It is better to send questions such as this to the
R-SIG-Mixed-Models@R-project.org mailing list where a wider variety of
opinions can be obtained.  I am cc:ing the list on this reply.


On Thu, Mar 20, 2014 at 9:23 AM, Adianto Pangaribuan <
adianto_pangaribuan@yahoo.com> wrote:

> Prof,  My name is Adianto Pangaribuan. I'm undergraduated student from
> Indonesia. I want to ask something about MLE and RMLE.
> I want to compare estimation MLE and RMLE for Linear Mixed Effects Model
> using AIC, BIC and value log-likelihood. The result, best estimation is
> MLE. Am I wrong with it? But, many books say that the RMLE is preferred
> estimation than MLE because the variance component is biased. Can you help
> me prof, why the MLE is best estimation?
>

The AIC and BIC criteria are derived from the log-likelihood of the model's
parameters given the observed data.  The MLE's, as the name implies, are
chosen to maximize the log-likelihood.  The REML estimates are chosen to
optimize another criterion.  So, by definition, the log-likelihood at the
MLE's must be at least as large as the log-likelihood at the REML
estimates.  If you compare the two estimators on the basis of the
log-likelihood or criteria derived from it the MLE's will always be
superior.

In other words, it doesn't make sense to compare MLE's and REML estimates
using these criteria.

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