A mathematical programming approach to variable selection in logistic regression / Yasmine Mohamed Mohsen Refai ; Supervised Ramadan Hamed , Ali Elhefnawy , Sahar Elsheneity

Thesis (M.Sc.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

Binary logistic regression models the relationship between a binary response variable and a set of explanatory variables, defining the boundary between the classified two groups. It can yield better results in case of applying the proper variables selection method. Logistic regression was introduced in earlier research under the framework of mathematical programming, using non-linear goal programming approach. Variables selection method was introduced to mixed integer mathematical programming models for maximizing classification accuracy. In this study, a new model is proposed as a mathematical programming approach to variable selection in logistic regression, with the aim of minimizing the residuals, maximizing the percentage of correct classification and reaching the best model having the least number of selected explanatory variables. A simulation study is presented to evaluate the performance of the proposed model and compare it to that of the classical logistic regression model in case of applying forward stepwise variables selection method. This new model showed higher results for the percentage of correct classification criterion, at different sample sizes and overlapped groups, for most of the cases. It was outperformed by classical maximum likelihood estimation (MLE) method in small sample size with limited degree of overlap (quasi-separated). Both methods give similar results for large sample size. For the number of selected variables criterion, in case of large sample sizes, both models give nearly the same results, however in case of small, medium and moderately large sample sizes, the number of selected variables is higher for the new proposed model than that of the classical logistic regression model

Issued also as CD