Scoring Frequency Data for Discriminant Analysis: Perhaps Discrete Procedures can be Avoided

Abstract

Because of the availability of easy-to-use canned computer software packages such as SPSS and BMDP, the marketing practitioner is likely to continue to rely on the linear discriminant function (LDF) when faced with a discrimination problem. However, results of prior simulation studies suggest that when categorical predictors are used in the LDF its performance can be adversely affected. The authors extend previous work on LDF performance in nonoptimal settings by considering situations in which the categorical predictors can take on more than two levels. First, they examine whether a “scoring” of the raw frequency data can improve LDF performance in situations where it is known to perform poorly. Second, as the effect of using such data in an LDF analysis is not clear, they study LDF performance as the number of levels of a categorical variable is increased to determine whether the relative gains from using discrete discriminant procedures disappear. The results of Monté Carlo sampling experiments suggest that as the number of levels a variable can take on is increased, a simple dummy variable coding of the raw frequency data followed by an LDF analysis does as well as the discrete discriminant procedure.