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Entropy coefficient of determination for generalized linear models

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  • Eshima, Nobuoki
  • Tabata, Minoru

Abstract

The objective of the present paper is to propose a predictive power measure for generalized linear models (GLMs). First, basic predictive power measures for GLMs are compared with respect to some desirable properties. We propose a generalized coefficient of determination for GLMs, which is referred to as the entropy coefficient of determination (ECD). The advantage of the measure is discussed in the GLM framework. Second, the asymptotic properties of the maximum likelihood estimator of ECD are discussed. Third, ECDÂ is applied to GLMs with polytomous response variables. Finally, discussions and a conclusion to this study are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1381-1389
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    References listed on IDEAS

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    1. 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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    1. 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.
    2. Takahashi, Akihito & Kurosawa, Takeshi, 2016. "Regression correlation coefficient for a Poisson regression model," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 71-78.
    3. Cheng, C.-L. & Shalabh, & Garg, G., 2016. "Goodness of fit in restricted measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 101-116.
    4. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.
    5. 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.

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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.
    3. 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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