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.
翻译:确定系数对于线性模型来说是明确定义的,对于混合效应模型来说,确定系数的延伸是长期需要的。我们重新审视其扩展范围,以界定整个模型所解释的变异比例、仅固定效应和仅随机效应。我们提议根据个别随机效应和/或固定效应计算无法解释的变异,以便保持现有预测器带来的个别异异质。虽然对线性混合模型来说是自然定义的,但这些措施可以按其变异功能所测量的距离来界定一个通用的线性混合模型,考虑到其变异性。