[R] Mixed-effects model for overdispersed count data?

[Ben Bolker]

Marie-Hélène Hachey <marie_helene48 <at> hotmail.com> writes:

> 
> 
> Hi,
> 
> I have to analyse the number of provisioning trips to nestlings
> according to a number of biological and
> environmental factors. I was thinking of building a mixed-effects model 
> with species and nestid as
> random effects, using a Poisson distribution, but the data are 
> overdispersed (variance/mean = 5). I then
> thought of using a mixed-effects model with negative binomial 
> distribution, but I have 2 problems:
> 
> 1- The only package building mixed models with neg. bin. 
> distribution I found is the package glmmADMB but I
> have a hard time understanding the output. Anyone knows of a R 
> package with an output that gives p values?
> 
> 2- Two people I asked advice to told me that I should use either a 
> mixed-effect model with a Poisson
> distribution (the random effects will take care of the overdispersion) 
> OR a glm using neg. bin.
> distribution but not both at the same time, which would be unnecessary. 
> 

  Several pieces of advice:

* this question is probably most appropriate for r-sig-mixed-models
(or perhaps r-sig-ecology)

* glmmADMB is admittedly a bit scratchy at the moment, but you
may not find a package that gives much easier-to-understand output --
almost all packages will give output in terms of fixed effect
coefficients, standard errors, and variances/covariances/standard deviations
of random effects.

* you might want to consider Poisson-lognormal models instead,
which allow for overdispersion and are a bit easier to fit in
the context of mixed models, by defining an individual-level
random effect: see e.g.
Elston, D. A., R. Moss, T. Boulinier, C. Arrowsmith, and X. Lambin. 2001.
Analysis of Aggregation, a Worked Example: Numbers of Ticks on Red Grouse
Chicks. Parasitology 122, no. 05: 563-569. doi:10.1017/S0031182001007740.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=82701.

  Such models can be fitted in (at least) MCMCglmm and recent versions
of glmer.

* p values will be tricky indeed.  sorry about that.

* as to the advice about using either mixed models or NB models but not
both -- that's an empirical question.  It may indeed be the case that
one or the other takes care of the overdispersion, but you won't know
until you try.  It is certainly possible to have overdispersion even
within a species/nestid combination.

I would suggest <http://glmm.wikidot.com/faq> as a starting point for
further reading ...

   good luck