[R-sig-ME] GLMM with overdispersion and Wald test

[tmerklin at cict.fr]

Dear list members,

This is my first post on the list. I hope that I will be clear.

I'm studying chick feeding in a bird species and I want to know if  
parents feed their male chicks more than their female chicks.
I have data concerning feeding bouts (count data) and I also consider  
chick rank (1st born or 2nd born) and chick age (in classes), because  
they can possibly influence feeding.

Firstly, I only consider feeding events, so that I don't have any zero  
in my data. Observations have been made during 15 minutes three times  
a day. I calculate the number of feedings for each chick per day, if a  
chick is not fed during an observation it will not appear in the  
dataset. Is this a problem if my data don't contain any zero, when  
Poisson or quasipoisson is specified ?

I specified my model as following:
model<-lmer(Number~SexChick*EggRank*AgeClass+(1|ChickID/Nest)+(1|Date),data=feeding,family="quasipoisson",REML=FALSE)

I assessed overdispersion using: (phi<-lme4:::sigma(model)), and its  
values was between 1.5 and 4 depending on the analyses.

Is it correct ?

Then, to test the interactions and the variables I used the function  
anova(model1,model2) with both models differing from only one term  
i.e. I used likelihood ratio test (LRT). However I recently read in  
Bolker et al 2009 TREE that LRT are not the best solution when sample  
size is small to moderate and especially when data are oversdispersed.

They adviced to run F Wald test or to use QAIC.However the problem  
seems to be that the software is unable to calculate the residual  
degrees of freedom (rdf). I could not find a method in R to assess  
these rdf.
Have I missed something ?

Finally, assuming that I find a way to assess these rdf I'm not use  
how to use F Wald test. There is a function in the aod library called  
wald.test(). I don't understand if we have to test each coefficients  
from the full model or if we need to run models with and without a  
specified tems to test its significance. Can you help concerning this  
function too ?

I don't want to use QAIC because I have other analyse that I've made  
using p-values so I don't want to mix the two approaches.

I hope that I have been clear in the explanations of my problem and I  
hope that someone will be able to help me !

Thank you by advance!
Thomas Merkling