On the estimation of the expected probability of misclassification in discriminant analysis with mixed binary and continuous variables

Abstract

Monte Carlo estimates have been obtained for the unconditional probability of misclassification incurred by the “estimative” optimum allocation rule in discriminant analysis involving mixtures of binary and continuous variables. The rule is based on the location model and leads effectively to a different linear discriminant function for each of the multinomial locations defined by the binary variables. A comparison is made between the Monte Carlo estimates and an approximation based on an asymptotic expansion of the distribution of the location “estimative” linear discriminant function derived by Vlachonikolis. Results are presented for various combinations involving equal sample sizes of 50, 100 and 200; two and three binary variables; one, three and five continuous variables; three different settings of location Mahalanobis distances and several choices of location probabilities.