Inference for High-Dimensional Linear Mixed-Effects Models: A Quasi-Likelihood Approach

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional fixed effects. The proposed method is applicable to general settings where the dimension of the random effects and the cluster sizes are possibly large. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures that do not rely on the structural information of the variance components. We also study the estimation of variance components with high-dimensional fixed effects in general settings. The algorithms are easy to implement and computationally fast. The proposed methods are assessed in various simulation settings and are applied to a real study regarding the associations between body mass index and genetic polymorphic markers in a heterogeneous stock mice population.

线性混合效应模型（Linear mixed-effects models）被广泛应用于聚类数据及重复测量数据的分析。针对带有高维固定效应（high-dimensional fixed effects）的线性混合效应模型，我们提出了一种拟似然（quasi-likelihood）方法，用于模型中未知参数的估计与统计推断。所提方法可适配随机效应维度与聚类样本量均可能较大的通用场景。针对固定效应部分，我们给出了速率最优估计量（rate optimal estimators）与无需依赖方差分量（variance components）结构信息的有效统计推断流程。此外，我们还针对通用场景下带有高维固定效应的模型，研究了其方差分量的估计方法。所提算法易于实现且计算效率优异。我们通过多种模拟场景对所提方法进行了性能评估，并将其应用于一项真实研究：该研究旨在探究远交群小鼠种群中身体质量指数（body mass index）与遗传多态性标记（genetic polymorphic markers）之间的关联关系。