Determining Significant Principal Components: a Probability Test For Eigenvalues

Abstract

When employing factor analysis a major problem confronting researchers is the determination of how many components to retain for subsequent investigation. Many marketing scholars address this issue by automatically invoking the Kaiser-Guttman, or eigenvalue-greater-than-one, procedure. Yet this procedure is not without certain limitations. The authors therefore propose an alternative measure, a probability test for the significance of eigenvalues, based upon a random intercepts model. Preliminary results of the application of the model on marketing and psychology data are presented.