2019/06/12 by Stephanie T. Chen, Luo Xiao, Chen, Stephanie T. +3
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.1906.04889
openalex publication_date 2019/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily complex for a data application. Hypothesis testing can be used to guide model selection by determining if a functional predictor is necessary. Using a mixed effects representation with penalized splines and variance component tests, we propose a framework for testing functional linear models with responses from exponential family distributions. The proposed method can accommodate dense and sparse functional data, and be used to test functional predictors for no effect and form of the effect. We show via simulation study that the proposed method achieves the nominal level and has high power, and we demonstrate its utility with two data applications.