I have several data sets on wildlife disease incidence. One of the issues with my dependent variable is that it represents only current infection status, therefore 0 (no disease) can represent either an animal who has never had the disease or has had it and recovered (it is an acute viral infection).
There is evidence of overdispersion in my datasets. Therefore I after having already performed model selection on a binomial glmm (in R,
lme4 package), I decided that perhaps beta-binomial model would be preferable. I fitted all subsets of models in R's
hglm package and performed model selection based on AICc (I believe this is calculated from the h-likelihood). The results of this model selection process are quite different to those from the binomial glmm, as one would expect, however I'm inclined to be a bit suspicious of the results from the beta-bin model, as in all 4 cases the global model was chosen as best - so perhaps this measure is just not parsimonious enough? Am I using the right information criteria?