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

[Ben Bolker]

Joshua Wiley <jwiley.psych at ...> writes:

> 
> 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.
> 

  I think it depends on whether you focus on ch 12 of Agresti (which
is about classical GLMMs) or ch 13 (which is about other kinds of mixture
models).  One possible confusion is that negative binomial models are
right at the edge of what one can define as GLMMs, because the NB
with unspecified overdispersion parameter (k) is not in the exponential
family -- NB models like those in MASS::glm.nb() use an outer loop
over possible values.  The NB mixed models that glmmADMB fits are
a bit of a hybrid -- one can think of them as models with Poisson
responses that use Gamma-distributed random effects at the
among-individual level, and log-normal distributed random effects
at all of the other levels.

   Ben

> 
> 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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