Modified quadratic analysis in prediction with mixed binary and continuous explanatory variables

Abstract

We propose a new technique of modified quadric analysis for prediction or classificatory problems involving both continuous as well as binary random variables. This technique is distribution- free, in the sense that it does not make the assumption of multivariate normality of the continuous explanatory variables. The technique is compared with the method of linear discriminant function with location model, the method of logistic discrimination and the method of quadratic discriminant function with location model in terms of the mean actual error rates using the estimation method given by Lachenbruch and Mickey (1968). It is also compared with the convex hull method and the order statistic method proposed by Kendall (1966). The distribution-free methods of Modified Quadric Analysis are illustrated by predicting whether a prostate cancer patient has positive nodal involvement or no nodal involvement using the data from Brown Jr. (1980). Our calculations show that the methods of Modified Quadric Analysis gave satisfactory results. Also the error rates of our methods were quite comparable to the error rates of other methods of classification, particularly, the Logistic Regression and Quadratic Discriminant Function with location model, in case of this particular data set.