A Data Envelopment Analysis approach to Discriminant Analysis

Abstract

Data Envelopment Analysis (DEA) and Discriminant Analysis (DA) are similar in that both may be used to classify units as exhibiting either good or poor performance. Both use linear programming to select a set of factor weights that determines group membership relative to a "threshold" or hyperplane. This similarity was pointed out in an earlier paper, in which several methods which combine aspects of DA and DEA were suggested. This paper further develops one of these hybrid methods, which can be described as an efficiency approach to Discriminant Analysis. The various formulation options are considered with respect to their effects on solution quality and stability. The stability issue is raised by the fact that solution equivalence under data transformation (including both translation and rotation) is considered important in DA, and has significantly affected model formulation. Thus, the data transformation issue is studied for the hybrid method, and also for DEA. The hybrid method is applied to an insurance data set, where some firms are solvent and others in financial distress, to further evaluate the method and its possible formulations. DA methods are applied to the same data set to provide a basis for comparison. The hybrid method is shown to outperform the general discriminant models.