Evaluating the effect of gap size in a single function mathematical programming model for the three-group classification problem

Evaluating the effect of gap size in a single function mathematical programming model for the three-group classification problem

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Article ID: iaor20021426
Country: United Kingdom
Volume: 52
Issue: 8
Start Page Number: 896
End Page Number: 904
Publication Date: Aug 2001
Journal: Journal of the Operational Research Society
Authors: ,
Keywords: programming: integer, statistics: multivariate
Abstract:

This study examines the impact that the size of the classification gap can have on the classificatory performance of a mathematical programming based discriminant model. In mathematical programming based models that project the discriminant scores onto a line, the discriminant score of an observation may fall into the gap between adjacent group intervals; thus there is no clear cut way to determine the group in which the observation should be classified. We examine a procedure that we refer to as the split gap approach. The split gap approach is defined as a strategy of estimating the performance of a mathematical programming based model using a nonzero gap size to separate group intervals and then splitting the gap between adjacent group intervals to classify future observations. Studies that propose models with a classification gap generally do not assess the effect of the gap on the performance of the model. This paper investigates this effect. A theoretical assessment and a Monte Carlo simulation are used to determine the impact of different gap sizes on a mixed integer programming model using a single function classification model for the three-group case.

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