Ideal point discriminant analysis

A new method of multiple discriminant analysis was developed that allows a mixture of continuous and discrete predictors. The method can be justified under a wide class of distributional assumptions on the predictor variables. The method can also handle three different sampling situations, conditional, joint and separate. In this method both subjects (cases or any other sampling units) and criterion groups are represented as points in a multidimensional euclidean space. The probability of a particular subject belonging to a particular criterion group is stated as a decreasing function of the distance between the corresponding points. A maximum likelihood estimation procedure was developed and implemented in the form of a FORTRAN program. Detailed analyses of two real data sets were reported to demonstrate various advantages of the proposed method. These advantages mostly derive from model evaluation capabilities based on the Akaike Information Criterion (AIC).The work reported in this paper has been supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada and by a leave grant from the Social Sciences and Humanities Research Council of Canada to the first author. Portions of this study were conducted while the first author was at the Institute of Statistical Mathematics in Tokyo on leave from McGill University. He would like to express his gratitude to members of the Institute for their hospitality. Thanks are also due to T. Komazawa at the Institute for letting us use his data, to W. J. Krzanowski at the University of Reading for providing us with Armitage, McPherson, and Copas' data, and to Don Ramirez, Jim Ramsay and Stan Sclove for their helpful comments on an earlier draft of this paper.