The Analysis of Count Data: Overdispersion and Autocorrelation

I begin this paper by describing several methods that can be used to analyze count data. Starting with relatively familiar maximum likelihood methods-Poisson and negative binomial regression-I then introduce the less well known (and less well understood) quasi-likelihood approach. This method (like negative binomial regression) allows one to model overdispersion, but it can also be generalized to deal with autocorrelation. I then investigate the small-sample properties of these estimators in the presence of overdispersion and autocorrelation by means of Monte Carlo simulations. Finally, I apply these methods to the analysis of data on the foundings of labor unions in the U.S. Quasi-likelihood methods are found to have some advantages over Poisson and negative binomial regression, especially in the presence of autocorrelation.