Component Analysis: an Alternative System

TLDR: In this paper, the authors introduce a system of components as a substitute for the principal components and show that the use of the latter components may lead to conclusions different from those obtained by means of the former.

Abstract: Summary The main purpose of the paper is to introduce a system of components as a substitute for the principal components. Some difficulties involved in the use of the principal components are pointed out and an alternative system, regression components, is described. It is shown that the use of the latter components may lead to conclusions different from those obtained by means of the former. The results of analyses for a number of examples are reported, and comparisons with principal components have been drawn. The effect of changing the sign of variates is also dealt with, and results for two examples are reported. The use of components as regressors in regression analysis and the methods of studying relationship between groups of variates are discussed. It is suggested that the use of canonical variates should be supplemented or substituted by other methods. It is emphasized that the variates must be chosen and used so as to obtain meaningful results.