Overdispersed Models

This chapter examines a common problem in the analysis of count data, when the variance of the data is larger than that assumed by the model. This phenomenon, known as data overdispersion, can be caused by a latent heterogeneity or independence assumption. However, it does not hold in all cases, including the case where the overdispersion parameter changes through the values of explanatory variables, when the dispersion parameter is modeled as a function of explanatory variables. Poisson normal and binomial normal models are particular cases where the explanatory variables do not make a statistical contribution to explaining the dispersion parameter&s;s behavior. Finally, an approximation of underdispersion models is also considered.