Restricted Likelihood Ratio Tests for Functional Effects in the Functional Linear Model

The goal of our article is to provide a transparent, robust, and computationally feasible statistical approach for testing in the context of scalar-on-function linear regression models. Assuming linearity between response and predictors, we are interested in testing for the necessity of functional effects. Our methods are motivated by and applied to a large longitudinal study involving diffusion tensor imaging of intracranial white matter tracts in a susceptible cohort. In the context of this study, we conduct hypothesis tests that are motivated by anatomical knowledge and support recent findings regarding the relationship between cognitive impairment and white matter demyelination. R code and data are in the examples of refund::rlrt.pfr(). Supplementary materials for this article are available online.

本文旨在提出一种透明、稳健且计算可行的统计方法，用于标量对函数线性回归（scalar-on-function linear regression）模型框架下的假设检验。在假设响应变量与预测变量间存在线性关系的前提下，我们聚焦于检验函数型效应的必要性。我们的方法源于一项针对易感队列的大规模纵向研究，并应用于该研究——该研究针对颅内白质束开展了扩散张量成像（diffusion tensor imaging）。基于该研究场景，我们开展了依托解剖学知识的假设检验，为认知障碍与脑白质脱髓鞘之间关联的近期研究发现提供了支撑。本文的R代码与数据集可在refund::rlrt.pfr()函数的示例中获取。本文的补充材料可在线获取。