Notes on the Use and Interpretation of Discriminant Analysis

Abstract

This article focuses on two problems in applications of discriminant analysis in political research: first, evaluating the success of classification, and, second, determining the importance of predictor variables when the classification variable is a polychotomy. Discussion of the former rejects the existing procedures for evaluating classification success and advances an empirical simulation technique that is more appropriate. Discussion of the latter focuses on canonical correlation analysis and the misleading and inappropriate conclusions that may be drawn when the categorical variable is a polychotomy. Most important, this second discussion advances an alternative interpretation of eigenvalues; presents the redundancy measure, which is the appropriate measure of association between the independent variable set and the multi-categorical variable set; and suggests a method of evaluating the importance of the independent variables and the multi-categories of the group variable. We illustrate our discussion with random number data. Finally, we apply the techniques advanced in a public policy analysis.