Modeling Motor Learning Using Heteroscedastic Functional Principal Components Analysis

We propose a novel method for estimating population-level and subject-specific effects of covariates on the variability of functional data. We extend the functional principal components analysis framework by modeling the variance of principal component scores as a function of covariates and subject-specific random effects. In a setting where principal components are largely invariant across subjects and covariate values, modeling the variance of these scores provides a flexible and interpretable way to explore factors that affect the variability of functional data. Our work is motivated by a novel dataset from an experiment assessing upper extremity motor control, and quantifies the reduction in movement variability associated with skill learning. The proposed methods can be applied broadly to understand movement variability, in settings that include motor learning, impairment due to injury or disease, and recovery. Supplementary materials for this article are available online.

本研究提出一种全新方法，用于估计协变量对功能数据（functional data）变异性的群体水平效应与个体特异性效应。我们将主成分得分的方差建模为协变量与个体特异性随机效应的函数，以此拓展了功能主成分分析（functional principal components analysis）框架。在主成分在不同个体与协变量取值下大体保持不变的场景中，对这类得分的方差进行建模，可为探索影响功能数据变异性的因素提供一种灵活且可解释的研究路径。本研究的灵感来源于一项评估上肢运动控制的实验所生成的全新数据集，并量化了与技能学习相关的运动变异性降幅。所提出的方法可被广泛应用于运动变异性的相关研究，适用场景涵盖运动学习、损伤或疾病所致的运动功能损害，以及康复过程。本文的补充材料可在线获取。