This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number of wars or coups d'etat in a year. I discuss several generalizations of the Poisson regression model, presented in King (1988), to allow for substantively interesting stochastic processes that do not fit into the Poisson framework. Individual models that cope with, and help analyze, heterogeneity, contagion, and negative contagion are each shown to lead to specific statistical models for event count data. In addition, I derive a new generalized event count (GEC) model that enables researchers to extract significant amounts of new information from existing data by estimating features of these unobserved substantive processes. Applications of this model to congressional challenges of presidential vetoes and superpower conflict demonstrate the dramatic advantages of this approach.
Software to implement this approach is available in the Gauss Statistical package's Maxlik option, and in the stand alone, public domain COUNT statistical package. Also see the related article "The Generalization in the Generalized Event Count Model, With Comments on Achen, Amato, and Londregan." (Article: PDF | Abstract: HTML) Also see related research.