一种用于重复测量函数型数据的高效二维函数型混合效应模型框架
An Efficient Two-Dimensional Functional Mixed-Effect Model Framework for Repeatedly Measured Functional Data
AI总结：
本文针对可穿戴设备重复测量的函数型数据提出二维函数型混合效应模型（2dFMM）及快速三阶段估计方法，并用于揭示青少年身体活动与心理健康的日内和日间动态关联。
摘要：
随着可穿戴设备技术的快速发展，加速度计能够连续多日逐分钟记录身体活动，这为大规模人群研究中身体活动强度与心理健康结局之间的动态关联提供了重要洞察。利用上海学校青少年队列，我们估计了健康评估结果对加速度计记录的整周身体活动轨迹的影响，这类数据被视为重复测量的函数型数据。为实现这一目标，我们针对此类特殊数据提出了一种创新的二维函数型混合效应模型（2dFMM），该模型在纵向逐日观测上平滑变化，并具有依赖协变量的均值函数和协方差函数。该建模框架刻画了纵向结构和函数型结构，同时纳入了感兴趣协变量的二维固定效应。我们还开发了一种快速的三阶段估计程序，以提供准确的固定效应推断，从而保证模型的可解释性，并在面对大型数据集时提高计算效率。我们在队列人群中发现了强有力的证据，表明身体活动与心理健康评估之间存在日内和日间变化的显著关联，这为针对日常身体活动模式制定干预策略以改善学校青少年心理健康提供了启示。我们的方法还被用于环境数据，以展示其广泛的适用性。本文的补充材料可在网上获取。
英文摘要：
With the rapid development of wearable device technologies, accelerometers can record minute-by-minute physical activity for consecutive days, which provides important insight into a dynamic association between the intensity of physical activity and mental health outcomes for large-scale population studies. Using Shanghai school adolescent cohort we estimate the effect of health assessment results on physical activity profiles recorded by accelerometers throughout a week, which is recognized as repeatedly measured functional data. To achieve this goal, we propose an innovative two-dimensional functional mixed-effect model (2dFMM) for the specialized data, which smoothly varies over longitudinal day observations with covariate-dependent mean and covariance functions. The modeling framework characterizes the longitudinal and functional structures while incorporating two-dimensional fixed effects for covariates of interest. We also develop a fast three-stage estimation procedure to provide accurate fixed-effect inference for model interpretability and improve computational efficiency when encountering large datasets. We find strong evidence of intraday and interday varying significant associations between physical activity and mental health assessments among our cohort population, which shed light on possible intervention strategies targeting daily physical activity patterns to improve school adolescent mental health. Our method is also used in environmental data to illustrate the wide applicability. Supplementary materials for this article are available online.
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