14 - Poisson Regression, Logistic Regression, and Loglinear Models for Random Counts

Abstract

This chapter provides a unified discussion of Poisson regression, logistic regression, and loglinear modeling of contingency tables. These are three special cases of the general loglinear model, wherein expected category counts are products of effects of independent variables. This contrasts with the general linear model in which expected means of continuous measurements are sums of such effects. Poisson and logistic regression each provide regression, analysis of variance (ANOVA), and analysis of covariance (ANCOVA)-like analyses for response counts with, respectively, one and two levels. Poisson regression is most commonly used to analyze rates, whereas logistic regression is used to analyze proportions. The chapter considers statistical models for counts of independently occurring random events, and counts at different levels of one or more categorical outcomes. Furthermore, this chapter introduces and illustrates the methods for nonlinear modeling of counts that form the foundation of contemporary categorical data methodology.