. == .p17. 1.268 1 0.260
3 .p4. == .p18. 0.044 1 0.833
4 .p10. == .p24. 0.108 1 0.743
5 .p11. == .p25. 0.881 1 0.348
6 .p12. == .p26. 5.498 1 0.019
7 .p13. == .p27. 15.885 1 0.000parTable(fit_scalar_gvcldcr) id lhs op rhs user block group free ustart exo label plabel start est se
1 1 welf_supp =~ gvslvol 1 1 1 0 1 0 .p1. 1.000 1.000 0.000
2 2 welf_supp =~ gvslvue 1 1 1 1 NA 0 .p2. .p2. 0.646 0.607 0.043
3 3 welf_supp =~ gvhlthc 1 1 1 2 NA 0 .p3. .p3. 0.831 0.885 0.042
4 4 welf_supp =~ gvcldcr 1 1 1 3 NA 0 .p4. .p4. 0.624 0.685 0.040
5 5 gvslvol ~~ gvslvol 0 1 1 4 NA 0 .p5. 1.144 0.644 0.083
6 6 gvslvue ~~ gvslvue 0 1 1 5 NA 0 .p6. 2.008 3.404 0.171
7 7 gvhlthc ~~ gvhlthc 0 1 1 6 NA 0 .p7. 1.077 0.914 0.075
8 8 gvcldcr ~~ gvcldcr 0 1 1 7 NA 0 .p8. 1.772 2.823 0.145
9 9 welf_supp ~~ welf_supp 0 1 1 8 NA 0 .p9. 0.050 1.623 0.122
10 10 gvslvol ~1 0 1 1 9 NA 0 .p10. .p10. 7.855 7.851 0.050
11 11 gvslvue ~1 0 1 1 10 NA 0 .p11. .p11. 6.006 6.049 0.051
12 12 gvhlthc ~1 0 1 1 11 NA 0 .p12. .p12. 8.060 8.016 0.047
13 13 gvcldcr ~1 0 1 1 12 NA 0 .p13. .p13. 7.116 7.286 0.049
14 14 welf_supp ~1 0 1 1 0 0 0 .p14. 0.000 0.000 0.000
15 15 welf_supp =~ gvslvol 1 2 2 0 1 0 .p15. 1.000 1.000 0.000
16 16 welf_supp =~ gvslvue 1 2 2 13 NA 0 .p2. .p16. 0.600 0.607 0.043
17 17 welf_supp =~ gvhlthc 1 2 2 14 NA 0 .p3. .p17. 0.933 0.885 0.042
18 18 welf_supp =~ gvcldcr 1 2 2 15 NA 0 .p4. .p18. 0.752 0.685 0.040
19 19 gvslvol ~~ gvslvol 0 2 2 16 NA 0 .p19. 1.051 0.716 0.078
20 20 gvslvue ~~ gvslvue 0 2 2 17 NA 0 .p20. 1.667 2.831 0.141
21 21 gvhlthc ~~ gvhlthc 0 2 2 18 NA 0 .p21. 1.088 1.039 0.075
22 22 gvcldcr ~~ gvcldcr 0 2 2 19 NA 0 .p22. 1.317 1.985 0.103
23 23 welf_supp ~~ welf_supp 0 2 2 20 NA 0 .p23. 0.050 1.408 0.108
24 24 gvslvol ~1 0 2 2 21 NA 0 .p10. .p24. 7.891 7.851 0.050
25 25 gvslvue ~1 0 2 2 22 NA 0 .p11. .p25. 6.110 6.049 0.051
26 26 gvhlthc ~1 0 2 2 23 NA 0 .p12. .p26. 8.007 8.016 0.047
27 27 gvcldcr ~1 0 2 2 24 NA 0 .p13. .p27. 7.431 7.286 0.049
28 28 welf_supp ~1 0 2 2 25 NA 0 .p28. 0.000 0.044 0.066
29 29 .p2. == .p16. 2 0 0 0 NA 0 0.000 0.000 0.000
30 30 .p3. == .p17. 2 0 0 0 NA 0 0.000 0.000 0.000
31 31 .p4. == .p18. 2 0 0 0 NA 0 0.000 0.000 0.000
32 32 .p10. == .p24. 2 0 0 0 NA 0 0.000 0.000 0.000
33 33 .p11. == .p25. 2 0 0 0 NA 0 0.000 0.000 0.000
34 34 .p12. == .p26. 2 0 0 0 NA 0 0.000 0.000 0.000
35 35 .p13. == .p27. 2 0 0 0 NA 0 0.000 0.000 0.0005 Ex.2 – Multi-group mediation analysis
- Fit a model where egalitarianism (gincdif, dfincac, smdfslv) mediates the relationship between age (agea), education (eduyrs), income (hinctnta) and welfare support (gvslvol, gvslvue, gvhlthc) in a multigroup model where all paths coefficients are free to vary across group
- Y is the dependent variable (Welfare support)
- X is a vector of predictors (age, education, income)
- M is a mediator (Egalitarianism)
- G is a grouping variable (Gender)
- Assess if the model fits the data well
- Use lavaan syntax to calculate indirect and direct effects for each predictor in each group.
- Interpret the difference in the path coefficients between male and female
- Assess if the path from Education to Egalitarianism (Path A) can be set equal across the two groups
- Assess if the Indirect effect of Education on Welfare Support (a*b) can be set equal across the two groups (OPTIONAL)
- Think of a method to assess if path coefficients are statistically different using the := operator (OPTIONAL)
All free
model_mediation_mg <- '
## Welfare Support Factor ##
welf_supp =~ gvslvol + gvslvue + gvhlthc
## Egalitarianism ##
egual =~ gincdif + dfincac + smdfslv
## Direct effect ##
welf_supp ~ c("c_inc_1", "c_inc_2")*hinctnta
welf_supp ~ c("c_age_1", "c_age_2")*agea
welf_supp ~ c("c_edu_1", "c_edu_2")*eduyrs
## Mediator ##
# Path A
egual ~ c("a_inc_1", "a_inc_2")*hinctnta
egual ~ c("a_age_1", "a_age_2")*agea
egual ~ c("a_edu_1", "a_edu_2")*eduyrs
# Path B
welf_supp ~ c("b1", "b2")*egual
## Indirect effect (a*b) ##
# G1
ab_inc_g1 := a_inc_1*b1
ab_age_g1 := a_age_1*b1
ab_edu_g1 := a_edu_1*b1
# G2
ab_inc_g2 := a_inc_2*b2
ab_age_g2 := a_age_2*b2
ab_edu_g2 := a_edu_2*b2
## Total effect c + (a*b) ##
# G1
total_inc_g1 := c_inc_1 + (a_inc_1*b1)
total_age_g1 := c_age_1 + (a_age_1*b1)
total_edu_g1 := c_edu_1 + (a_edu_1*b1)
# G1
total_inc_g2 := c_inc_2 + (a_inc_2*b2)
total_age_g2 := c_age_2 + (a_age_2*b2)
total_edu_g2 := c_edu_2 + (a_edu_2*b2)
'
fit_mediation_mg <- cfa(model_mediation_mg, # model formula
data = ess_df, # data frame
group = "gndr", # grouping variable (G)
group.equal = c("loadings") # equal loadings
)
summary(fit_mediation_mg,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 99 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 50
Number of equality constraints 4
Number of observations per group: Used Total
Male 779 864
Female 772 896
Model Test User Model:
Test statistic 138.860
Degrees of freedom 44
P-value (Chi-square) 0.000
Test statistic for each group:
Male 89.341
Female 49.519
Model Test Baseline Model:
Test statistic 1674.649
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.941
Tucker-Lewis Index (TLI) 0.912
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -14754.970
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 29601.940
Bayesian (BIC) 29847.887
Sample-size adjusted Bayesian (BIC) 29701.755
Root Mean Square Error of Approximation:
RMSEA 0.053
90 Percent confidence interval - lower 0.043
90 Percent confidence interval - upper 0.063
P-value RMSEA <= 0.05 0.310
Standardized Root Mean Square Residual:
SRMR 0.036
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.363 0.889
gvslvue (.p2.) 0.557 0.047 11.781 0.000 0.759 0.375
gvhlthc (.p3.) 0.796 0.052 15.291 0.000 1.085 0.740
egual =~
gincdif 1.000 0.709 0.654
dfincac (.p5.) -0.585 0.058 -10.007 0.000 -0.415 -0.395
smdfslv (.p6.) 0.868 0.079 11.049 0.000 0.616 0.613
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp ~
hnctnt (c_n_1) 0.021 0.025 0.857 0.392 0.015 0.036
agea (c_g_1) 0.011 0.003 3.527 0.000 0.008 0.140
eduyrs (c_d_1) 0.010 0.016 0.655 0.513 0.007 0.028
egual ~
hnctnt (a_n_1) 0.036 0.015 2.417 0.016 0.050 0.117
agea (a_g_1) -0.005 0.002 -2.606 0.009 -0.007 -0.119
eduyrs (a_d_1) 0.038 0.009 4.087 0.000 0.053 0.199
welf_supp ~
egual (b1) -0.466 0.106 -4.380 0.000 -0.242 -0.242
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.336 0.289 25.420 0.000 7.336 4.788
.gvslvue 5.667 0.175 32.382 0.000 5.667 2.803
.gvhlthc 7.626 0.233 32.792 0.000 7.626 5.199
.gincdif 1.703 0.176 9.660 0.000 1.703 1.570
.dfincac 2.854 0.109 26.119 0.000 2.854 2.717
.smdfslv 2.046 0.154 13.280 0.000 2.046 2.035
.welf_supp 0.000 0.000 0.000
.egual 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.490 0.123 3.989 0.000 0.490 0.209
.gvslvue 3.511 0.184 19.065 0.000 3.511 0.859
.gvhlthc 0.974 0.091 10.672 0.000 0.974 0.453
.gincdif 0.673 0.060 11.142 0.000 0.673 0.572
.dfincac 0.931 0.052 17.881 0.000 0.931 0.844
.smdfslv 0.632 0.050 12.709 0.000 0.632 0.625
.welf_supp 1.703 0.156 10.947 0.000 0.917 0.917
.egual 0.456 0.060 7.650 0.000 0.905 0.905
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.234 0.880
gvslvue (.p2.) 0.557 0.047 11.781 0.000 0.687 0.374
gvhlthc (.p3.) 0.796 0.052 15.291 0.000 0.982 0.682
egual =~
gincdif 1.000 0.679 0.657
dfincac (.p5.) -0.585 0.058 -10.007 0.000 -0.397 -0.375
smdfslv (.p6.) 0.868 0.079 11.049 0.000 0.589 0.626
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp ~
hnctnt (c_n_2) -0.003 0.023 -0.143 0.886 -0.003 -0.006
agea (c_g_2) 0.008 0.003 2.725 0.006 0.006 0.114
eduyrs (c_d_2) 0.035 0.015 2.263 0.024 0.028 0.101
egual ~
hnctnt (a_n_2) 0.038 0.015 2.591 0.010 0.056 0.134
agea (a_g_2) -0.002 0.002 -0.995 0.320 -0.003 -0.048
eduyrs (a_d_2) 0.012 0.010 1.178 0.239 0.017 0.061
welf_supp ~
egual (b2) -0.473 0.098 -4.820 0.000 -0.260 -0.260
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.302 0.285 25.654 0.000 7.302 5.207
.gvslvue 5.776 0.171 33.718 0.000 5.776 3.143
.gvhlthc 7.522 0.230 32.661 0.000 7.522 5.224
.gincdif 1.837 0.182 10.098 0.000 1.837 1.778
.dfincac 2.935 0.112 26.286 0.000 2.935 2.774
.smdfslv 2.119 0.158 13.379 0.000 2.119 2.253
.welf_supp 0.000 0.000 0.000
.egual 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.445 0.107 4.178 0.000 0.445 0.226
.gvslvue 2.906 0.154 18.878 0.000 2.906 0.860
.gvhlthc 1.108 0.087 12.675 0.000 1.108 0.534
.gincdif 0.607 0.056 10.794 0.000 0.607 0.569
.dfincac 0.962 0.053 18.036 0.000 0.962 0.859
.smdfslv 0.538 0.045 11.966 0.000 0.538 0.608
.welf_supp 1.394 0.132 10.594 0.000 0.916 0.916
.egual 0.444 0.057 7.790 0.000 0.963 0.963
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab_inc_g1 -0.017 0.008 -2.137 0.033 -0.012 -0.028
ab_age_g1 0.002 0.001 2.263 0.024 0.002 0.029
ab_edu_g1 -0.018 0.006 -3.046 0.002 -0.013 -0.048
ab_inc_g2 -0.018 0.008 -2.308 0.021 -0.015 -0.035
ab_age_g2 0.001 0.001 0.976 0.329 0.001 0.013
ab_edu_g2 -0.006 0.005 -1.148 0.251 -0.004 -0.016
total_inc_g1 0.004 0.024 0.180 0.857 0.003 0.007
total_age_g1 0.013 0.003 4.282 0.000 0.010 0.169
total_edu_g1 -0.007 0.015 -0.491 0.623 -0.005 -0.020
total_inc_g2 -0.021 0.023 -0.927 0.354 -0.017 -0.041
total_age_g2 0.008 0.003 3.003 0.003 0.007 0.127
total_edu_g2 0.029 0.016 1.894 0.058 0.024 0.085Path A education to Egalitarianism set equal across the two groups
model_mediation_mg_path_a <- '
## Welfare Support Factor ##
welf_supp =~ gvslvol + gvslvue + gvhlthc
## Egalitarianism ##
egual =~ gincdif + dfincac + smdfslv
## Direct effect ##
welf_supp ~ c("c_inc_1", "c_inc_2")*hinctnta
welf_supp ~ c("c_age_1", "c_age_2")*agea
welf_supp ~ c("c_edu_1", "c_edu_2")*eduyrs
## Mediator ##
# Path A
egual ~ c("a_inc_1", "a_inc_2")*hinctnta
egual ~ c("a_age_1", "a_age_2")*agea
egual ~ c("a_edu", "a_edu")*eduyrs
# Path B
welf_supp ~ c("b1", "b2")*egual
## Indirect effect (a*b) ##
# G1
ab_inc_g1 := a_inc_1*b1
ab_age_g1 := a_age_1*b1
ab_edu_g1 := a_edu*b1
# G2
ab_inc_g2 := a_inc_2*b2
ab_age_g2 := a_age_2*b2
ab_edu_g2 := a_edu*b2
## Total effect c + (a*b) ##
# G1
total_inc_g1 := c_inc_1 + (a_inc_1*b1)
total_age_g1 := c_age_1 + (a_age_1*b1)
total_edu_g1 := c_edu_1 + (a_edu*b1)
# G1
total_inc_g2 := c_inc_2 + (a_inc_2*b2)
total_age_g2 := c_age_2 + (a_age_2*b2)
total_edu_g2 := c_edu_2 + (a_edu*b2)
'
fit_mediation_mg_path_a <- cfa(model_mediation_mg_path_a, # model formula
data = ess_df, # data frame
group = "gndr", # grouping variable (G)
group.equal = c("loadings") # equal loadings
)
anova(fit_mediation_mg,
standardized=TRUE,
fit.measures = TRUE
)Chi-Squared Test Statistic (unscaled)
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
Saturated 0 0.00
Model 44 29602 29848 138.86 138.86 44 0.000000000009203 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Path B Egalitarianism to Welfare Support set equal across the two groups
model_mediation_mg_path_ab <- '
## Welfare Support Factor ##
welf_supp =~ gvslvol + gvslvue + gvhlthc
## Egalitarianism ##
egual =~ gincdif + dfincac + smdfslv
## Direct effect ##
welf_supp ~ c("c_inc_1", "c_inc_2")*hinctnta
welf_supp ~ c("c_age_1", "c_age_2")*agea
welf_supp ~ c("c_edu_1", "c_edu_2")*eduyrs
## Mediator ##
# Path A
egual ~ c("a_inc_1", "a_inc_2")*hinctnta
egual ~ c("a_age_1", "a_age_2")*agea
egual ~ c("a_edu", "a_edu")*eduyrs
# Path B
welf_supp ~ c("b", "b")*egual
## Indirect effect (a*b) ##
# G1
ab_inc_g1 := a_inc_1*b
ab_age_g1 := a_age_1*b
ab_edu_g1 := a_edu*b
# G2
ab_inc_g2 := a_inc_2*b
ab_age_g2 := a_age_2*b
ab_edu_g2 := a_edu*b
## Total effect c + (a*b) ##
# G1
total_inc_g1 := c_inc_1 + (a_inc_1*b)
total_age_g1 := c_age_1 + (a_age_1*b)
total_edu_g1 := c_edu_1 + (a_edu*b)
# G1
total_inc_g2 := c_inc_2 + (a_inc_2*b)
total_age_g2 := c_age_2 + (a_age_2*b)
total_edu_g2 := c_edu_2 + (a_edu*b)
'
fit_mediation_mg_path_ab <- cfa(model_mediation_mg_path_ab, # model formula
data = ess_df, # data frame
group = "gndr", # grouping variable (G)
group.equal = c("loadings") # equal loadings
)
anova(fit_mediation_mg_path_a,fit_mediation_mg_path_ab)Chi-Squared Difference Test
Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
fit_mediation_mg_path_a 45 29604 29844 142.63
fit_mediation_mg_path_ab 46 29602 29837 142.63 0.0011676 1 0.9727Using the := for simple slope difference
model_mediation_mg_diff <- '
## Welfare Support Factor ##
welf_supp =~ gvslvol + gvslvue + gvhlthc
## Egalitarianism ##
egual =~ gincdif + dfincac + smdfslv
## Direct effect ##
welf_supp ~ c("c_inc_1", "c_inc_2")*hinctnta
welf_supp ~ c("c_age_1", "c_age_2")*agea
welf_supp ~ c("c_edu_1", "c_edu_2")*eduyrs
## Mediator ##
# Path A
egual ~ c("a_inc_1", "a_inc_2")*hinctnta
egual ~ c("a_age_1", "a_age_2")*agea
egual ~ c("a_edu_1", "a_edu_2")*eduyrs
# Path B
welf_supp ~ c("b1", "b2")*egual
## Indirect effect (a*b) ##
# G1
ab_inc_g1 := a_inc_1*b1
ab_age_g1 := a_age_1*b1
ab_edu_g1 := a_edu_1*b1
# G2
ab_inc_g2 := a_inc_2*b2
ab_age_g2 := a_age_2*b2
ab_edu_g2 := a_edu_2*b2
## Total effect c + (a*b) ##
# G1
total_inc_g1 := c_inc_1 + (a_inc_1*b1)
total_age_g1 := c_age_1 + (a_age_1*b1)
total_edu_g1 := c_edu_1 + (a_edu_1*b1)
# G1
total_inc_g2 := c_inc_2 + (a_inc_2*b2)
total_age_g2 := c_age_2 + (a_age_2*b2)
total_edu_g2 := c_edu_2 + (a_edu_2*b2)
## Slope Differences ##
tot_edu_diff := total_edu_g1 - total_edu_g2
'
fit_mediation_mg_diff <- cfa(model_mediation_mg_diff, # model formula
data = ess_df, # data frame
group = "gndr", # grouping variable (G)
group.equal = c("loadings") # equal loadings
)
summary(fit_mediation_mg_diff,
standardized=TRUE,
fit.measures = TRUE
)lavaan 0.6-10 ended normally after 99 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 50
Number of equality constraints 4
Number of observations per group: Used Total
Male 779 864
Female 772 896
Model Test User Model:
Test statistic 138.860
Degrees of freedom 44
P-value (Chi-square) 0.000
Test statistic for each group:
Male 89.341
Female 49.519
Model Test Baseline Model:
Test statistic 1674.649
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.941
Tucker-Lewis Index (TLI) 0.912
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -14754.970
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 29601.940
Bayesian (BIC) 29847.887
Sample-size adjusted Bayesian (BIC) 29701.755
Root Mean Square Error of Approximation:
RMSEA 0.053
90 Percent confidence interval - lower 0.043
90 Percent confidence interval - upper 0.063
P-value RMSEA <= 0.05 0.310
Standardized Root Mean Square Residual:
SRMR 0.036
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Group 1 [Male]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.363 0.889
gvslvue (.p2.) 0.557 0.047 11.781 0.000 0.759 0.375
gvhlthc (.p3.) 0.796 0.052 15.291 0.000 1.085 0.740
egual =~
gincdif 1.000 0.709 0.654
dfincac (.p5.) -0.585 0.058 -10.007 0.000 -0.415 -0.395
smdfslv (.p6.) 0.868 0.079 11.049 0.000 0.616 0.613
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp ~
hnctnt (c_n_1) 0.021 0.025 0.857 0.392 0.015 0.036
agea (c_g_1) 0.011 0.003 3.527 0.000 0.008 0.140
eduyrs (c_d_1) 0.010 0.016 0.655 0.513 0.007 0.028
egual ~
hnctnt (a_n_1) 0.036 0.015 2.417 0.016 0.050 0.117
agea (a_g_1) -0.005 0.002 -2.606 0.009 -0.007 -0.119
eduyrs (a_d_1) 0.038 0.009 4.087 0.000 0.053 0.199
welf_supp ~
egual (b1) -0.466 0.106 -4.380 0.000 -0.242 -0.242
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.336 0.289 25.420 0.000 7.336 4.788
.gvslvue 5.667 0.175 32.382 0.000 5.667 2.803
.gvhlthc 7.626 0.233 32.792 0.000 7.626 5.199
.gincdif 1.703 0.176 9.660 0.000 1.703 1.570
.dfincac 2.854 0.109 26.119 0.000 2.854 2.717
.smdfslv 2.046 0.154 13.280 0.000 2.046 2.035
.welf_supp 0.000 0.000 0.000
.egual 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.490 0.123 3.989 0.000 0.490 0.209
.gvslvue 3.511 0.184 19.065 0.000 3.511 0.859
.gvhlthc 0.974 0.091 10.672 0.000 0.974 0.453
.gincdif 0.673 0.060 11.142 0.000 0.673 0.572
.dfincac 0.931 0.052 17.881 0.000 0.931 0.844
.smdfslv 0.632 0.050 12.709 0.000 0.632 0.625
.welf_supp 1.703 0.156 10.947 0.000 0.917 0.917
.egual 0.456 0.060 7.650 0.000 0.905 0.905
Group 2 [Female]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp =~
gvslvol 1.000 1.234 0.880
gvslvue (.p2.) 0.557 0.047 11.781 0.000 0.687 0.374
gvhlthc (.p3.) 0.796 0.052 15.291 0.000 0.982 0.682
egual =~
gincdif 1.000 0.679 0.657
dfincac (.p5.) -0.585 0.058 -10.007 0.000 -0.397 -0.375
smdfslv (.p6.) 0.868 0.079 11.049 0.000 0.589 0.626
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
welf_supp ~
hnctnt (c_n_2) -0.003 0.023 -0.143 0.886 -0.003 -0.006
agea (c_g_2) 0.008 0.003 2.725 0.006 0.006 0.114
eduyrs (c_d_2) 0.035 0.015 2.263 0.024 0.028 0.101
egual ~
hnctnt (a_n_2) 0.038 0.015 2.591 0.010 0.056 0.134
agea (a_g_2) -0.002 0.002 -0.995 0.320 -0.003 -0.048
eduyrs (a_d_2) 0.012 0.010 1.178 0.239 0.017 0.061
welf_supp ~
egual (b2) -0.473 0.098 -4.820 0.000 -0.260 -0.260
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 7.302 0.285 25.654 0.000 7.302 5.207
.gvslvue 5.776 0.171 33.718 0.000 5.776 3.143
.gvhlthc 7.522 0.230 32.661 0.000 7.522 5.224
.gincdif 1.837 0.182 10.098 0.000 1.837 1.778
.dfincac 2.935 0.112 26.286 0.000 2.935 2.774
.smdfslv 2.119 0.158 13.379 0.000 2.119 2.253
.welf_supp 0.000 0.000 0.000
.egual 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.gvslvol 0.445 0.107 4.178 0.000 0.445 0.226
.gvslvue 2.906 0.154 18.878 0.000 2.906 0.860
.gvhlthc 1.108 0.087 12.675 0.000 1.108 0.534
.gincdif 0.607 0.056 10.794 0.000 0.607 0.569
.dfincac 0.962 0.053 18.036 0.000 0.962 0.859
.smdfslv 0.538 0.045 11.966 0.000 0.538 0.608
.welf_supp 1.394 0.132 10.594 0.000 0.916 0.916
.egual 0.444 0.057 7.790 0.000 0.963 0.963
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab_inc_g1 -0.017 0.008 -2.137 0.033 -0.012 -0.028
ab_age_g1 0.002 0.001 2.263 0.024 0.002 0.029
ab_edu_g1 -0.018 0.006 -3.046 0.002 -0.013 -0.048
ab_inc_g2 -0.018 0.008 -2.308 0.021 -0.015 -0.035
ab_age_g2 0.001 0.001 0.976 0.329 0.001 0.013
ab_edu_g2 -0.006 0.005 -1.148 0.251 -0.004 -0.016
total_inc_g1 0.004 0.024 0.180 0.857 0.003 0.007
total_age_g1 0.013 0.003 4.282 0.000 0.010 0.169
total_edu_g1 -0.007 0.015 -0.491 0.623 -0.005 -0.020
total_inc_g2 -0.021 0.023 -0.927 0.354 -0.017 -0.041
total_age_g2 0.008 0.003 3.003 0.003 0.007 0.127
total_edu_g2 0.029 0.016 1.894 0.058 0.024 0.085
tot_edu_diff -0.037 0.022 -1.700 0.089 -0.029 -0.105