A Coefficient of Determination for Generalized Linear Models
A Coefficient of Determination for Generalized Linear Models
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DOI：
10.1080/00031305.2016.1256839
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发表时间：
2017-01-01
影响因子：
1.8
通讯作者：
Zhang, Dabao
中科院分区：
文献类型：
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作者：
Zhang, Dabao
决定系数，a.k.a. R-2在线性回归模型中定义良好，测量模型中包含的预测因子解释的因变量的变异比例。为了将其扩展到广义线性模型，我们使用方差函数来定义因变量的总变差，以及在对自变量的预测效果建模后因变量的剩余变差。与其他需要完全指定似然函数的定义不同，我们的R-2定义只需要知道均值和方差函数，因此适用于更一般的准模型。它与经典的不确定性度量方法一致，当考虑线性回归模型时，它简化为经典的决定系数定义。
The coefficient of determination, a.k.a. R-2, 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 R-2 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.