Group-Orthogonal Subsampling for Hierarchical Data Based on Linear Mixed Models
针对分层数据中可能存在的异质性，提出组正交子抽样方法，通过平衡组间样本量和组内组合正交性选取信息子集，使线性混合模型参数估计高效且最优，适用于大数据场景。
Hierarchical data analysis is crucial in various fields for making discoveries. The linear mixed model is often used for training hierarchical data, but its parameter estimation is computationally expensive, especially with big data. Subsampling techniques have been developed to address this challenge. However, most existing subsampling methods assume homogeneous data and do not consider the possible heterogeneity in hierarchical data. To address this limitation, we develop a new approach called group-orthogonal subsampling (GOSS) for selecting informative subsets of hierarchical data that may exhibit heterogeneity. GOSS selects subdata with balanced data size among groups and combinatorial orthogonality within each group, resulting in subdata that are D- and A-optimal for building linear mixed models. Estimators of parameters trained on GOSS subdata are consistent and asymptotically normal. GOSS is shown to be numerically appealing via simulations and a real data application. Theoretical proofs, R codes, and supplementary numerical results are accessible online as supplementary materials.