Choosing between Logistic Regression and Discriminant Analysis

TLDR

Discriminant analysis classifies observations into populations, while logistic regression relates qualitative variables to outcomes; although estimators from one are often used in the other, discriminant analysis is preferred under normality with equal covariances, but most applications involve qualitative variables that violate normality. The article aims to summarize arguments comparing logistic regression and discriminant analysis and present supportive empirical studies. The authors adopt a logistic regression model with maximum likelihood estimation to address both classification and regression problems under nonnormality. Empirical studies support the preference for logistic regression over discriminant analysis when data are nonnormal.

Abstract

Abstract Classifying an observation into one of several populations is discriminant analysis, or classification. Relating qualitative variables to other variables through a logistic cdf functional form is logistic regression. Estimators generated for one of these problems are often used in the other. If the populations are normal with identical covariance matrices, discriminant analysis estimators are preferred to logistic regression estimators for the discriminant analysis problem. In most discriminant analysis applications, however, at least one variable is qualitative (ruling out multivariate normality). Under nonnormality, we prefer the logistic regression model with maximum likelihood estimators for solving both problems. In this article we summarize the related arguments, and report on our own supportive empirical studies.