The coefficient of determination R² quantifies the amount of variance explained by regression coefficients in a linear model. It can be seen as the fixed-effects complement to the repeatability R (intra-class correlation) for the variance explained by random effects and thus as a tool for variance decomposition. The R² of a model can be further partitioned into the variance explained by a particular predictor or a combination of predictors using semi-partial (part) R² and structure coefficients, but this is rarely done due to a lack of software implementing these statistics. Here, we introduce partR2, an R package that quantifies part R² for fixed effect predictors based on (generalized) linear mixed-effect model fits. The package iteratively removes predictors of interest from the model and monitors the change in the variance of the linear predictor. The difference to the full model gives a measure of the amount of variance explained uniquely by a particular predictor or a set of predictors. partR2 also estimates structure coefficients as the correlation between a predictor and fitted values, which provide an estimate of the total contribution of a fixed effect to the overall prediction, independent of other predictors. Structure coefficients can be converted to the total variance explained by a predictor, here called 'inclusive' R², as the square of the structure coefficients times total R². Furthermore, the package reports beta weights (standardized regression coefficients). Finally, partR2 implements parametric bootstrapping to quantify confidence intervals for each estimate. We illustrate the use of partR2 with real example datasets for Gaussian and binomials GLMMs and discuss interactions, which pose a specific challenge for partitioning the explained variance among predictors.

中文翻译：

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partR2：在广义线性混合模型中对R2进行分区

确定系数R ²量化由线性模型中的回归系数解释的方差量。可以将其看作是对由随机效应解释的方差的可重复性R（类内相关性）的固定效果的补充，因此可以看作方差分解的工具。可以使用半部分（部分）R ²和结构系数将模型的R ²进一步划分为由特定预测变量或预测变量组合解释的方差，但是由于缺少实现这些统计信息的软件，因此很少这样做。在这里，我们介绍partR2，这是一个量化R ²的R包基于（广义）线性混合效应模型拟合的固定效应预测变量。程序包从模型中迭代删除感兴趣的预测变量，并监视线性预测变量方差的变化。与完整模型的差异给出了由特定预测变量或一组预测变量唯一解释的方差量的度量。partR2还估算结构系数，作为预测变量和拟合值之间的相关性，从而独立于其他预测变量来估算固定效应对总体预测的总贡献。结构系数可以转换为由预测变量解释的总方差，在这里称为“包含” R ²，即结构系数的平方乘以总R ²。此外，该软件包还报告了Beta权重（标准化回归系数）。最后，partR2实现参数自举以量化每个估计的置信区间。我们说明了partR2在高斯和二项式GLMM的真实示例数据集中的使用，并讨论了相互作用，这对在预测变量之间划分解释的方差提出了特殊的挑战。