Linear programming applied to separation detection in polytomous logistic regression

Abstract

The Logistic Regression Model is widely used in Discriminant Analysis. However, parameter estimation is affected by the data configuration and may not be achieved when there is  separation between the groups in the data set, which is a common problem in Discriminant Anal­  ysis. The use of linear programming to detect the separation between groups was proposed by [1], and a large number of linear programming approaches have been used to detect separate data in discriminant analysis. However, most research focuses on models for two groups and there are few models for classification problems in multiple groups. In this paper, a linear programming formulation is proposed to detect the separation between groups for the polytomous logistic regression model. The proposed model has a non-negative objective function that has a positive value when the separation is detected and allows to classify the data as completely separate, almost separated or overlapped, and can be used as part of the parameter estimation. A simulation, using data sets from the literature, shows that the proposed approach can be an efficient alternative for mathematical programming applied to problems with multiple groups.