Empirical decomposition of the explained variation in the variance components form of the mixed model
Empirical decomposition of the explained variation in the variance components form of the mixed model
复制标题
混合模型方差分量形式的解释变化的经验分解
DOI：
10.1101/2019.12.28.890061
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Schreck
中科院分区：
文献类型：
--
作者：
Schreck
决定系数是线性模型中的标准特征。它被广泛用于评估解释的变异比例，确定拟合优度和比较具有不同协变量的模型。然而，还没有一个类似的数量的线性混合模型类的协议。我们引入了一个自然的扩展，著名的调整系数的决定在线性模型的方差分量形式的线性混合模型。我们提出了一种新的决定系数，这是无量纲的，有一个直观和简单的定义方差解释，是添加剂的几个随机效应，并减少到调整后的决定系数的线性模型。为此，我们证明了一个完整的分解的解释和残差方差的自变量的平方和。基于限制的最大似然方程，我们引入了一种新的措施，我们专门分配的固定和随机协变量的模型的贡献的解释的变化。我们在两个基因组数据集上说明，新的决定系数可以用作复杂性状遗传力的改进估计。例如，我们将解释的变异分配到模式植物拟南芥的五条染色体上，并确定每条染色体对性状遗传力的贡献以及染色体之间的互相关性。
The coefficient of determination is a standard characteristic in linear models. It is widely used to assess the proportion of variation explained, to determine the goodness-of-fit and to compare models with different covariates. However, there has not been an agreement on a similar quantity for the class of linear mixed models yet. We introduce a natural extension of the well-known adjusted coefficient of determination in linear models to the variance components form of the linear mixed model. We propose a novel coefficient of determination which is dimensionless, has an intuitive and simple definition in terms of variance explained, is additive for several random effects and reduces to the adjusted coefficient of determination in the linear model. To this end, we prove a full decomposition of the sum of squares of the independent variable into the explained and residual variance. Based on the restricted maximum likelihood equations, we introduce a novel measure for the explained variation which we allocate specifically to the contribution of the fixed and the random covariates of the model. We illustrate on two genomic datasets that the novel coefficient of determination can be applied as an improved estimator of the heritability of complex traits. Exemplarily, we allocate the explained variation to the five chromosomes of the model plantArabidopsis thalianaand determine the contribution of each chromosome as well as cross-correlations between the chromosomes to the trait heritability.
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