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首页> 外文期刊>Journal of Multivariate Analysis: An International Journal >Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures
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Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures

机译：具有相关误差结构的线性混合效应模型的有效自由度及其在条件AIC中的应用

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摘要

The effective degrees of freedom is a useful concept for describing model complexity. Recently the number of effective degrees of freedom has been shown to relate to the concept of conditional Akaike information (cAI) in the mixed effects models. This relationship was made explicit under linear mixed-effects models with i.i.d. errors, and later also extended to the generalized linear and the proportional hazards mixed models. We show that under linear mixed-effects models with correlated errors, the number of effective degrees of freedom is. asymptotically equal to the trace of the usual 'hat' matrix plus the number of parameters in the error covariance matrix. Using it one can define a crude version of the conditional AIC (cAIC), which is known to be inaccurate due to the estimation of unknown variance parameters. We compare this crude version to several corrected versions of cAIC for linear mixed models with correlated errors, including one that is asymptotically unbiased counting for the unknown parameters, but one which is also difficult to compute without specific programming for each case of the error correlation structure. (C) 2014 Elsevier Inc. All rights reserved.
机译：有效自由度是描述模型复杂性的有用概念。最近，有效自由度的数量已显示出与混合效应模型中的条件Akaike信息（cAI）的概念有关。在具有i.i.d的线性混合效应模型下，此关系变得明确。错误，后来也扩展到广义线性和比例风险混合模型。我们表明，在具有相关误差的线性混合效应模型下，有效自由度的数量为。渐近地等于通常的“帽子”矩阵的轨迹加上误差协方差矩阵中的参数数量。使用它可以定义条件AIC（cAIC）的粗略版本，由于估计未知方差参数，该版本不准确。对于具有相关误差的线性混合模型，我们将该粗略版本与cAIC的多个校正版本进行了比较，其中包括对未知参数进行渐近无偏计数的一种，但是如果没有针对每种错误相关结构的具体编程，也很难计算出来。 。 （C）2014 Elsevier Inc.保留所有权利。

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