An empirical comparison of alternative methods for principal component extraction

Abstract

A major problem confronting users of principal component analysis is the determination of how many components to extract from an empirical correlation matrix. Using 30 such matrices obtained from marketing and psychology sources, the authors provide a comparative assessment of the extraction capabilities exhibited by five principal component decision rules. These are the Kaiser-Guttman, scree, Bartlett, Horn, and random intercepts procedures. Application of these rules produces highly discrepant results. The random intercepts and Bartlett formulations yield unacceptable component solutions by grossly under- and overfactoring respectively. The Kaiser-Guttman and scree rules performed equivalently, yet revealed tendencies to overfactor. In comparison Horn's test acquitted itself with distinction, and warrants greater attention from applied researchers.