Three-group classification with unequal misclassification costs: A mathematical programming approach

Mathematical programming approaches to the statistical classification problem have attracted considerable research interest since the early 1980s. In this paper a mixed-integer programming model is proposed for the minimization of misclassification costs in the three-group problem. In the proposed model, distinct costs c(h | g) can be assigned to the misclassification of an observation from one group to either of the other two groups. The standard parametric classification procedures (Fisher's linear discriminant function and Smith's quadratic discriminant function), as incorporated in commonly used statistical packages like SAS, SPSS and MINITAB, do not allow the assignment of distinct costs c(h | g), when the number of groups is three or more. Using MBA admissions data, it is shown that the proposed model may be useful in assisting an academic institution in its screening of MBA applications, once the relative costs of erroneous admission decisions are assessed.