A coefficient of determination (R2) for generalized linear mixed models
A coefficient of determination (R2) for generalized linear mixed models
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DOI：
10.1002/bimj.201800270
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发表时间：
2019-07-01
影响因子：
1.7
通讯作者：
Piepho, Hans-Peter
中科院分区：
文献类型：
--
作者：
Piepho, Hans-Peter
线性模型的扩展在生物数据分析中非常常用。虽然线性模型的拟合优度度量（如决定系数（R-2）或调整后的R-2）已经很好地建立，但对于广义线性和混合模型，如何定义这些度量并不明显。到目前为止，已经提出了几项建议，但尚未就在这些情况下采取何种最佳统一办法达成共识。特别是，它是一个悬而未决的问题，如何最好地说明异方差和协方差存在于残差或随机效应引起的观察。本文提出了一种新的方法，解决了这个问题，是普遍适用于任意方差-协方差结构，包括空间模型和重复测量。它是用三个生物学的例子来说明的。
Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R-2) or the adjusted R-2 are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance-covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.