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A Coefficient of Determination for Generalized Linear Models

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  • Dabao Zhang

Abstract

The coefficient of determination, a.k.a. R2, is well-defined in linear regression models, and measures the proportion of variation in the dependent variable explained by the predictors included in the model. To extend it for generalized linear models, we use the variance function to define the total variation of the dependent variable, as well as the remaining variation of the dependent variable after modeling the predictive effects of the independent variables. Unlike other definitions that demand complete specification of the likelihood function, our definition of R2 only needs to know the mean and variance functions, so applicable to more general quasi-models. It is consistent with the classical measure of uncertainty using variance, and reduces to the classical definition of the coefficient of determination when linear regression models are considered.

Suggested Citation

  • Dabao Zhang, 2017. "A Coefficient of Determination for Generalized Linear Models," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 310-316, October.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:4:p:310-316
    DOI: 10.1080/00031305.2016.1256839
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    References listed on IDEAS

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    1. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.
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    1. Dabao Zhang, 2022. "Coefficients of Determination for Mixed-Effects Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 674-689, December.
    2. Peng Gao & Jiaxing Xie & Mingxin Yang & Ping Zhou & Wenbin Chen & Gaotian Liang & Yufeng Chen & Xiongzhe Han & Weixing Wang, 2021. "Improved Soil Moisture and Electrical Conductivity Prediction of Citrus Orchards Based on IoT Using Deep Bidirectional LSTM," Agriculture, MDPI, vol. 11(7), pages 1-22, July.
    3. Tobias Keller & Martin Glaum & Andreas Bausch & Thorsten Bunz, 2023. "The “CEO in context” technique revisited: A replication and extension of Hambrick and Quigley (2014)," Strategic Management Journal, Wiley Blackwell, vol. 44(4), pages 1111-1138, April.
    4. Zhonggen Yu & Liheng Yu, 2023. "Examining Factors That Influence Learner Retention in MOOCs During the COVID-19 Pandemic Time," SAGE Open, , vol. 13(2), pages 21582440231, May.

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