chapter  13
Alternative Regression Models: Logistic, Poisson Regression, and the Generalized Linear Model
Pages 57

Throughout the text we have used the ordinary least squares regression (OLS) model. For statistical inference, OLS regression assumes that the residuals from our analysis are both normally distributed and exhibit homoscedasticity (see Section 4.3). But we are sometimes confronted with a dependent variable Y that does not result in our meeting these assumptions. For example, Y may be dichotomous, as when someone is diagnosed with a disease or not, referred to in the epidemiological literature as "case" versus "noncase" (e.g., Fleiss, 1981 ). Or Y may be in the form of counts of rare outcomes, for example, the number of bizarre behaviors exhibited by individuals in a given period of time. When the objects or events counted are rare (e.g., many people exhibit no bizarre behavior), many individuals have zero counts, so that the count variable Y is very positively skewed. By the nature of the dichotomous and count dependent variables, residuals from OLS regression of these dependent variables do not standardly meet OLS assumptions. In such instances the OLS regression model is not efficient and may well lead to i/naccuracies in inference. A class of statistical approaches subsumed under a broad model, the generalized linear model (Fahrmier & Tutz, 1994; Long, 1997; McCullagh & Neider, 1989) has been developed to handle such dependent variables that lead to residuals that violate OLS assumptions.