Examination of the classificatory performance of MIP models with secondary goals for the two-group discriminant problem

This paper examines the classificatory performance of several two-goal mathematical programming models for the two-group discriminant problem. The goal of minimizing the number of misclassifications in the training sample is assigned preemptive priority. While many papers in the literature have suggested the inclusion of secondary goals, no published study has compared the performance of MIP models with various secondary goals to solve the classification problem. The goal of maximizing the deviation between the projected group means is introduced as a secondary goal in the context of two MIP models. Theoretical results are presented to guarantee the preemptive priority of the minimization of the number of misclassifications in the training sample. A Monte Carlo simulation study is conducted to compare the performance of four MIP models with secondary goals. The results of the simulation study indicate that the choice of the secondary goal can have a significant effect on the classificatory performance of the MIP model.