Discriminant analysis when all variables are ordered.

Determination of the equation that relates an ordered dependent variable to ordered independent variables is sought. One solution, non-parametric discriminant analysis (NPD), involves obtaining the best monotonic step function by means of a computer search procedure. Although one can use alternative selection criteria in obtaining the equation, the illustrative examples use absolute distance. This paper compares the prediction procedures obtained from NPD with those from linear discriminant analysis, linear regression (with and without transformed variables), and logistic regression. We show that NPD is analogous to regression tree analysis with incorporation of ordered variables and monotonicity. We use various prediction functions to predict the example data, the data using the leave-one-out technique, and a verification set. Consistently, non-parametric discriminant analysis performs as good as or better than the tested alternatives.