The Relation Between Factor Score Estimates, Image Scores, and Principal Component Scores

Abstract

Theoretical problems with the factor analysis model, such as the factor indeterminacy issue, have resulted in increased interest in component analysis as an alternative. Indeed, component analysis alternatives are already in common use. It is, therefore, of interest to assess empirically some of the assumed differences between the methods. Of particular interest is the relation between component scores and "factor score estimates." The correlations between principal component scores, rescaled image scores, and three factor score estimates are investigated. Three pattern positions are considered: (1) the "canonical" position, (2) the varimax position, and (3) a position of "maximal" similarity which was achieved by procrustes rotation. The correlations between corresponding factors were near unity for both the canonical and "maximal" position. The correlations for the varimax position are slightly lower, generally in the .80 to .90 range. These results suggest there is little practical difference between principal component scores, rescaled image scores, and factor score estimates.