Basic Count Regression

Abstract

INTRODUCTION This chapter is intended to provide a self-contained treatment of basic crosssection count data regression analysis. It is analogous to a chapter in a standard statistics text that covers both homoskedastic and heteroskedastic linear regression models. The most commonly used count models are Poisson and negative binomial. For readers interested only in these models, it is sufficient to read sections 3.1 to 3.5, along with preparatory material in sections 1.2 and 2.2. As indicated in Chapter 2, the properties of an estimator vary with the assumptions made on the dgp . By correct specification of the conditional mean or variance or density, we mean that the functional form and explanatory variables in the specified conditional mean or variance or density are those of the dgp . The simplest regression model for count data is the Poisson regression model. For the Poisson MLE, the following can be shown: Consistency requires correct specification of the conditional mean. It does not require that the dependent variable y be Poisson distributed. Valid statistical inference using default computed maximum likelihood standard errors and t statistics requires correct specification of both the conditional mean and variance. This requires equidispersion, that is, equality of conditional variance and mean, but not Poisson distribution for y . Valid statistical inference using appropriately computed standard errors is still possible if data are not equidispersed, provided the conditional mean is correctly specified. […]