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On generalized degrees of freedom with application in linear mixed models selection

机译：广义自由度及其在线性混合模型选择中的应用

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摘要

The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.
机译：自由度的概念在统计建模中起着重要的作用，通常用于测量模型的复杂性。在线性回归模型中通常用作自由度的未知参数的数量可能无法在某些建模过程中起作用，尤其是对于线性混合效应模型。在本文中，我们提出了线性混合效应模型中广义自由度的新定义。它是通过使用预期拟合值相对于其基础真实均值的敏感性总和得出的。我们探索并比较数据扰动和残差自举以凭经验估计模型的复杂性。我们还表明，这种经验性的广义自由度测度满足一些期望的特性，对于选择线性混合效应模型很有用。

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