Discriminant Function Analysis

Discriminant function analysis is used to predict group membership based on a linear combination of interval predictor variables. The procedure begins with a set of observations, whereby both group membership and the values of the predictor variables are known, with the end result being a linear combination of the interval variables that allows prediction of group membership. The way in which the interval variables combine allows a greater understanding and simplification of a multivariate data set. Discriminant analysis, based on matrix theory, is an established technology that has the advantage of a clearly defined decision-making process. Machine learning techniques such as neural networks may be used alternatively for predicting group membership from similar data, often with more accurate predictions, as long as the statistician is willing to accept decision-making without much insight into the process.

For example, a researcher might have a large data set of information from a high school about its former students. Each student belongs to a single group: (a) did not graduate from high school, (b) graduated from high school or obtained a General Educational Development, and (c) attended. The researcher wishes to predict student outcome group using interval predictor variables such as grade point average, attendance, degree of participation in various extracurricular activities (e.g., band, athletics), weekly amount of screen time, and parental educational level. Given this [Page 526]complex multivariate data set and the discriminant function analysis procedure, the researcher can find a subset of variables that in a linear combination allows prediction of group membership. As a bonus, the relative importance of each variable in this subset is part of the output. Often researchers are satisfied with this understanding of the data set and stop at this point.

Discriminant function analysis is a sibling to multivariate analysis of variance as both share the same canonical analysis parent. Where multivariate analysis of variance received the classical hypothesis testing gene, discriminant function analysis often contains the Bayesian probability gene, but in many other respects, they are almost identical.

This entry explains the procedure by breaking it down into its component parts and then assembling them into a whole. The two main component parts in discriminant function analysis are implicit in the title: discriminating between groups and functional analysis. Because knowledge of how to discriminate between groups is necessary for an understanding of the later functional analysis, it is presented first.