McFadden PseudoR2 and BIC choosing opposite models-Poisson vs Negative binomial

[Buki Peters]

Hello,
I am trying to build a count regression model using Stata 14. I built a Poisson model, but considering there were signs of over-dispersion (the variance was almost six times more than the mean of the variable), I moved to a negative binomial model. I used step-wise regression and purposeful selection of variables to select the variables for the two different models and decided to compare the better fit. The results showed that the BIC for the negative binomial was smaller and preferred, but the Pseudo R-squared for the Poisson is much larger, making it preferred? Is one fit-assessment preferred over the other or are there further tests I can carry out to select a better model?

(I am a Public Policy student, so these were the comparison tests I was comfortable using at my level)

[Richard Williams]

You are using different variables and different methods. It doesn't seem like a fair comparison. Based on pure empiricism and the fact that a Poisson model is seldom correct, I would go with the Nbreg model, possibly adding voter to it.

[Buki Peters]

Okay makes sense. Thanks!