An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

Nobuoki Eshima; Claudio Giovanni Borroni; Minoru Tabata; Takeshi Kurosawa

doi:10.3390/e23020140

An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

Entropy (Basel). 2021 Jan 24;23(2):140. doi: 10.3390/e23020140.

Authors

Nobuoki Eshima¹, Claudio Giovanni Borroni², Minoru Tabata³, Takeshi Kurosawa⁴

Affiliations

¹ Center for Educational Outreach and Admissions, Kyoto University, Yoshida-machi, Sakyoku, Kyoto 660-8501, Japan.
² Department of Statistics and Quantitative Methods, University of Milano Bicocca, 20126 Milano, Italy.
³ Department of Mathematical Sciences. Osaka Prefecture University, Osaka 599-8532, Japan.
⁴ Department of Applied Mathematics, Tokyo University of Science, Kagurazaka, Shinzyukuku, Tokyo 162-0825, Japan.

Abstract

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.

Keywords: canonical common factor; canonical factor analysis; entropy; factor contribution.