# Can I use AIC/BIC to compare a Poisson model to a negative Binomial model?

I would please like to enquire if it's appropriate for me to compare the fit of a Poisson vs. a negative Binomial model for my data, given that the two models are nested, i.e. the negative Binomial and Poisson regression are the same model when the one additional parameter the negative Binomial model adds (alpha, which captures the overdispersion present) is zero.

Thank you for any insight. It's extremely appreciated.

• Let us know if you have further questions or need more explanation. If this answer or any other one solved your issue, please mark it as accepted :) Dec 18, 2020 at 10:06

• Comparing different likelihoods is precisely the point of model comparison ! I think the confusion might come from your definition of likelihood: a likelihood is not some kind of function that is unique to a model and cannot be used for another one. When comparing models $\mathcal{M}_1$ and $\mathcal{M}_2$ based on data $\mathcal{D}$, you compare their respective likelihoods $p(\mathcal{D}|\mathcal{M}_1)$ and $p(\mathcal{D}|\mathcal{M}_2)$. The probability $p$ can be used for different models. Dec 10, 2020 at 15:14