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Entropy correlation coefficient for measuring predictive power of generalized linear models

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  • Eshima, Nobuoki
  • Tabata, Minoru

Abstract

By considering properties of generalized linear models (GLMs), a correlation coefficient, which is referred to as the entropy multiple correlation coefficient, is proposed as a predictive power measure of GLMs. This correlation coefficient is a measure of linearity of response variables and the canonical parameters, and can be viewed as the proportion of reduced uncertainty of response variables by explanatory variables.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:6:p:588-593
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    References listed on IDEAS

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    1. 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.
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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, 2010. "Entropy coefficient of determination for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1381-1389, May.
    3. 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.
    4. Takahashi, Akihito & Kurosawa, Takeshi, 2016. "Regression correlation coefficient for a Poisson regression model," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 71-78.

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    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.

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