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Canonical Concordance Correlation Analysis

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  • Stan Lipovetsky

    (Independent Researcher, Minneapolis, MN 55305, USA)

Abstract

A multivariate technique named Canonical Concordance Correlation Analysis (CCCA) is introduced. In contrast to the classical Canonical Correlation Analysis (CCA) which is based on maximization of the Pearson’s correlation coefficient between the linear combinations of two sets of variables, the CCCA maximizes the Lin’s concordance correlation coefficient which accounts not just for the maximum correlation but also for the closeness of the aggregates’ mean values and the closeness of their variances. While the CCA employs the centered data with excluded means of the variables, the CCCA can be understood as a more comprehensive characteristic of similarity, or agreement between two data sets measured simultaneously by the distance of their mean values and the distance of their variances, together with the maximum possible correlation between the aggregates of the variables in the sets. The CCCA is expressed as a generalized eigenproblem which reduces to the regular CCA if the means of the aggregates are equal, but for the different means it yields a different from CCA solution. The properties and applications of this type of multivariate analysis are described. The CCCA approach can be useful for solving various applied statistical problems when closeness of the aggregated means and variances, together with the maximum canonical correlations are needed for a general agreement between two data sets.

Suggested Citation

  • Stan Lipovetsky, 2022. "Canonical Concordance Correlation Analysis," Mathematics, MDPI, vol. 11(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:99-:d:1015387
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    References listed on IDEAS

    as
    1. Stan Lipovetsky, 2012. "Dual Pls Analysis," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 879-891.
    2. Agnan Kessy & Alex Lewin & Korbinian Strimmer, 2018. "Optimal Whitening and Decorrelation," The American Statistician, Taylor & Francis Journals, vol. 72(4), pages 309-314, October.
    3. Ronald Christensen, 2022. "Comment on “On Optimal Correlation-Based Prediction,” by Bottai et al. (2022)," The American Statistician, Taylor & Francis Journals, vol. 76(4), pages 322-322, October.
    4. Paul Horst, 1961. "Relations amongm sets of measures," Psychometrika, Springer;The Psychometric Society, vol. 26(2), pages 129-149, June.
    5. Adrover, Jorge G. & Donato, Stella M., 2015. "A robust predictive approach for canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 356-376.
    6. Stan Lipovetsky & Asher Tishler & W. Michael Conklin, 2002. "Multivariate least squares and its relation to other multivariate techniques," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(4), pages 347-356, October.
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