[ADMB Users] NLMM Model Selection

[Chris Gast]

I hadn't thought this would be a difficult question, but perhaps I was
wrong.  I'll try and rephrase in hopes of inspiring some more interest.

1) Is it correct to say that the objective function value returned in the
.par value of a RE model is the approximation to the marginal likelihood,
post-integration?

2a) Is it correct to obtain the conditional likelihood value by
re-evaluating the likelihood function at the MLEs (for fixed parameters) and
empirical Bayes estimates of REs?

2b) If 2a is true, can this value be obtained in a single ADMB model-fit, or
do I need to first fit the model, then re-run the model using the optimum
values from the previous run and output an initial likelihood value to get
the conditional likelihood?

3) Or am I way off here?

I used to output the objective function value to the report file, but I
noticed that it did not match the value from the .par file (the former was
not the minimum).



Thanks again,

Chris Gast




-----------------------------
Chris Gast
cmgast at gmail.com


On Wed, Feb 9, 2011 at 10:49 AM, Chris Gast <cmgast at gmail.com> wrote:

> So, ADMB reports the (optimal) marginal loglikelihood approximation in
> the .par file (correct?).
>
> In order to obtain the (maximum) conditional loglikelihood value, one
> would re-evaluate the likelihood function at the MLEs along with the
> empirical Bayes estimates of RE terms.  Is that correct?
>
> If the latter statement is correct, could this be obtained by
> outputting the final objective function value (following SE
> estimation) in the report file?  Or do I need to re-evaluate the
> function after fitting the model?
>
>
>
> Thanks again,
>
> Chris Gast
>
>
>
> -----------------------------
> Chris Gast
> cmgast at gmail.com
>
>
>
> On Sun, Feb 6, 2011 at 11:54 AM, Ben Bolker <bbolker at gmail.com> wrote:
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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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