[R-sig-ME] lmer: ML and REML estimation

[Peter Dalgaard]

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
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907