Chapter 12. Discriminant Analysis
In this chapter we describe the method of discriminant analysis, which is a model-based approach to classification. We discuss the main principle, where classification is based on the distance of an observation from each class average. We explain the underlying measure of "statistical distance," which takes into account the correlation between predictors. The output of a discriminant analysis procedure generates estimated "classification functions," which are then used to produce classification scores that can be translated into classifications or probabilities of class membership. One can also directly integrate misclassification costs into the discriminant analysis setup, and we explain how this is achieved. Finally, we discuss the underlying model assumptions, the practical robustness to some, and the advantages of discriminant analysis when the assumptions are reasonably met (e.g., the sufficiency of a small training sample).
Discriminant analysis is another classification method. Like logistic regression, it is a classical statistical technique that can be used for classification and profiling. It uses continuous variable measurements on different classes of items to classify new items into one of those classes (classification). Common uses of the method have been in classifying organisms into species and subspecies; classifying applications for loans, credit cards, and insurance into low- and high-risk categories; classifying customers ...