#install.packages("tmvnsim", dependencies = TRUE)
#install.packages("mnormt", dependencies = TRUE)
#install.packages("lavaan", dependencies = TRUE) #lavaan package depends on tmvnsim and mnormt
#install.packages("semPlot", dependencies = TRUE)
library(lavaan)
library(semPlot) #package to visulize SEM
df <- read.csv("~/Dropbox/Labs/SLM637/esports viewership.csv") #note that you need to specify the full file address here in R Markdown (regardless your working directory setup)
#str(df)
#no missing value issue involved. If yes, please refer back to the PCA file.
model_spec = "
# measurement model
SKI =~ SKI_1 + SKI_2 + SKI_3 + SKI_4 + SKI_5 + SKI_6
EXC =~ EXC_1 + EXC_2 + EXC_3 + EXC_4
# relationship model
Hours_Watch ~ SKI + EXC
"
#no need to specify the relationship between SKI and EXC. It will be automatically included in the estimation.
model <- sem(model_spec, df)
summary(model, fit.measures=TRUE, standardized = TRUE) #standardized=T gives the standardized factor loadings in the measurement model and standardized regression coefficients. So you can compare the loading values/coefficient values across different items/variables: compare factor loadings with factor loadings; compare coefficients with coefficients.
## lavaan 0.6.15 ended normally after 32 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Number of observations 633
##
## Model Test User Model:
##
## Test statistic 120.681
## Degrees of freedom 42
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 5458.952
## Degrees of freedom 55
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.985
## Tucker-Lewis Index (TLI) 0.981
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -9161.967
## Loglikelihood unrestricted model (H1) -9101.626
##
## Akaike (AIC) 18371.933
## Bayesian (BIC) 18478.744
## Sample-size adjusted Bayesian (SABIC) 18402.547
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.054
## 90 Percent confidence interval - lower 0.043
## 90 Percent confidence interval - upper 0.066
## P-value H_0: RMSEA <= 0.050 0.248
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.036
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SKI =~
## SKI_1 1.000 1.152 0.840
## SKI_2 0.945 0.036 25.898 0.000 1.088 0.836
## SKI_3 0.980 0.043 22.542 0.000 1.129 0.764
## SKI_4 1.011 0.037 27.573 0.000 1.164 0.869
## SKI_5 0.883 0.039 22.878 0.000 1.016 0.772
## SKI_6 0.984 0.037 26.454 0.000 1.134 0.848
## EXC =~
## EXC_1 1.000 1.042 0.854
## EXC_2 1.110 0.033 33.746 0.000 1.157 0.934
## EXC_3 1.174 0.034 34.886 0.000 1.223 0.950
## EXC_4 1.188 0.039 30.759 0.000 1.239 0.891
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Hours_Watch ~
## SKI -0.076 0.048 -1.572 0.116 -0.087 -0.067
## EXC 0.182 0.053 3.451 0.001 0.190 0.146
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SKI ~~
## EXC 0.349 0.054 6.496 0.000 0.291 0.291
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .SKI_1 0.552 0.038 14.518 0.000 0.552 0.294
## .SKI_2 0.508 0.035 14.623 0.000 0.508 0.300
## .SKI_3 0.909 0.057 15.898 0.000 0.909 0.416
## .SKI_4 0.438 0.032 13.563 0.000 0.438 0.244
## .SKI_5 0.702 0.044 15.802 0.000 0.702 0.405
## .SKI_6 0.504 0.035 14.317 0.000 0.504 0.282
## .EXC_1 0.404 0.026 15.607 0.000 0.404 0.271
## .EXC_2 0.197 0.017 11.886 0.000 0.197 0.128
## .EXC_3 0.162 0.016 9.995 0.000 0.162 0.098
## .EXC_4 0.396 0.027 14.590 0.000 0.396 0.205
## .Hours_Watch 1.647 0.093 17.767 0.000 1.647 0.980
## SKI 1.326 0.103 12.843 0.000 1.000 1.000
## EXC 1.087 0.082 13.315 0.000 1.000 1.000
semPaths(model) #Model graph without estimation
semPaths(model, "std", residuals = T) #Model graph with standardized coefficients and residuals
