[R-sig-ME] Model selection GLM vs. GLMMs

[Ben Bolker]

Nelida Villasenor <nelida.villasenor at ...> writes:

> 
> Dear all,
 
> I'm performing model selection based on AICc on a set of GLMMs that
> only vary in their fixed effects. The data comes from 12 transects
> (5 measures along each transect), then each transect is modelled as
> a random effect "+(1|transect)". As the response variable was
> proportions (presences/n), I fitted the models using binomial family
> and the total number of points (n) as weights.
 
> Given that some models had boundary problems

  meaning singular fits (estimated zero variances and/or +/- 1 correlations
and/or values of estimated theta=0) ?

> I ran the model
> selection on a set of GLMs instead of GLMMs. The results were almost
> identical in terms of the list of models with the highest support
> (for 7 response variables where model selection was performed
> independently).
 
> I'm wondering which approach is correct? Or, as my results show, it
> does not really matter, because the random effect does not change in
> my GLMMs?

  I think you would find a bit of disagreement among experts about the
best procedure -- whether it would be to drop random effects until you
got a sensible non-singular fit, or to keep them in even though
they're singular.  Keep in mind that you should get the same estimates
with a GLM or a GLMM if the variance estimates are all zero ... Since
it doesn't sound as though it affects your einference/model selection
on the fixed effects, I would say you could choose either approach
(and explain clearly what you did).

  Ben Bolker