Selection in discriminant analysis with continuous and discrete variables

• Published in: Computational statistics & data analysis 1999-12, Vol.32 (2), p.161-175
• Main Authors: Daudin, J.J., Bar-Hen, A.
• Format: Article
• Language: English
• Subjects: Akaike criterion; Decision theory; Discrimination with discrete and continuous variables; Distribution theory; Exact sciences and technology; Hellinger distance; Kullback–Leibler divergence; Location model; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Selection of variables; Statistics
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(99)00027-4

A problem frequently encountered by the practitioner in Discriminant Analysis is how to select the best variables. In mixed discriminant analysis (MDA), i.e., discriminant analysis with both continuous and discrete variables, the problem is more difficult because of the different nature of the variables. Various methods have been proposed in recent years for selecting variables in MDA. In this paper we use two versions of a generalized Mahalanobis distance between populations based on the Kullback–Leibler divergence for the first and on the Hellinger–Matusita distance for the second. Stopping rules are established from distributional results. A simulation experiment is used to compare the two proposed selection methods and a third based on a modified version of the Akaike Information Criterion (AIC). Since the simulations focus on situations with just one continuous and one binary variable, they can only give indications concerning a few variables and caution is recommended if extended to more usual situations.