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.
Best Answer
Section 7.3 of the excellent book Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN by Fränzi Korner-Nievergelt et al. (2015) states the following in connection with REML and ML:
"For our purposes, the relevant difference between the two methods is that the ML estimates are unbiased for the fixed effects but biased for the random effects, whereas the REML estimates are biased for the fixed effects and unbiased for the random effects. However, when sample size is large compared to the number of model parameters, the differences between the ML and REML estimates become negligible. As a guideline, use REML if the interest is in the random effects (variance parameters) and ML if the interested is in the fixed effects."