Negative Binomial and Small Samples

[Rachel German]

Hello listers,

I have a count dv with one continuous iv and one dichotomous iv, and I am using a negative binomial regression due to the poisson appearing overdispersed. The confidence interval for alpha excluded zero further confirming the inappropriateness of poisson. I'm concerned however, about the small sample size (20 years, by year) as I've seen recommendations not to use negative binomial for small samples. Can anyone recommend other estimators or ways to correct for this? I read about a quantile-adjusted conditional maximum likelihood estimator but not sure how to do this in stata. Thanks for your help!

[Joao Santos Silva]

Dear Rachel,

You need to tell as more to get any useful advice. In particular, it would be good if you could let us now a bit more about the nature of the problem and the purpose of the model.

Best wishes,

Joao

[Rachel German]

Dear Rachel,

You need to tell as more to get any useful advice. In particular, it would be good if you could let us now a bit more about the nature of the problem and the purpose of the model.

Best wishes,

Joao

Thanks for the advice! My dependent variable is the number of actions taken by an entity and I'm testing for a relationship with the continuous independent variable- the percentage of total cases by another entity the previous year. The dichotomous IV is a measure of political ideology.

[Mike Lacy]

I'd still agree that your data structure is a bit opaque, but it sounds like you have N = 20 observations on an entity, one for each year. If so, there is no statistical procedure that is going to give you much useful information about your data here. One problem is that, yes, the negative binomial model (and similar models) and other regression procedures will give biased estimates at small sample sizes. But the other and bigger issue is that with only 20 observations, any estimate of a slope will have such a huge variance as to be uninformative. If I'm misunderstanding about N = 20, of course, the answer might be different. I'd consider N = 200 to be a reasonable sample size at which you might get meaningful results from a model like this.

[Joao Santos Silva]

Dear Rachel,

Thanks for the additional information. I generally agree with Mike, but if your purpose is just to test the existence of a relationship I would try a simple Poisson regression with robust standard errors.

Best wishes,

Joao

[Phil Bromiley]

Mike and Joao - Would it make sense to look at OLS regression? Regression violates some assumptions, but poisson only has asymptotic properties and imposes a different functional form.

Interestingly, the example in the Stata manual uses a very small sample (N=9). If the estimator has largely asymptotic properties, a large sample example might be better.

[Joao Santos Silva]

Dear Phil,

I think it all depends on the counts. If the dependent variable only takes a handful of different values and is close to the lower bound, Poisson may be preferable, although it does not hurt to try OLS. My experience is that Poisson regression is reasonably well behaved with small samples and even if we use OLS we'll need to rely on asymptotic results for inference.

Best wishes,

Joao