Alpha In Negative Binomial Result

[Hm Saleh]

Hello Dears,

I have used Poisson and negative binomial regressions in my paper. Everything in Poisson regression was well, but the negative binomial of the Alpha and InAlpha disappears only dots (.).

-What is the Alpha importance in the result?
-Deas this means I can't use a negative binomial?
-How can I solve this problem?

[Nick Cox]

What's the precise problem? Negative binomial models are in practice often hard to fit. Exactly what that means otherwise is hard to say without any output shown.

[Carlo Lazzaro]

Hm:
see https://www.stata.com/statalist/arch.../msg00374.html

[Hm Saleh]

My understanding is as follows. If I am wrong, please correct me.
"
When the alpha is not found, it could be due to the absence of evidence of underdispersion in my data. -nbreg- tries to give me a negative estimate of alpha and, because that is impossible, essentially finds alpha = 0. With stronger under-dispersion, -nbreg- would probably not converge. So, I should not use negative binomial regression because of the underdispersion in my data. It has no robustness properties when the variance-mean relationship is violated."

[Hm Saleh]

Now, what is your opinion about my negative binomial regression, and how can I solve this problem?

[Maarten Buis]

You gave us a selection of the output. That is a bad idea. We need everything to diagnose your problem. It is annoying for you to repeatedly hear "give us more", and it is annoying for us to have to repeatedly say "give us more". Better to give us immediately what we need. Admittedly, it is hard for you to know what we need to answer your question. Just assume that with these type of questions it is the details that matter. There is no one answer for all situations, but it always depends. We don't know your research project, your data, the aims of your project, etc., etc., etc., so you need to tell us. At the very least, you should have given us the entire output, including the command, and told us what the variables are.

The first thing to look at when you see these results is whether you have continuous variables in your data and whether these have the value 0 within or reasonably close to the range in the data. You can think of alpha as a parameter for distribution/model for the constant. If the constant is way outside the range of the data, then models like these can get into trouble. A common problem variable is year of birth, so the constant refers to someone born in the year 0. This is usually a huge extrapolation, and a model like nbreg can start to struggle with that. (This is ignoring the problem that the year 0 may not exist depending on the calendar you are using: https://en.wikipedia.org/wiki/Year_zero . ) The solution is to center your variable to some meaningful number within the range of the data. So you do something like:

gen byr_c = byr-1970

and than use byr_c instead of byr in your nbreg model. Less extreme, but often still problematic is age.

[Nick Cox]

Good advice from Maarten Buis, but the link in #2 nails the main point, it seems. Alpha is reported as essentially zero, implying that negative binomial regression is quite unhelpful.

There is nothing negative about the estimate of alpha. It is just very small. Its logarithm is negative because it is (much) smaller than 1.

Stata is holding more digits than it shows, but this calculation shows what is going on.

. di ln(5.59e-14)
-30.515212

Whether there are other problems with your model is a bundle of different questions. In my fields, various environmental sciences, almost all the interest in papers I try to emulate is in models with a very small number of predictors. In many social science and medical problems, a large bundle of predictors may have small effects detectable in very large samples, and it can be better to have them in the model as quantified effects than outside the model as predictors you didn't use that your reviewers will campaign for.

As Maarten says, much more detail is needed for a better answer.