Rotation in Correspondence Analysis from the Canonical Correlation Perspective

Naomichi Makino ()
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Naomichi Makino: Benesse Educational Research and Development Institute

Psychometrika, 2022, vol. 87, issue 3, No 11, 1045-1063

Abstract: 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 analysis; canonical correlation analysis; rotation; simple structure; network diagram (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11336-021-09833-7

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