9 - Canonical Correlation Analysis

Abstract

Canonical correlation analysis is viewed as the most general of the traditional least-squares methods for the analysis of data structures. This chapter describes set and canonical correlation analysis as a widely applicable taxonomy for data analysis, shows how they are related, and explains how all other least-squares procedures can be derived as conceptual special cases. One factor that contributes to poor methodology in canonical analysis is that there are no fully adequate computer programs generally available to researchers. Each major statistics package can perform a canonical analysis, but none of them include all of the desirable features. Furthermore, the chapter discusses the traditional canonical analysis model, shows its relations to principal components analysis, and reviews significance tests and other interpretive aids such as redundancy and the rotation of canonical components. Finally, the chapter concludes with a discussion of methodological issues in the use of canonical analysis, including stepwise procedures and the need for cross-validation.