Kernel-based discriminant techniques for educational placement

Abstract

This article considers the problem of educational placement. Several discriminant techniques are applied to a data set from a survey project of science ability. A profile vector for each student consists of five science-educational indictors. The students are intended to be placed into three reference groups: advanced, regular, and remedial. Various discriminant techniques, including Fisher’s discriminant analysis and kernel-based nonparametric discriminant analysis, are compared. The evaluation work is based on the leaving-one-out misclassification score. Results from the five school data sets and 500 bootstrap samples reveal that the kernel-based nonparametric approach with bandwidth selected by cross validation performs reasonably well. The authors regard kernel-based nonparametric procedures as desirable competitors to Fisher’s discriminant rule for handling problems of educational placement.