[R-sig-ME] lmer: ML and REML estimation
p.dalgaard at biostat.ku.dk
Thu Mar 26 09:57:20 CET 2009
Douglas Bates wrote:
> I would claim that maximum likelihood estimates are well-defined for
> generalized linear mixed models but REML estimates are not. (It is
> true that Mary Lindstrom and I did offer a definition of REML
> estimates for nonlinear mixed-effects models but I consider that a
> youthful indiscretion and I didn't inhale. :-)
> The bottom line is that REML only makes sense for linear mixed-effects models.
Presumably this requires some qualification.
It's not like people haven't tried. I have seen at least one paper
attempting to make REML work with some GLM cases (it's been a while, but
I think I can still locate the pile in which I put it...).
What is certainly true is that it is not usually possible to achieve the
clean separation of the sample space into the linear mean value subspace
and its orthogonal (or quotient space if you like), that REML relies on.
In the other hand, it's not like the biases that REML tries to overcome
suddenly disappears when things become nonlinear, so _some_ form of
adjusted likelihood may be appropriate, it's just not necessarily REML.
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
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