Using a Measure of Variable Importance to Investigate the Standardization of Discriminant Coefficients

Abstract

This article addresses the issue of standardization of discriminant functions, which has recently been debated in the literature by Mueller & Cozad (1988, 1993) and Nordlund & Nagel (1991). It is argued that instead of using the standardized discriminant coefficients (DCs) to assess variable importance, the parallel and total discriminant ratio coefficients (DRCs) proposed by Thomas (1992) should be used. Furthermore, it is argued that the parallel DRCs should be adopted as the actual importance measures. The issue of standardization is then investigated by considering the effect of different definitions of discriminant coefficients and structure coefficients on the parallel DRCs. The main finding is that either of the two competing standardizations (within or total) can be used provided that the normalization and standardization of the discriminant coefficients is consistent, and consistent also with the definition of the structure coefficients. However, consistent total standardization is shown to lead to particularly convenient definitions of the total DRCs. It is also shown that standardized DCs based on total quantities are numerically closer to parallel DRCs than are standardized DCs based on within-group quantities.