Objective
Replicate study reported by LaBarbera et al 2020, originally applied without the use of SEM.
Method: CB-SEM using R's Lavaan Package. The semPlots and semTools Package were used for visualizations.
Summary: Model inspired on the La Barbera's data, on the assessment of Sustainability awareness through the attitudes toward energy saving, and the implications on intention:
Data: La Barbera, F. Moderating Role of Control in the Theory of Planned Behavior: A Replication and Extension [Dataset] [Data set]. ZPID (Leibniz Institute for Psychology Information). https://doi.org/10.23668/psycharchives.2759
Data acquisition
datat<-read_sav('LaBarbera2020.sav')
CFA - confirmatory factor analysis
For simplicity, the adjustment and verification for each construct is not presented. We present just the fit for CFA with the all measurement models already adjusted.
Model<-"intention=~v_34+v_26+v_13+v_16+v_20
attitude=~v_18+v_39+v_14+v_21+v_30
subjNorm=~v_38+v_22+v_19+v_35+v_17+v_24+v_27+v_29+v_31+v_33
BehControl=~v_25+v_28+v_15
v_34~~v_26
v_13~~v_16
v_34~~v_16
v_21~~v_30
v_38~~v_22
v_38~~v_19
v_22~~v_19
v_19~~v_17
v_35~~v_24"
fit<-cfa(Model,data)
summary(fit, fit.measures=TRUE)
## lavaan 0.6-12 ended normally after 60 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 61
##
## Number of observations 399
##
## Model Test User Model:
##
## Test statistic 597.693
## Degrees of freedom 215
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8615.675
## Degrees of freedom 253
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.954
## Tucker-Lewis Index (TLI) 0.946
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -13103.074
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 26328.148
## Bayesian (BIC) 26571.474
## Sample-size adjusted Bayesian (BIC) 26377.918
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.067
## 90 Percent confidence interval - lower 0.060
## 90 Percent confidence interval - upper 0.073
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.051
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## intention =~
## v_34 1.000
## v_26 1.054 0.033 31.520 0.000
## v_13 0.767 0.040 19.105 0.000
## v_16 0.951 0.038 25.240 0.000
## v_20 1.101 0.037 29.989 0.000
## attitude =~
## v_18 1.000
## v_39 1.017 0.040 25.351 0.000
## v_14 0.914 0.039 23.364 0.000
## v_21 0.869 0.049 17.666 0.000
## v_30 0.825 0.043 19.354 0.000
## subjNorm =~
## v_38 1.000
## v_22 1.088 0.045 23.954 0.000
## v_19 0.917 0.046 19.817 0.000
## v_35 1.117 0.071 15.818 0.000
## v_17 0.657 0.083 7.951 0.000
## v_24 0.756 0.064 11.750 0.000
## v_27 1.134 0.071 15.891 0.000
## v_29 1.115 0.070 16.009 0.000
## v_31 1.147 0.070 16.288 0.000
## v_33 1.035 0.072 14.461 0.000
## BehControl =~
## v_25 1.000
## v_28 1.113 0.044 25.409 0.000
## v_15 0.788 0.053 14.919 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 ~~
## .v_26 0.113 0.036 3.111 0.002
## .v_13 ~~
## .v_16 0.143 0.040 3.530 0.000
## .v_34 ~~
## .v_16 -0.083 0.026 -3.156 0.002
## .v_21 ~~
## .v_30 0.380 0.056 6.799 0.000
## .v_38 ~~
## .v_22 1.055 0.103 10.290 0.000
## .v_19 1.081 0.105 10.259 0.000
## .v_22 ~~
## .v_19 0.994 0.105 9.483 0.000
## .v_19 ~~
## .v_17 0.407 0.090 4.495 0.000
## .v_35 ~~
## .v_24 0.194 0.058 3.373 0.001
## intention ~~
## attitude 1.595 0.133 11.956 0.000
## subjNorm 1.165 0.125 9.349 0.000
## BehControl 1.512 0.130 11.654 0.000
## attitude ~~
## subjNorm 1.030 0.114 9.060 0.000
## BehControl 1.318 0.118 11.175 0.000
## subjNorm ~~
## BehControl 0.900 0.107 8.432 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 0.410 0.041 9.908 0.000
## .v_26 0.581 0.052 11.208 0.000
## .v_13 0.908 0.069 13.169 0.000
## .v_16 0.476 0.043 11.143 0.000
## .v_20 0.426 0.041 10.455 0.000
## .v_18 0.445 0.042 10.686 0.000
## .v_39 0.471 0.044 10.770 0.000
## .v_14 0.525 0.045 11.711 0.000
## .v_21 1.105 0.085 13.053 0.000
## .v_30 0.775 0.061 12.775 0.000
## .v_38 1.538 0.116 13.202 0.000
## .v_22 1.586 0.121 13.074 0.000
## .v_19 1.842 0.134 13.705 0.000
## .v_35 0.735 0.063 11.698 0.000
## .v_17 3.018 0.217 13.927 0.000
## .v_24 1.327 0.099 13.428 0.000
## .v_27 0.734 0.063 11.660 0.000
## .v_29 0.670 0.058 11.512 0.000
## .v_31 0.613 0.055 11.097 0.000
## .v_33 1.091 0.086 12.754 0.000
## .v_25 0.450 0.047 9.654 0.000
## .v_28 0.381 0.049 7.732 0.000
## .v_15 1.287 0.097 13.233 0.000
## intention 1.924 0.165 11.640 0.000
## attitude 1.625 0.146 11.155 0.000
## subjNorm 1.449 0.186 7.792 0.000
## BehControl 1.562 0.143 10.928 0.000
Note how the measurement models are fitting well. The following present the visualization using the semPlot package.
parTable<-parameterEstimates(fit,standardized=TRUE)%>%as.data.frame()
table2<-parTable[!parTable$lhs==parTable$rhs,]
table2$sig=ifelse(table2$pvalue<0.001,'***',
ifelse(table2$pvalue<0.01,'**',
ifelse(table2$pvalue<0.05,'*','')
)
)
b<-ifelse(table2$pvalue<=0.05,paste0(round(table2$std.all,3), table2$sig),"")
semPlot::semPaths(fit,what='std',layout='circle2',
edgeLabels=b,
residuals=FALSE,
whatLabels = "std",
shapeMan='rectangle',
sizeMan = 5, sizeMan2=2,
edge.label.cex = 0.5,label.cex=1,
curve=TRUE,
nCharNodes = 0,fade=FALSE,
shapeLat='ellipse',
sizeLat = 13,sizeLat2=4)
#SEM
The Structural Equation Model is conducted adding the path model to the CFA model.
modelSEM<-"intention~attitude+subjNorm+BehControl
intention=~v_34+v_26+v_13+v_16+v_20
attitude=~v_18+v_39+v_14+v_21+v_30
subjNorm=~v_38+v_22+v_19+v_35+v_17+v_24+v_27+v_29+v_31+v_33
BehControl=~v_25+v_28+v_15
v_34~~v_26
v_13~~v_16
v_34~~v_16
v_21~~v_30
v_38~~v_22
v_38~~v_19
v_22~~v_19
v_19~~v_17
v_35~~v_24"
fit_SEM=sem(modelSEM,data)
summary(fit_SEM,fit.meas=TRUE)
## lavaan 0.6-12 ended normally after 51 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 61
##
## Number of observations 399
##
## Model Test User Model:
##
## Test statistic 597.693
## Degrees of freedom 215
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8615.675
## Degrees of freedom 253
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.954
## Tucker-Lewis Index (TLI) 0.946
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -13103.074
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 26328.148
## Bayesian (BIC) 26571.474
## Sample-size adjusted Bayesian (BIC) 26377.918
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.067
## 90 Percent confidence interval - lower 0.060
## 90 Percent confidence interval - upper 0.073
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.051
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## intention =~
## v_34 1.000
## v_26 1.054 0.033 31.520 0.000
## v_13 0.767 0.040 19.105 0.000
## v_16 0.951 0.038 25.240 0.000
## v_20 1.101 0.037 29.989 0.000
## attitude =~
## v_18 1.000
## v_39 1.017 0.040 25.351 0.000
## v_14 0.914 0.039 23.364 0.000
## v_21 0.869 0.049 17.666 0.000
## v_30 0.825 0.043 19.354 0.000
## subjNorm =~
## v_38 1.000
## v_22 1.088 0.045 23.954 0.000
## v_19 0.917 0.046 19.817 0.000
## v_35 1.117 0.071 15.819 0.000
## v_17 0.657 0.083 7.951 0.000
## v_24 0.756 0.064 11.750 0.000
## v_27 1.134 0.071 15.891 0.000
## v_29 1.115 0.070 16.009 0.000
## v_31 1.147 0.070 16.288 0.000
## v_33 1.035 0.072 14.461 0.000
## BehControl =~
## v_25 1.000
## v_28 1.113 0.044 25.409 0.000
## v_15 0.788 0.053 14.919 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## intention ~
## attitude 0.539 0.064 8.415 0.000
## subjNorm 0.159 0.041 3.886 0.000
## BehControl 0.421 0.060 7.067 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 ~~
## .v_26 0.113 0.036 3.111 0.002
## .v_13 ~~
## .v_16 0.143 0.040 3.530 0.000
## .v_34 ~~
## .v_16 -0.083 0.026 -3.157 0.002
## .v_21 ~~
## .v_30 0.380 0.056 6.799 0.000
## .v_38 ~~
## .v_22 1.055 0.103 10.290 0.000
## .v_19 1.081 0.105 10.259 0.000
## .v_22 ~~
## .v_19 0.994 0.105 9.483 0.000
## .v_19 ~~
## .v_17 0.407 0.090 4.495 0.000
## .v_35 ~~
## .v_24 0.194 0.058 3.373 0.001
## attitude ~~
## subjNorm 1.030 0.114 9.060 0.000
## BehControl 1.318 0.118 11.175 0.000
## subjNorm ~~
## BehControl 0.900 0.107 8.432 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 0.410 0.041 9.908 0.000
## .v_26 0.581 0.052 11.208 0.000
## .v_13 0.908 0.069 13.169 0.000
## .v_16 0.476 0.043 11.143 0.000
## .v_20 0.426 0.041 10.455 0.000
## .v_18 0.445 0.042 10.686 0.000
## .v_39 0.471 0.044 10.770 0.000
## .v_14 0.525 0.045 11.711 0.000
## .v_21 1.105 0.085 13.053 0.000
## .v_30 0.775 0.061 12.775 0.000
## .v_38 1.538 0.116 13.202 0.000
## .v_22 1.586 0.121 13.074 0.000
## .v_19 1.842 0.134 13.705 0.000
## .v_35 0.735 0.063 11.698 0.000
## .v_17 3.018 0.217 13.927 0.000
## .v_24 1.327 0.099 13.428 0.000
## .v_27 0.734 0.063 11.660 0.000
## .v_29 0.670 0.058 11.512 0.000
## .v_31 0.613 0.055 11.097 0.000
## .v_33 1.091 0.086 12.754 0.000
## .v_25 0.450 0.047 9.654 0.000
## .v_28 0.381 0.049 7.732 0.000
## .v_15 1.287 0.097 13.233 0.000
## .intention 0.242 0.033 7.340 0.000
## attitude 1.625 0.146 11.155 0.000
## subjNorm 1.449 0.186 7.792 0.000
## BehControl 1.562 0.143 10.928 0.000
Considering it fits well, we can proceed to interpretation and visualization.
parTable<-parameterEstimates(fit_SEM,standardized=TRUE)%>%as.data.frame()
table2<-parTable[!parTable$lhs==parTable$rhs,]
table2$sig=ifelse(table2$pvalue<0.001,'***',
ifelse(table2$pvalue<0.01,'**',
ifelse(table2$pvalue<0.05,'*','')
)
)
b<-ifelse(table2$pvalue<=0.05,paste0(round(table2$std.all,3), table2$sig),"")
semPlot::semPaths(fit_SEM,rotation=2,structural=FALSE,edgeLabels=b,
what='std',shapeLat='ellipse',
sizeLat=15,sizeLat2=3,nCharNodes=0)
Preparing for Moderation
We need to create a new data.frame with the interaction indicators
#
moderator<-semTools::indProd(data = data,
var1 = c( "v_25", "v_28","v_15"), #Bhcontrol
var2 = c("v_18","v_39", "v_14"), #Attitude #those with higher loadings
match = T, #use match-paired approach (it produces the product of the first indicators of each variable, the product of the second indicator of each latent variable...
meanC = T, # mean centering the main effect indicator before making the products
residualC = T, #residual centering the products by the main effect indicators
doubleMC = T)
moderator<-semTools::indProd(data = moderator,
var1 = c("v_38", "v_22" ,"v_19"), #subjNorm
var2 = c("v_18","v_39", "v_14"), #Attitude #those with higher loadings
match = T, #use match-paired approach (it produces the product of the first indicators of each variable, the product of the second indicator of each latent variable...
meanC = T, # mean centering the main effect indicator before making the products
residualC = T, #residual centering the products by the main effect indicators
doubleMC = T)
CFA moderators
It is always a good idea to check if the moderator terms fit well at CFA before including in the SEM model
Model=paste0("BhC_x_Att=~v_25.v_18+v_28.v_39+v_15.v_14",'\n',
"subjNorm_x_Att=~v_38.v_18+v_22.v_39+v_19.v_14"
)
fit<-cfa(Model,moderator)
summary(fit, fit.measures=TRUE)
## lavaan 0.6-12 ended normally after 39 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 399
##
## Model Test User Model:
##
## Test statistic 54.759
## Degrees of freedom 8
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1165.112
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.959
## Tucker-Lewis Index (TLI) 0.924
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5122.606
## Loglikelihood unrestricted model (H1) -5095.227
##
## Akaike (AIC) 10271.212
## Bayesian (BIC) 10323.068
## Sample-size adjusted Bayesian (BIC) 10281.819
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.121
## 90 Percent confidence interval - lower 0.092
## 90 Percent confidence interval - upper 0.152
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.039
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## BhC_x_Att =~
## v_25.v_18 1.000
## v_28.v_39 0.922 0.052 17.721 0.000
## v_15.v_14 0.751 0.051 14.803 0.000
## subjNorm_x_Att =~
## v_38.v_18 1.000
## v_22.v_39 0.852 0.058 14.611 0.000
## v_19.v_14 0.836 0.056 14.873 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## BhC_x_Att ~~
## subjNorm_x_Att 3.279 0.358 9.152 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .v_25.v_18 0.534 0.214 2.497 0.013
## .v_28.v_39 3.125 0.288 10.849 0.000
## .v_15.v_14 3.829 0.301 12.728 0.000
## .v_38.v_18 2.218 0.279 7.936 0.000
## .v_22.v_39 2.846 0.269 10.597 0.000
## .v_19.v_14 2.488 0.244 10.200 0.000
## BhC_x_Att 5.601 0.481 11.639 0.000
## subjNorm_x_Att 4.934 0.534 9.240 0.000
CFA all
And also if there is no unexpected correlation with the original variables (that’s frequent), and adjust properly before SEM.
Model<-"intention=~v_34+v_26+v_13+v_16+v_20
attitude=~v_18+v_39+v_14+v_21+v_30
subjNorm=~v_38+v_22+v_19+v_35+v_17+v_24+v_27+v_29+v_31+v_33
BehControl=~v_25+v_28+v_15
BhC_x_Att=~v_25.v_18+v_28.v_39+v_15.v_14
subjNorm_x_Att=~v_38.v_18+v_22.v_39+v_19.v_14
v_34~~v_26
v_13~~v_16
v_34~~v_16
v_21~~v_30
v_38~~v_22
v_38~~v_19
v_22~~v_19
v_19~~v_17
v_35~~v_24"
fit<-cfa(Model,moderator)
summary(fit, fit.measures=TRUE)
## lavaan 0.6-12 ended normally after 91 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
##
## Number of observations 399
##
## Model Test User Model:
##
## Test statistic 861.097
## Degrees of freedom 353
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 10011.255
## Degrees of freedom 406
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.947
## Tucker-Lewis Index (TLI) 0.939
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -18214.768
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 36593.536
## Bayesian (BIC) 36920.631
## Sample-size adjusted Bayesian (BIC) 36660.441
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.060
## 90 Percent confidence interval - lower 0.055
## 90 Percent confidence interval - upper 0.065
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.046
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## intention =~
## v_34 1.000
## v_26 1.054 0.033 31.540 0.000
## v_13 0.770 0.040 19.166 0.000
## v_16 0.952 0.038 25.240 0.000
## v_20 1.104 0.037 30.032 0.000
## attitude =~
## v_18 1.000
## v_39 1.017 0.040 25.339 0.000
## v_14 0.915 0.039 23.377 0.000
## v_21 0.869 0.049 17.650 0.000
## v_30 0.825 0.043 19.365 0.000
## subjNorm =~
## v_38 1.000
## v_22 1.088 0.045 23.953 0.000
## v_19 0.917 0.046 19.821 0.000
## v_35 1.117 0.071 15.822 0.000
## v_17 0.658 0.083 7.967 0.000
## v_24 0.758 0.064 11.784 0.000
## v_27 1.135 0.071 15.902 0.000
## v_29 1.114 0.070 16.001 0.000
## v_31 1.147 0.070 16.293 0.000
## v_33 1.033 0.072 14.444 0.000
## BehControl =~
## v_25 1.000
## v_28 1.112 0.044 25.438 0.000
## v_15 0.791 0.053 15.009 0.000
## BhC_x_Att =~
## v_25.v_18 1.000
## v_28.v_39 0.918 0.051 17.864 0.000
## v_15.v_14 0.746 0.050 14.844 0.000
## subjNorm_x_Att =~
## v_38.v_18 1.000
## v_22.v_39 0.863 0.058 14.807 0.000
## v_19.v_14 0.838 0.056 14.925 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 ~~
## .v_26 0.119 0.036 3.280 0.001
## .v_13 ~~
## .v_16 0.141 0.040 3.502 0.000
## .v_34 ~~
## .v_16 -0.080 0.026 -3.064 0.002
## .v_21 ~~
## .v_30 0.380 0.056 6.804 0.000
## .v_38 ~~
## .v_22 1.055 0.103 10.293 0.000
## .v_19 1.081 0.105 10.260 0.000
## .v_22 ~~
## .v_19 0.994 0.105 9.486 0.000
## .v_19 ~~
## .v_17 0.406 0.090 4.493 0.000
## .v_35 ~~
## .v_24 0.191 0.058 3.317 0.001
## intention ~~
## attitude 1.593 0.133 11.950 0.000
## subjNorm 1.164 0.125 9.347 0.000
## BehControl 1.509 0.130 11.650 0.000
## BhC_x_Att 0.080 0.175 0.456 0.648
## subjNorm_x_Att -0.185 0.173 -1.068 0.286
## attitude ~~
## subjNorm 1.030 0.114 9.060 0.000
## BehControl 1.317 0.118 11.177 0.000
## BhC_x_Att 0.003 0.164 0.016 0.987
## subjNorm_x_Att -0.001 0.162 -0.007 0.994
## subjNorm ~~
## BehControl 0.900 0.107 8.435 0.000
## BhC_x_Att -0.146 0.154 -0.947 0.344
## subjNorm_x_Att -0.098 0.152 -0.646 0.518
## BehControl ~~
## BhC_x_Att 0.000 0.162 0.000 1.000
## subjNorm_x_Att 0.109 0.160 0.682 0.495
## BhC_x_Att ~~
## subjNorm_x_Att 3.267 0.357 9.145 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 0.416 0.041 10.083 0.000
## .v_26 0.586 0.052 11.310 0.000
## .v_13 0.903 0.069 13.179 0.000
## .v_16 0.478 0.043 11.226 0.000
## .v_20 0.421 0.040 10.477 0.000
## .v_18 0.445 0.042 10.702 0.000
## .v_39 0.472 0.044 10.784 0.000
## .v_14 0.524 0.045 11.711 0.000
## .v_21 1.107 0.085 13.059 0.000
## .v_30 0.774 0.061 12.776 0.000
## .v_38 1.537 0.116 13.203 0.000
## .v_22 1.587 0.121 13.077 0.000
## .v_19 1.842 0.134 13.705 0.000
## .v_35 0.735 0.063 11.698 0.000
## .v_17 3.016 0.217 13.926 0.000
## .v_24 1.322 0.098 13.422 0.000
## .v_27 0.732 0.063 11.653 0.000
## .v_29 0.673 0.058 11.529 0.000
## .v_31 0.612 0.055 11.096 0.000
## .v_33 1.096 0.086 12.765 0.000
## .v_25 0.451 0.046 9.728 0.000
## .v_28 0.384 0.049 7.848 0.000
## .v_15 1.279 0.097 13.227 0.000
## .v_25.v_18 0.501 0.210 2.382 0.017
## .v_28.v_39 3.145 0.286 10.987 0.000
## .v_15.v_14 3.849 0.301 12.796 0.000
## .v_38.v_18 2.264 0.276 8.213 0.000
## .v_22.v_39 2.782 0.265 10.516 0.000
## .v_19.v_14 2.510 0.243 10.348 0.000
## intention 1.918 0.165 11.618 0.000
## attitude 1.624 0.146 11.152 0.000
## subjNorm 1.449 0.186 7.793 0.000
## BehControl 1.561 0.143 10.927 0.000
## BhC_x_Att 5.634 0.480 11.740 0.000
## subjNorm_x_Att 4.889 0.530 9.222 0.000
SEM with moderation study
modelSEM<-paste0(
'intention~attitude+subjNorm+BehControl+BhC_x_Att+subjNorm_x_Att
', '\n',Model)
fit_SEM=sem(modelSEM,moderator)
summary(fit_SEM,fit.meas=TRUE)
## lavaan 0.6-12 ended normally after 81 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 82
##
## Number of observations 399
##
## Model Test User Model:
##
## Test statistic 861.097
## Degrees of freedom 353
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 10011.255
## Degrees of freedom 406
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.947
## Tucker-Lewis Index (TLI) 0.939
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -18214.768
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 36593.536
## Bayesian (BIC) 36920.631
## Sample-size adjusted Bayesian (BIC) 36660.441
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.060
## 90 Percent confidence interval - lower 0.055
## 90 Percent confidence interval - upper 0.065
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.046
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## intention =~
## v_34 1.000
## v_26 1.054 0.033 31.540 0.000
## v_13 0.770 0.040 19.166 0.000
## v_16 0.952 0.038 25.240 0.000
## v_20 1.104 0.037 30.032 0.000
## attitude =~
## v_18 1.000
## v_39 1.017 0.040 25.338 0.000
## v_14 0.915 0.039 23.377 0.000
## v_21 0.869 0.049 17.649 0.000
## v_30 0.825 0.043 19.365 0.000
## subjNorm =~
## v_38 1.000
## v_22 1.088 0.045 23.953 0.000
## v_19 0.917 0.046 19.821 0.000
## v_35 1.117 0.071 15.822 0.000
## v_17 0.658 0.083 7.967 0.000
## v_24 0.758 0.064 11.784 0.000
## v_27 1.135 0.071 15.902 0.000
## v_29 1.114 0.070 16.001 0.000
## v_31 1.147 0.070 16.293 0.000
## v_33 1.033 0.072 14.444 0.000
## BehControl =~
## v_25 1.000
## v_28 1.112 0.044 25.438 0.000
## v_15 0.791 0.053 15.009 0.000
## BhC_x_Att =~
## v_25.v_18 1.000
## v_28.v_39 0.918 0.051 17.864 0.000
## v_15.v_14 0.746 0.050 14.844 0.000
## subjNorm_x_Att =~
## v_38.v_18 1.000
## v_22.v_39 0.863 0.058 14.807 0.000
## v_19.v_14 0.838 0.056 14.925 0.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## intention ~
## attitude 0.522 0.063 8.271 0.000
## subjNorm 0.159 0.040 3.945 0.000
## BehControl 0.441 0.059 7.452 0.000
## BhC_x_Att 0.072 0.020 3.632 0.000
## subjNorm_x_Att -0.092 0.022 -4.118 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 ~~
## .v_26 0.119 0.036 3.280 0.001
## .v_13 ~~
## .v_16 0.141 0.040 3.502 0.000
## .v_34 ~~
## .v_16 -0.080 0.026 -3.064 0.002
## .v_21 ~~
## .v_30 0.380 0.056 6.804 0.000
## .v_38 ~~
## .v_22 1.055 0.103 10.293 0.000
## .v_19 1.081 0.105 10.260 0.000
## .v_22 ~~
## .v_19 0.994 0.105 9.486 0.000
## .v_19 ~~
## .v_17 0.406 0.090 4.493 0.000
## .v_35 ~~
## .v_24 0.191 0.058 3.317 0.001
## attitude ~~
## subjNorm 1.030 0.114 9.060 0.000
## BehControl 1.317 0.118 11.177 0.000
## BhC_x_Att 0.003 0.164 0.016 0.987
## subjNorm_x_Att -0.001 0.162 -0.007 0.994
## subjNorm ~~
## BehControl 0.900 0.107 8.435 0.000
## BhC_x_Att -0.146 0.154 -0.947 0.344
## subjNorm_x_Att -0.098 0.152 -0.646 0.518
## BehControl ~~
## BhC_x_Att 0.000 0.162 0.000 1.000
## subjNorm_x_Att 0.109 0.160 0.682 0.495
## BhC_x_Att ~~
## subjNorm_x_Att 3.267 0.357 9.145 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .v_34 0.416 0.041 10.083 0.000
## .v_26 0.586 0.052 11.310 0.000
## .v_13 0.903 0.069 13.179 0.000
## .v_16 0.478 0.043 11.226 0.000
## .v_20 0.421 0.040 10.477 0.000
## .v_18 0.445 0.042 10.702 0.000
## .v_39 0.472 0.044 10.784 0.000
## .v_14 0.524 0.045 11.711 0.000
## .v_21 1.107 0.085 13.059 0.000
## .v_30 0.774 0.061 12.776 0.000
## .v_38 1.537 0.116 13.203 0.000
## .v_22 1.587 0.121 13.077 0.000
## .v_19 1.842 0.134 13.705 0.000
## .v_35 0.735 0.063 11.698 0.000
## .v_17 3.016 0.217 13.926 0.000
## .v_24 1.322 0.098 13.422 0.000
## .v_27 0.732 0.063 11.653 0.000
## .v_29 0.673 0.058 11.529 0.000
## .v_31 0.612 0.055 11.096 0.000
## .v_33 1.096 0.086 12.765 0.000
## .v_25 0.451 0.046 9.728 0.000
## .v_28 0.384 0.049 7.848 0.000
## .v_15 1.279 0.097 13.227 0.000
## .v_25.v_18 0.501 0.210 2.382 0.017
## .v_28.v_39 3.145 0.286 10.987 0.000
## .v_15.v_14 3.849 0.301 12.796 0.000
## .v_38.v_18 2.264 0.276 8.213 0.000
## .v_22.v_39 2.782 0.265 10.516 0.000
## .v_19.v_14 2.510 0.243 10.348 0.000
## .intention 0.213 0.031 6.778 0.000
## attitude 1.624 0.146 11.151 0.000
## subjNorm 1.449 0.186 7.793 0.000
## BehControl 1.561 0.143 10.927 0.000
## BhC_x_Att 5.634 0.480 11.740 0.000
## subjNorm_x_Att 4.889 0.530 9.222 0.000
Considering the model fits well, we can proceed with the interpretations.
parTable<-parameterEstimates(fit_SEM,standardized=TRUE)%>%as.data.frame()
table2<-parTable[!parTable$lhs==parTable$rhs,]
table2$sig=ifelse(table2$pvalue<0.001,'***',
ifelse(table2$pvalue<0.01,'**',
ifelse(table2$pvalue<0.05,'*','')
)
)
b<-ifelse(table2$pvalue<=0.05,paste0(round(table2$std.all,3), table2$sig),"")
semPlot::semPaths(fit_SEM,rotation=2,structural=FALSE,edgeLabels=b,
what='std',shapeLat='ellipse',
sizeLat=15,sizeLat2=3,nCharNodes=0)
Illustration on the moderation effect
The major objectives in moderation study is focused in how the moderator is able (or not) to change the independent variable’s effect on the dependent variable, graphically illustrated as a change in the slope.
probe <- semTools::probe2WayMC(fit_SEM, nameX = c("attitude", "BehControl", "BhC_x_Att"),
nameY = "intention", modVar = "BehControl", valProbe = c(-1, 0, 1))
semTools::plotProbe(probe,xlim=c(-1.5,1.5),xlab='attitude',ylab='intention')
