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Rotation in Correspondence Analysis from the Canonical Correlation Perspective

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  • Naomichi Makino

    (Benesse Educational Research and Development Institute)

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.

Suggested Citation

  • Naomichi Makino, 2022. "Rotation in Correspondence Analysis from the Canonical Correlation Perspective," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1045-1063, September.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:3:d:10.1007_s11336-021-09833-7
    DOI: 10.1007/s11336-021-09833-7
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    References listed on IDEAS

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    1. Robert Jennrich, 2002. "A simple general method for oblique rotation," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 7-19, March.
    2. de Leeuw, Jan & Mair, Patrick, 2009. "Simple and Canonical Correspondence Analysis Using the R Package anacor," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i05).
    3. Norman Cliff & David Krus, 1976. "Interpretation of canonical analysis: Rotated vs. unrotated solutions," Psychometrika, Springer;The Psychometric Society, vol. 41(1), pages 35-42, March.
    4. Michel Velden & Henk A.L. Kiers, 2005. "Rotation in Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 251-271, September.
    5. Henk Kiers, 1994. "Simplimax: Oblique rotation to an optimal target with simple structure," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 567-579, December.
    6. Urbano Lorenzo-Seva, 2003. "A factor simplicity index," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 49-60, March.
    7. Hironori Satomura & Kohei Adachi, 2013. "Oblique Rotaton in Canonical Correlation Analysis Reformulated as Maximizing the Generalized Coefficient of Determination," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 526-537, July.
    8. John Carroll, 1953. "An analytical solution for approximating simple structure in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 23-38, March.
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