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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?

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Since the negative binomial distribution is a true distribution, models based on it has a true likelihood, and not only a quasi-likelihood as is the case with a quasi-Poisson model. So the usual AIC is defined, and could be used.

There is so no reason to use a quasi-AIC.

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