Two-Stage Tensor Linear Mixed Model for Multi-Scale Longitudinal Data Analysis

Tensor-structured multi-scale longitudinal data are quite prevalent in epidemiological, clinical, and other follow-up research. A key challenge in their statistical analysis is to simultaneously realize dimension reduction and longitudinal correlation capture while preserving the intrinsic information and cross-scale associations of the data. To address this issue, we propose a novel two-stage tensor linear mixed model (2STLMM). The proposed method employs a decoupled estimation strategy for low-rank fixed effects and random-effects variance components, and it incorporates a residual block bootstrap procedure to enable efficient statistical inference by refitting only the fixed-effect terms. Monte Carlo simulation results demonstrate that the proposed 2STLMM delivers superior Type I and Type II error control, robust inferential performance, and improved computational efficiency. As a robust and efficient analytical tool for tensor-structured multi-scale longitudinal data, the 2STLMM can well accommodate the modeling demands of multi-scale longitudinal data in epidemiological and clinical follow-up research.