[R-sig-ME] glmm AIC/LogLik reliability
Ben Bolker
bolker at ufl.edu
Thu Jan 29 23:45:31 CET 2009
Andrew Beckerman wrote:
> Perhaps the question was not clear enough (I helped Duncan try and
> articulate this....)
>
> Lets assume that we maintain random effects structure in all models,
> but we have a large multiple regression problem in the fixed effects
> (say 8 variables potentially affecting reproduction in a population).
Maintaining the random effects structure takes care of the issue
of counting degrees of freedom for random effects, EXCEPT in the
finite-data (AICc or equivalent) case.
>
> Can we assume that the LogLik calculations work in this instance?
I would guess that you would get correct log-likelihoods/deviances
in this case, if you use ML rather than REML. (These will essentially
be marginal deviances, integrated over the random effects.)
> If we can say yes to this, then we can assume that some calculation of
> AIC is possible. The adjustement of the LogLik by # of paramters can
> be manipulated by the researcher, deciding on what df means to him or
> her, etc. The crux of the questions is not whether inference is
> correct, but whether the bits/mechanics about getting an AIC value for
> a set of nested models with the same random effects are internally
> consistent.
If you're not worried about inference, then I'd say you're OK.
Likelihood/deviance should correctly rank models with the same degree
of complexity. But I don't see how you're going to be able to
confidently rank models unless (a) your Ns are so large
that you can assert that you are in "asymptopia" (and N here means
both (?) number of random-effects units and total sample size)
or (b) you can figure out how to inflate penalties based on
"residual df" ...
As always, I'm happy to be corrected.
[blatant plug: I have a GLMM paper available online now
<http://dx.doi.org/10.1016/j.tree.2008.10.008> although much of what
it says will be well known to everyone here ...]
Ben Bolker
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