I have a question about comparing negative binomial models by AIC versus QAIC.
My dependent variable is a count, and I have one random term (I am using generalised linear mixed models fitted with the glmmTMB function in R). I initially used a poisson distribution but the models were overdispersed so I switched to a negative binomial distribution.
I want to compare a series of potential predictors (models differing for fixed effects but all with the same random effect). I have read that QAIC is preferred over AIC when dealing with overdispersed count data. My question though is: if I use a negative binomial distribution, which is already taking into account the overdispersion, should I then just rank my models by AIC or should I still choose QAIC?