Negative binomial regression

In this and subsequent chapters we shall discuss the nature and utility of some 25 varieties of negative binomial regression that are useful for modeling count response data. In addition, we also examine certain models that are related to the negative binomial family of models. This chapter will primarily be devoted to an examination of the derivation of the negative binomial model and to the two foremost methods of its estimation. We also consider how the probabilities generated from a negative binomial model differ from the Poisson, as well as how they differ among various negative binomial models based on both mean and ancillary parameters.