R help - Aug 2010 - Modelling poisson distribution with variance structure

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

Thanks so much,

Karen Moore
PhD Researcher,
FORESTBIO,
Department of Botany,
Trinity College Dublin
Ireland

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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.