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Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures
Journal of Multivariate Analysis ( IF 1.6 ) Pub Date : 2014-11-01 , DOI: 10.1016/j.jmva.2014.08.004 Rosanna Overholser 1 , Ronghui Xu 2
Journal of Multivariate Analysis ( IF 1.6 ) Pub Date : 2014-11-01 , DOI: 10.1016/j.jmva.2014.08.004 Rosanna Overholser 1 , Ronghui Xu 2
Affiliation
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.
中文翻译:
有效自由度及其在具有相关误差结构的线性混合效应模型的条件 AIC 中的应用
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被证明与混合效应模型中的条件 Akaike 信息 (cAI) 的概念有关。这种关系在具有 iid 误差的线性混合效应模型下得到了明确,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,有效自由度的数量渐近地等于通常的“帽子”矩阵的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,由于未知方差参数的估计,已知该版本是不准确的。
更新日期:2014-11-01
中文翻译:
有效自由度及其在具有相关误差结构的线性混合效应模型的条件 AIC 中的应用
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被证明与混合效应模型中的条件 Akaike 信息 (cAI) 的概念有关。这种关系在具有 iid 误差的线性混合效应模型下得到了明确,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,有效自由度的数量渐近地等于通常的“帽子”矩阵的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,由于未知方差参数的估计,已知该版本是不准确的。