高维混合效应模型的统计推断：一种新的方法

Statistical Inference of High-Dimensional Mixed Effects Models: A New Approach

摘要: 线性混合效应模型广泛应用于分析聚类或重复测量数据。本文提出了一种拟似然结合弹性网的方法来估计高维线性混合模型中的未知参数，包括固定效应及随机效应的方差分量部分。在此基础上，也提出了相关的统计推断。所提出的方法适用于一般设置，其中随机效应的维度和簇可能很大。关于固定效应，我们提供的方法不依赖于方差分量的结构信息，即对方差分量中所涉及到的复杂未知参数使用代理矩阵进行简化。并且对所提出的方法在各种模拟设置中分别进行了固定效应的误差，假设检验的性能以及方差分量的估计误差的评估，均表现出较优的结果。

Abstract: The linear mixed-effects model is widely used for analyzing clustered or repeated measurements data. This paper proposes a pseudo-likelihood method combined with the elastic net to estimate unknown parameters in high-dimensional linear mixed models, including the variance components of both fixed and random effects. Furthermore, relevant statistical inferences are also presented. The proposed method is applicable to general settings where the dimension and clusters of random effects can be substantial. Regarding fixed effects, our approach does not rely on structural infor-mation about the variance components. Instead, it simplifies the complex unknown parameters in-volved in the variance components using surrogate matrices. The performance of the proposed method is evaluated for fixed effects errors, hypothesis testing, and variance component estimation errors in various simulation settings, all of which demonstrate superior results.