The aim of this book is to present a detailed, but thoroughly clear and understandable, analysis of the nature and scope of the varieties of negative binomial model that are currently available for use in research. Modeling count data using the standard negative binomial model, termed NB2, has recently become a foremost method of analyzing count response models, yet relatively few researchers or applied statisticians are familiar with the varieties of available negative binomial models, or how best to incorporate them into a research plan.

Note that the Poisson regression model, traditionally considered as the basic count model, is in fact an instance of NB2 – it is an NB2 with a heterogeneity parameter of value 0. We shall discuss the implications of this in the book, as well as other negative binomial models that differ from the NB2. Since Poisson is a variety of the NB2 negative binomial, we may regard the latter as more general and perhaps as even more representative of the majority of count models used in everyday research.

I began writing this second edition of the text in mid-2009, some two years after the first edition of the text was published. Most of the first edition was authored in 2006. In just this short time – from 2006 to 2009/2010 – a number of advancements have been made to the modeling of count data.