[R-sig-ME] family for random coefficients in glmmADMB?

[Joshua Wiley]

Hi Ben,

Thanks for the information.  If normal is the usual case, that is
fine.  Mostly I just wanted to know what was done---from reading
Agresti's book on Categorical Data Analysis, I got the sense that
different distributions were used, but I could have just misread.

Thanks again,

Josh

On Wed, Jan 18, 2012 at 6:43 AM, Ben Bolker <bbolker at gmail.com> wrote:
> Joshua Wiley <jwiley.psych at ...> writes:
>
>> Apologies if this is an obvious question.  I have been playing with
>> some random coefficient count models using the glmmADMB package.  I
>> can specify the family for the response (poisson or negative binomial,
>> in my case), but I am wondering what distribution is assumed for the
>> random parameters?  I know it is common to use the conjugate prior of
>> the response family (gamma for poisson or beta for negative binomial),
>> but others are theoretically possible, no?
>
>  The random variables are assumed to be normally distributed
> on the linear predictor scale (as is almost always the case for GLMMs --
> there is a little bit of literature on nonparametric estimation of
> mixing/random-effects distributions, and some for different frailty
> distributions in survival analysis, but the standard definition of
> GLMMs is as I stated).  So in your case the assumed RE distribution
> would be lognormal (unless you're using a nonstandard link for your
> Poisson or NB models).
>
> If you wanted badly enough to change this it might be hackable, but
> I'm not sure how the math underlying the Laplace approximation (or
> other approximations used) would hold up under this variation.  If
> you really want to experiment with different RE distributions I think
> I would suggest the Bayesian (BUGS/JAGS etc. route).
>
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-- 
Joshua Wiley
Ph.D. Student, Health Psychology
Programmer Analyst II, Statistical Consulting Group
University of California, Los Angeles
https://joshuawiley.com/