[R] Modelling poisson distribution with variance structure

[Ben Bolker]

Karen Moore <kmoore <at> tcd.ie> writes:

> 
> I'm dealing with count data that's nested and has spatial dependence.
> I ran a glmm in lmer with a random factor for nestedness. Spatial dependence
> seems to have been accommodated by model. However I can't add a variance
> strcuture to this model (to accommodate heterogeneity).
> 
> Is there a model that can have a poisson distribution *AND*  a variance
> structure *AND* have AIC in output (for model comparison and selection)?
> Some we've looked at that can't:
> 
>    - glmmPQL  - can add structures BUT can't have AIC (you can calculate it
>    but it doesn't give correct AIC with this model)
>    - glmm in lme4 (lmer)  - won't allow variance structure
>    - gls -  can add variance but can't have Poisson


  [Any further discussion should probably go to 
r-sig-mixed-models at r-project.org ...]

  I'm not sure I know what you mean by Poisson + variance structure --
if the data are really Poisson (not overdispersed in some way), then
the variance structure is completely defined.  If you want to deal
with overdispersion, and have a well-defined AIC, you may be able
to add a per-observation random effect in lme4.  Alternatively,
you could just use a weights= argument in glmmPQL to set some sensible
mean-variance relationship, overlooking the fact that the data
are discrete and positive rather than being normally distributed
with an equivalent variance structure.  <http://glmm.wikidot.com/faq>
may also be useful.