13 - Probabilistic Methods: Multivariate Statistics II: Clustering and Classification Techniques

Abstract

This chapter focuses on the clustering and classification techniques based on the general linear model. Many of the procedures needed to carry out the classification strategies are highly technical and require extensive practice before they can be comfortably interpreted. The chapter focuses on geometrical formulations to support the analytic descriptions. Although probability estimates accompany many steps in factor, discriminant, and canonical correlation analysis, these procedures are all useful for descriptive purposes rather than inferentially for extrapolation from a sample or for comparison of samples. New classification techniques, especially ones that are used with ordinal or nominal data, are being developed in profusion. Factor analysis is a multivariate technique whose purpose is to replace a collection of intercorrelated variables by another set of variables, called factors, which are fewer in number, relatively independent, and conceptually meaningful, that is, plausible in theoretical terms. When a factor analysis is successfully carried out in a particular study, the proportion of combined variability accounted for by the factors is approximately the same as that accounted for by the original variables.