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Canonical exponential models for analysis of association between two sets of variables

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  • Eshima, Nobuoki

Abstract

The present paper discusses canonical exponential models for analysis of association between two sets of variables. First, properties of the models are discussed in view of entropy. It is shown that entropy in the models is decreasing in canonical association parameters. Second, the present paper proposes a summary measure of association in the models that is decomposed into canonical association components. The present approach is applied to the RC(M) association model and canonical correlation analysis with the multivariate normal distribution.

Suggested Citation

  • Eshima, Nobuoki, 2004. "Canonical exponential models for analysis of association between two sets of variables," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 135-144, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:2:p:135-144
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    References listed on IDEAS

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    1. D. R. Cox, 2002. "On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution," Biometrika, Biometrika Trust, vol. 89(2), pages 462-469, June.
    2. Becker, Mark P., 1989. "On the bivariate normal distribution and association models for ordinal categorical data," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 435-440, October.
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    Cited by:

    1. Takeshi Kurosawa & Francis K.C. Hui & A.H. Welsh & Kousuke Shinmura & Nobuoki Eshima, 2020. "On goodness‐of‐fit measures for Poisson regression models," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 340-366, September.
    2. Eshima, Nobuoki & Tabata, Minoru, 2011. "Three predictive power measures for generalized linear models: The entropy coefficient of determination, the entropy correlation coefficient and the regression correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3049-3058, November.
    3. Eshima, Nobuoki & Tabata, Minoru, 2007. "Entropy correlation coefficient for measuring predictive power of generalized linear models," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 588-593, March.

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