Overdispersion parameter alpha in nbreg STATA

[Selina Schoen]

Hi there!

I have a question regarding the size of the alpha when using a negative binomial model. The alpha is the overdispersion parameter which allows in the negative binomial regression to have a greater variance than the mean in contrast to the Poisson regression, where these values are equal. If alpha = 0 the negative binomial regressions simplifies to a Poisson regression.

In my regression the alpha turned out to be 0.07 which is rather small compared with other examples I've seen. But is it too small to continue using the negative binomial regression? Because I have read that when alpha is very large or very small it can generate numerical instability and convergence of the algorithm is not guaranteed (Cameron & Travedi in Microeconometrics using Stata).

Despite the fact that my alpha is that small, Stata tells me that it is highly statistically significant. And also, other tests have shown me that I should choose Negative binomial regression over the Poisson regression (the former being slightly better)

I hope someone can help me with this and tell me what an appropriated size of alpha is? Thank you very much!

Selina

[Marcos Almeida]

Welcome to the Stata Forum / Statalist.

I gather that sharing the output would provide more "food for thought" to the query.

That said, theoretically, a significant p-value indicates that the negative binomial model fared (somewhat) better than the Poisson model.

That being said, we should probably go further and compared between negative binomial models (NB1 and NB2), let alon checking the scale of the variables and the best set of predictors..

Also, depending on the results, generalized models or zero-inflated, or zero-truncated, or hurdle models may come to the foreground.