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

Area of Science:

• Psychometrics
• Quantitative Psychology
• Statistical Modeling

Background:

• Factorial similarity is crucial in exploratory factor analysis (EFA).
• The congruence coefficient is a common but sometimes ambiguous index for assessing factor similarity.
• Existing methods lack a comprehensive framework for interpreting factor similarity.

Purpose of the Study:

• To introduce a novel profile-based framework for understanding factorial similarity in EFA.
• To clarify the interpretation and application of the congruence coefficient.
• To provide researchers with enhanced tools for examining factor similarity.

Main Methods:

• Development of a profile-based framework for factorial similarity.
• Articulation of the congruence coefficient using profile-based components.
• Secondary analyses to validate the framework against expert judgments.

Main Results:

• Factorial similarity can be understood through three components: general saturation, differential saturation, and configural similarity.
• The congruence coefficient was redefined using these and two additional profile-based components, resolving ambiguities.
• Empirical evidence shows profile-based components correlate with expert assessments of factor similarity.

Conclusions:

• The profile-based framework offers a nuanced understanding of factorial similarity in EFA.
• This approach enhances the interpretability and utility of the congruence coefficient.
• The framework has the potential to improve how researchers evaluate and understand factor similarity.