Predicting Student Retention by Linear Programming Discriminant Analysis

Abstract

The goal of the paper is to predict student retention with an ensemble method by combining linear programming (LP) discriminant analysis approaches together with bootstrapping and feature salience detection. In order to perform discriminant analysis, we linearize a fractional programming method by using Charnes-Cooper transformation (CCT) and apply linear programming, while comparing with an approach that uses deviation variables (DV) to tackle a similar multiple criteria optimization problem. We train a discriminatory hyperplane family and make the decision based on the average of the histograms created, thereby reducing variability of predictions. Feature salience detection is performed by using the peeling method, which makes the selection based on the proportion of variance explained in the correlation matrix. While the CCT method is superior in detecting true-positives, DV method excels in finding true-negatives. The authors obtain optimal results by selecting either all 14 (CCT) or the 8 (DV) most important student study related and demographic dimensions. They also create an ensemble. A quantitative course along with the age at accession are deemed to be the most important, whereas the two courses resulting in less than 2% of failures are amongst the least important, according to peeling. A five-fold Kolmogorov-Smirnov test is undertaken, in order to help university staff in devising intervention measures.