一种用于重复观测人体运动数据的多变量多水平纵向函数模型
A Multivariate Multilevel Longitudinal Functional Model for Repeatedly Observed Human Movement Data
AI总结：
针对重复观测的人体运动序列相关纵向函数数据，提出多变量多水平纵向函数模型，采用函数主成分基与标量纵向混合效应建模，在跑者数据中验证了速度的关节效应与个体变化识别能力，并通过模拟证实方法有效性。
摘要：
生物力学与人体运动研究通常会在整个运动过程中定期测量多个运动学或动力学变量，产生的数据呈现为平滑的多变量时变曲线，天然适用于函数型数据分析。如今，针对每个个体重复记录相同运动的情况日益普遍，由此产生的曲线存在序列相关性，可被视为纵向函数型数据。我们提出了一种用于建模多变量多水平纵向函数型数据的新方法，并将其应用于跑步机跑步过程中收集的休闲跑者运动学数据。对于每一步幅，跑者的髋、膝、踝关节角度被联合建模为依赖于个体特异性协变量的平滑多变量函数。我们采用纵向变化的多变量函数随机效应来捕捉相邻步幅之间的相关性，以及多变量函数在整个跑步机跑步过程中的变化。模型拟合采用基函数建模方法：我们使用多变量函数主成分基来表示每个观测值，并通过标量纵向混合效应模型对基系数进行建模。预测得到的随机效应用于理解和可视化多变量函数型数据在整个跑步机跑步过程中的变化。在我们的应用中，该方法量化了标量协变量对多变量函数型数据的影响，揭示了跑步速度对髋、膝、踝关节具有统计学显著的效应。对预测随机效应的分析表明，个体的运动学特征总体上保持稳定，但也能识别出在跑步过程中表现出强烈变化的特定个体。我们还开展了一项模拟研究，以验证所提出的方法在符合实际的数据生成场景下的有效性。
英文摘要：
Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to functional data analysis. It is now increasingly common to record the same movement repeatedly for each individual, resulting in curves that are serially correlated and can be viewed as longitudinal functional data. We present a new approach for modelling multivariate multilevel longitudinal functional data, with application to kinematic data from recreational runners collected during a treadmill run. For each stride, the runners' hip, knee and ankle angles are modelled jointly as smooth multivariate functions that depend on subject-specific covariates. Longitudinally varying multivariate functional random effects are used to capture the dependence among adjacent strides and changes in the multivariate functions over the course of the treadmill run. A basis modelling approach is adopted to fit the model -- we represent each observation using a multivariate functional principal components basis and model the basis coefficients using scalar longitudinal mixed effects models. The predicted random effects are used to understand and visualise changes in the multivariate functional data over the course of the treadmill run. In our application, our method quantifies the effects of scalar covariates on the multivariate functional data, revealing a statistically significant effect of running speed at the hip, knee and ankle joints. Analysis of the predicted random effects reveals that individuals' kinematics are generally stable but certain individuals who exhibit strong changes during the run can also be identified. A simulation study is presented to demonstrate the efficacy of the proposed methodology under realistic data-generating scenarios.
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