I have run negative binomial and quasi-Poisson models based on an hypothesis testing approach. My final models using both methods have different covariates and interactions. It seems that there are no patterns when I plot my residuals in both cases. Thus, I was wondering which test I could use to see which model fits my data better as the quasi-Poisson does not have any likelihood or AIC…
Also, I have a lot of overdispersion which makes me think that the negative binomial would be more appropriate, but I don't know if I can choose my model based on common sense…