Constrained Principal Component Analysis: Various Applications

Abstract

Constrained Principal Component Analysis (CPCA) is a method for structural analysis of multivariate data. It combines regression analysis and principal component analysis into a unified framework. This article provides example applications of CPCA that illustrate the method in a variety of contexts common to psychological research. We begin with a straightforward situation in which the structure of a set of criterion variables is explored using a set of predictor variables as row (subjects) constraints. We then illustrate the use of CPCA using constraints on the columns of a set of dependent variables. Two new analyses, decompositions into finer components and fitting higher order structures, are presented next, followed by an illustration of CPCA on contingency tables, and CPCA of residuals that includes assessing reliability using the bootstrap method.