[R] generalized linear mixed models - how to compare?

[Prof Brian Ripley]

On Wed, 20 Apr 2005, Nestor Fernandez wrote:

> Dear all,
>
> Thanks for the responses to this post.
> I understand that the topic still requires more research. However, I am a 
> non-statistician in a desperate need to analyze my ecological data with the 
> currently available tools. Please excuse again my non-expert question: Would 
> I commit a huge mistake if I use the likelihood estimates from GLMM as a 
> "good approximate" to the "real" log-likelihood, and therefore calculate AIC 
> from it? Should I use instead any of the existing corrections for AIC?

Yes.  This is not ML fitting and they are not accurate approximations 
and there is no supporting theory.  That has all already be stated.

The problem is not in the tools but in mastery in using them.

> Otherwise, can you suggest any other model selection approach suitable for 
> generalized mixed models?

Try suggesting to your statistical consultant that (s)he might use Wald 
tests to drop terms.

> Deepayan Sarkar wrote:
>> On Sunday 17 April 2005 12:07, Prof Brian Ripley wrote:
>> 
>>> On Sun, 17 Apr 2005, Deepayan Sarkar wrote:
>> 
>> 
>> [...]
>> 
>> 
>>>> GLMM uses (mostly) the same procedure to get parameter estimates,
>>>> but as a final step calculates the likelihood for the correct model
>>>> for those estimates (so the likelihood reported by it should be
>>>> fairly reliable).
>>> 
>>> Well, perhaps but I need more convincing.  The likelihood involves
>>> many high-dimensional non-analytic integrations, so I do not see how
>>> GLMM can do those integrals -- it might approximate them, but that
>>> would not be `calculates the likelihood for the correct model'.  It
>>> would be helpful to have a clarification of this claim.  (Our
>>> experiments show that finding an accurate value of the log-likelihood
>>> is difficult and many available pieces of software differ in their
>>> values by large amounts.)
>> 
>> 
>> You are right, of course. I left out too much trying to be brief (partly 
>> because this issue has been discussed before). I'll try to refrain from 
>> giving such partial answers in future.
>> 
>> Deepayan
>> 
>> [...]


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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