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

[Ben Bolker]

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).