Chapter 10: Models for Counts: Poisson and Negative Binomial GLMs

Abstract

generalized linear modelPoissoncount responsesThe need to count things is ubiquitous, so data in the form of counts arise often in practice. Examples include: the number of alpha particles emitted from a source of radiation in a given time; the number of cases of leukemia reported per year in a certain jurisdiction; the number of flaws per metre of electrical cable. This chapter is concerned with counts when the individual events being counted are independent, or nearly so, and where there is no clear upper limit for the number of events that can occur, or where the upper limit is very much greater than any of the actual counts. We first compile important information about the Poisson distribution, the distribution most often used with count data. Poisson regression, or models for count data described by covariates, has already been covered elsewhere. We then focus on describing models for rates and models for counts organized in tables. Overdispersion is then discussed, including a discussion negative binomial glms and quasi-Poisson models as alternative models.