# Why the standard errors are different between SEM and ols regression

This is a mediation model with a categorical exogenous variable. I am trying to compare the results by running SEM and regression. The third step regression was conducted and I found the estimates were the same, but the standard errors were different. Any idea? Thanks for your help.

library(rms)

library(lavaan)

y <- seq(1:10)
m <- c(1,4,5,3,6,3,5,7,4,9)
race <- c(1,3,2,1,2,3,3,2,2,2)
data <- data.frame(cbind(y, m, race))
A <- as.data.frame(model.matrix( y~ m*factor(race), data = data))
data$$rd2 <- A[,3] data$$rd3 <- A[,4]
data$$inter2 <- A[,5] data$$inter3 <- A[,6]
ols(y~m+rd2+rd3+inter2+inter3, data=data)
model <- 'm~rd2+rd3
y~m+rd2+rd3+inter2+inter3
m~~0*y'
fit<-sem(model, data=data)
summary(fit)
• Why do you set the residual covariance between m any to zero (m~~0*y)? This is basic model assumption that would be made anyhow. Therefore, I assume this is not what you actually intended to do. – StoryTeller0815 Aug 3 '19 at 6:22