A Profile-Based Framework for Factorial Similarity and the Congruence Coefficient

We present a novel profile-based framework for understanding factorial similarity in the context of exploratory factor analysis in general, and for understanding the congruence coefficient (a commonly used index of factor similarity) specifically. First, we introduce the profile-based framework articulating factorial similarity in terms of 3 intuitive components: general saturation similarity, differential saturation similarity, and configural similarity. We then articulate the congruence coefficient in terms of these components, along with 2 additional profile-based components, and we explain how these components resolve ambiguities that can be—and are—found when using the congruence coefficient. Finally, we present secondary analyses revealing that profile-based components of factorial are indeed linked to experts' actual evaluations of factorial similarity. Overall, the profile-based approach we present offers new insights into the ways in which researchers can examine factor similarity and holds the potential to enhance researchers' ability to understand the congruence coefficient.