Abstract

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (i) fit massively univariate pointwise mixed-effects models; (ii) apply any smoother along the functional domain; and (iii) obtain joint confidence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (i) Diffusion tensor imaging measured at multiple visits along the corpus callosum of multiple sclerosis patients; and (ii) physical activity (PA) data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the PA data application. Methods are accompanied by R software, though the method is “read-and-use,” as it can be implemented by any analyst who is familiar with mixed-effects model software. Supplementary files for this article are available online.

摘要

我们提出了纵向高斯和非高斯函数数据的快速单变量推理方法。该方法包括三个步骤：（i）拟合大规模单变量逐点混合效应模型；(ii) 沿功能域应用平滑器；(iii) 使用高斯数据的分析方法或非高斯数据的研究参与者的引导获得联合置信带。方法由两个应用程序驱动：（i）在多发性硬化症患者的胼胝体多次就诊时测量的扩散张量成像；(ii) 身体佩戴的加速度计连续多天测量的身体活动 (PA) 数据。广泛的模拟研究表明，模型拟合和推理比现有方法准确且速度快得多。而且，所提出的方法是唯一一种对于 PA 数据应用在计算上可行的方法。方法随附 ​​R 软件，尽管该方法是“即读即用”的，因为它可以由任何熟悉混合效应模型软件的分析师实施。本文的补充文件可在线获取。