Some Relationships Between Descriptive Comparisons of Components from Different Studies

This paper considers descriptive methods of comparing components from different studies, based on correlations between columns of component scores matrices, on congruence coefficients between columns of pattern, structure or component scores coefficient matrices, or on coefficients of invariance. Contrary to common belief, it is shown that coefficients of invariance are unrelated to correlations between component scores. On the other hand, having a perfect coefficient of invariance is shown to be equivalent to having a perfect congruence between corresponding columns of the component scores coefficient matrices. A similar but weaker relationship between the latter congruence and congruence between columns of pattern matrices is demonstrated.