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.



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
fit<-sem(model, data=data)
  • $\begingroup$ 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. $\endgroup$ – StoryTeller0815 Aug 3 '19 at 6:22

Typically, standard errors need to account for multi-stage procedures. It is the same for two-stage least squares; standard errors in the second stage do not adequately account for the sampling noise introduced by the fact that you have a "generated regressor", which also has sampling noise in it. Thus, multi-step procedures tend to have too low standard errors.

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  • $\begingroup$ Thanks, Superpronker. If I understand correctly, the standard errors from the ols are more trustworthy? $\endgroup$ – Andrew Dec 13 '16 at 21:35
  • 1
    $\begingroup$ Other way around, OLS standard errors do not account for the two step nature of the problem. $\endgroup$ – Superpronker Dec 14 '16 at 4:56
  • $\begingroup$ But when you take a look at the standard errors, it's the OLS regression that shows inflated standard errors... Isn't multicollinearity a better explanation? Some of the variables are extremely correlated. $\endgroup$ – StoryTeller0815 Aug 3 '19 at 6:22

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