A Grouping Algorithm for Qualitative Data with A Dichotomous Outcome Variable

Abstract

This paper presents an algorithm for grouping the values of qualitative predictor variables while minimizing the loss of information about a dichotomous dependent variable. The algorithm is based on Shannon's measure of uncertainty. Subpopulations corresponding to the predictor values are ranked by their conditional Bernoulli parameter. At each iteration the increase in uncertainty resulting from grouping each pair of adjacent subpopulations is computed, and the pair with the least increase is grouped. Stopping rules based on the number of values remaining, the cumulative loss of information and the Maximum Likelihood Chi-Square Statistic are proposed, A numerical example is included.