I have estimated a linear mixed model with REML and ML estimation. However, the estimated coefficients do not differ. The standard errors of the coefficients are slightly higher for the REML estimation. The regression output is the following:
My question is why don't the estimated coefficients differ? I thought the ML estimation is unbiased in case of the fixed effects, but biased for the REMl estimation.
The estimated models in R are: REML: fit_mixed<-lmer(formula=Brutto ~ Alter + Geschlecht + AusVolPra+ Deutsch + Englisch + Schuljahre + Kind + Religion+ Kurs + Analphabet+(1|Herkunftsland), data = daten)
ML:fit_mixed2<-lmer(Brutto ~ Alter + Geschlecht + AusVolPra+ Deutsch+ Englisch + Schuljahre + Kind + Religion+ Kurs + Analphabet+(1|Herkunftsland), data=daten, REML=FALSE)
Herkunftsland is the random effect.
Furthermore I noticed that the variance of the random effect Herkunftsland is 0 for the REML estimation but non-zero for the ML estimation. Why is this the case?
Thanks in advance for your help.