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Rotation in Correspondence Analysis from the Canonical Correlation Perspective

Published online by Cambridge University Press:  01 January 2025

Naomichi Makino Open the ORCID record for Naomichi Makino [Opens in a new window]
Naomichi Makino*
Affiliation:
Benesse Educational Research and Development Institute
*
Correspondence should be made to Naomichi Makino, Benesse Educational Research and Development Institute, 1-34, Ochiai, Tama-shi, Tokyo, Japan. Email: n-makino@mail.benesse.co.jp
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Abstract

Correspondence analysis (CA) is a statistical method for depicting the relationship between two categorical variables, and usually places an emphasis on graphical representations. In this study, we discuss a CA formulation based on canonical correlation analysis (CCA). In CCA-based formulation, the correlations within and between row/column categories in a reduced dimensional space can be expressed by canonical variables. However, in existing CCA-based formulations, only orthogonal rotation is permitted. Herein, we propose an alternative CCA-based formulation that permits oblique rotation. In the proposed formulation, the CA loss function can be defined as maximizing the generalized coefficient of determination, which is a measure of proximity between two variables. Simulation studies and real data examples are presented in order to demonstrate the benefits of the proposed formulation.

Keywords

correspondence analysiscanonical correlation analysisrotationsimple structurenetwork diagram
Type
Theory & Methods
Information
Psychometrika , Volume 87 , Issue 3 , September 2022 , pp. 1045 - 1063
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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