How to Describe the Difference between Factors and Corresponding Factor-Score Estimates

Because of factor score indeterminacy, there can be substantial shifts in the theoretical meaning of factors and their corresponding score estimates. Therefore, the original factor pattern should be compared with the regression-component loadings (Schönemann & Steiger, 1976) corresponding to the factor-score estimates in order to detect possible shifts in the theoretical meaning. Especially with large loading matrices the similarity of the original factor pattern and the regression components of the score estimates may be ascertained by means of congruency coefficients. It is shown that these congruencies contain information that is not already given by measures of factor-score indeterminacy. Two examples illustrate the use of regression-component analysis for different types of factor-score estimates. The analyses reveal that the Bartlett-score estimates are most appropriate when factor interpretation is based on the factor pattern, which is usually the case in confirmatory factor analysis.