混合效应模型的决定系数
Coefficients of Determination for Mixed-Effects Models
摘要：
对于线性模型，决定系数已得到很好的定义，而对于混合效应模型，决定系数的扩展一直是需要的。我们重新审视它的扩展，以定义整个模型、仅固定效应和仅随机效应解释的变异比例的度量。我们建议计算无法解释的变化条件下的个人随机和/或固定效应，以保持个人异质性所带来的可用的预测。虽然这些度量是为线性混合模型自然定义的，但可以使用沿其方差函数测量的距离为广义线性混合模型定义这些度量，从而解释其异方差性。
英文摘要：
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed effects only, and random effects only. We propose to calculate unexplained variations conditional on individual random and/or fixed effects so as to keep individual heterogeneity brought by available predictors. While naturally defined for linear mixed models, these measures can be defined for a generalized linear mixed model using a distance measured along its variance function, accounting for its heteroscedasticity.
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