[R-sig-ME] single argument anova for GLMMs not yet implemented

[David Duffy]

On Fri, 12 Dec 2008, Andrew Robinson wrote:

> Hi Drew,
>
> On Thu, Dec 11, 2008 at 03:52:06PM -0600, Andrew J Tyre wrote:
>> I also like the explanation of quasi-likelihood vs. glmm, but I can say
>> from an ecological perspective I frequently encounter situations in which
>> I have included all the random effects of blocks, plots, times etc, and
>> still have massive amounts of overdispersion. A student in my Ecological
>> Statistics class examined repeated counts of grasshoppers in plots that
>> have or have not received nitrogen addition. A poisson family glmm gives a
>> nice account of the effects of total veg biomass, date, and nitrogen
>> addition, but the residual deviance  is  > 1700 for a sample size of about
>> 400. I would love to be able to fit a negative binomial model in that
>> case; I typically resort to using WinBUGS and MCMC to do this, but that is
>> beyond what I can get my students to do in a one semester course.
>
> This looks like a promising example (so to speak) ... have you tried
> fitting a poisson family glmm and a negative binomial hierarchical
> model to these data in WinBUGS?  if so, how do the models compare
> within that framework?
>
>> I have encountered situations in which even using a negative binomial
>> model (for counts) or beta-binomial type model ( for proportion of success
>> data) are insufficient to explain the variability in ecological
>> situations. In these cases I usually have reason to believe that there is
>> a discrete mixture going on - ie the observations are coming from two or
>> more distinct populations which have not been distinguished by anything
>> the observer can record, or thought to record (immune status for parasite
>> hosts, for example). I have tried quasi- family models in those cases, but
>> always felt a little uncomfortable drawing much in the way of inference. I
>> understand likelihood!
>
> I'd suggest that if you have reason to believe that you have an
> underlying discrete mixture but no way to tease out the identity, then
> any modelling should be treated with great caution!  Or maybe EM would
> help?
>

There has been a certain amount of work on models where the 
distribution of the random effects is unspecified -- modelled 
as a mixture which is estimated by nonparametric ML (a paper by Murray 
Aitken in Biometrics is the earliest I know of).  These could probably 
slurp up overdispersion of the type described.  I imagine they are only 
tractable for simple models for the random effects (eg group 
membership/clusters).

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v