Discriminant Function Analysis

Abstract

The aim of cluster analysis, the subject of the previous chapter, is to discover whether multivariate data contains relatively distinct groups of observations. A further aspect of the classification of multivariate data concerns the derivation of rules and procedures for allocating individuals to one of a set of a priori defined groups in some optimal fashion. This is the province of assignment or discrimination techniques. In medicine, for example, patients’ conditions may only be able to be diagnosed without error at a postmortem. On the basis of a large number of postmortems, the characteristics of, say, disease and nondisease classes are established. From these training set observations, an investigator may wish to establish an allocation rule to be used on patients still alive, in the hope that their conditions can be diagnosed accurately and so treated appropriately. The information used in deriving a suitable allocation rule is the observations made on the training sample. One approach to discrimination or classification is to view the grouping variable as a univariate dependent variable and, in the case of two groups, use logistic regression (Chapter 9) or classifiaction and regression trees (Chapter 15) to predict group membership from a number of explanatory variables. In discriminant analysis, these ‘explanatory’ variables are viewed as the multivariate dependent variable and the grouping variable as the predictor.