[ADMB Users] NLMM Model Selection

[Ben Bolker]

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On 11-02-06 02:47 PM, dave fournier wrote:
> Something that has always bothered me about this random effects stuff
> is that if I fit a model with a neg bin dist it is just a parametric
> model with one more parameter than a Poisson with a Poisson at the
> end. I can do standard LR tests and random effects never come up. But
> that is just because one can do the integration analytically so that 
> the RE nature or interpretation never comes up. How can that be?  Why
> are other RE models different? 

  It really depends what you want to do. Dealing with random effects by
integrating them out (when that is possible) is called a marginal model,
and there are plenty of methods that take this approach (e.g.
generalized estimating equations).  Sometimes you're actually interested
in estimates of the 'random effects', which disappear in the marginal
approach. In some cases the marginal approach doesn't give you separate
estimates for different processes (e.g. variances from different random
effects components) that you would ideally like to distinguish.
Sometimes you wouldn't mind a marginal approach but it's just too hard.
 There are also differences in interpretation -- for example, estimated
slopes from marginal models (which give the overall expected,
unconditional slope) are shallower than those from 'non-marginal'
(conditional? don't know the right term) models, where one is estimating
the slope conditional on individuals within a group.

  Alan Agresti's book on Categorical Data Analysis has a very nice
discussion of this stuff, I think.

  Ben Bolker
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