CHAPTER 6 - Applying the Tools to Multivariate Data

Abstract

This chapter discusses the application of tools to multivariate data. Techniques can be distinguished by the nature of the transformation(s) used to affect the matching and the characteristics of the transformed numbers. The typical multiple regression model considers each variable as intervally scaled. If matrix inversion and rank are the hallmarks of single-criterion, multiple-predictor association, then eigenstructures are the key concepts in dimension-reducing methods such as factor analysis. Eigenstructures are also essential in multiple-criterion, multiple-predictor association. Component loadings are product-moment correlations of each original variable with each set of component scores. Factor analysis—either principal components or other type of factoring procedure—represents only one class of methods for effecting dimensional reduction of one's data. Multivariate techniques can differ according to the nature of the allowable transformations and the properties that the transformed matrices exhibit in the matching process.