This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Thomas, D. R. Articles by Zumbo, B. D. Search for Related Content Social Bookmarking                         What's this?

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

Carleton University

Bruno D. Zumbo

University of Northern British Columbia

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.

Key Words: variable importance • standardization • discriminant coefficients • structure coefficients • discriminant ratio coefficients

Journal of Educational and Behavioral Statistics, Vol. 21, No. 2, 110-130 (1996)
DOI: 10.3102/10769986021002110


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?

This article has been cited by other articles:

				D. R. Thomas, P. Zhu, and Y. J. Decady Point Estimates and Confidence Intervals for Variable Importance in Multiple Linear Regression Journal of Educational and Behavioral Statistics, March 1, 2007; 32(1): 61 - 91. [Abstract] [Full Text] [PDF]

				R. Azen and D. V. Budescu Comparing Predictors in Multivariate Regression Models: An Extension of Dominance Analysis Journal of Educational and Behavioral Statistics, January 1, 2006; 31(2): 157 - 180. [Abstract] [PDF]

				D. R. Thomas A Note on Huberty and Wisenbaker's "Views of Variable Importance" Journal of Educational and Behavioral Statistics, January 1, 1997; 22(3): 309 - 322. [Abstract] [PDF]