Can anyone tell me under what conditions the beta estimates differ between lm and lmer with a random intercept? I came across a situation where the fixed effect differed considerably. I thought the std errors should change but the fixed effects should remain unchanged. The difference does not seem to be due to having different cluster sizes or having a large number of clusters with a single observation.
I cannot supply the data but have concocted a simplified example below. In this case the correlation within clusters should be negligible.
library(lme4) x=c(rep(0,10),rep(1,10)) y=rnorm(length(x),mean=3100,sd=400)-200*x m=c(1,2,3,4,4,6,7,8,8,10,11,12,13,14,15,16,17,18,20,20) summary(lm(y~x)) summary(lmer(y~x+(1|m)))