Fixed Effects Regression Methods for Longitudinal Data Using SAS

4.4. Fixed Effects Negative Binomial Models for Count Data

As we just saw in the last section, Poisson regression models often run into problems with overdispersion. That's a bit surprising for fixed effects models because these models already allow for unobserved heterogeneity across individuals by way of the α_i parameters. But that heterogeneity is presumed to be time-invariant. There might still be unobserved heterogeneity that is specific to particular points in time, leading to observed overdispersion. As we've seen, the standard errors can be corrected for overdispersion by a simple method based on the ratio of the deviance (or Pearson chi-square) to its degrees of freedom.

Although that's not a bad method, we might do better by directly ...