Minimum distance probability discriminant analysis for mixed variables

Abstract

Minimum distance probability (MDP) is a robust discriminant algorithm based on a distance function. In this article, we generalize the use of MDP to the case of mixed (continuous and categorical) variables by means of the individual-score (IS) distance. This distance assumes an underlying parametric model and is based on the score transformation of the data. We have adapted it to the usual case of ignoring the distribution of the whole set of observed variables, but assuming that some knowledge about the marginal distributions is available. Finally, MDP with IS distance (IS-MDP) is compared with other discriminant methods (including those designed for mixed data) in several examples and simulations. IS-MDP is shown to be the most efficient method according the leave-one-out criterion.