Predicting student retention by comparing histograms of bootstrapping for Charnes-Cooper transformationlinear programming discriminant analysis

摘要

The goal of the paper is to predict student retention by using linear discriminant analysis with bootstrapping. The result (93%) provides accuracy superior to the bootstrapping of a comparative method, as well as to the non-bootstrapping variations. In order to perform discriminant analysis, we linearize a fractional programming method by using Charnes-Cooper transformation and apply linear programming, while the comparative approach uses deviation variables to tackle a similar multiple criteria optimization problem. We train the discriminatory hyperplane family and apply it to the testing set — thus arriving at a set of histograms. We analyze the histograms by using the simple mean — best for prediction — and a five-fold Kolmogorov-Smirnov test — best used for resources allocation, in order to act on the final results. Final results are the outcome of applying the hyperplane family on freshman data.