VARIABLE SELECTION IN LINEAR MIXED EFFECTS MODELS.
VARIABLE SELECTION IN LINEAR MIXED EFFECTS MODELS.
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DOI：
10.1214/12-aos1028
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发表时间：
2012-08-01
影响因子：
4.5
通讯作者：
Li R
中科院分区：
文献类型：
--
作者：
Fan Y;Li R
本文讨论线性混合效应模型中固定效应和随机效应的选择和估计。提出了一类选择和估计重要固定效应的非凹惩罚轮廓似然方法。为了克服随机效应的协方差矩阵未知的困难，我们建议在惩罚轮廓似然中使用代理矩阵。我们建立的代理矩阵的选择条件，并表明，所提出的程序享有模型选择的一致性，其中固定效应的数量允许与样本量呈指数增长。我们进一步提出了一个组变量选择策略，同时选择和估计重要的随机效应，其中未知的随机效应的协方差矩阵被替换为代理矩阵。我们证明了，适当地选择代理矩阵，所提出的程序可以识别所有的真随机效应的渐近概率为1，其中随机效应向量的维数允许与样本容量呈指数增长。蒙特卡洛模拟研究进行了研究所提出的程序的有限样本性能。我们通过一个真实的数据例子进一步说明了所提出的程序。
This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.