Generalized Multilevel Functional Regression

Abstract We introduce Generalized Multilevel Functional Linear Models (GMFLMs), a novel statistical framework for regression models where exposure has a multilevel functional structure. We show that GMFLMs are, in fact, generalized multilevel mixed models. Thus, GMFLMs can be analyzed using the mixed effects inferential machinery and can be generalized within a well-researched statistical framework. We propose and compare two methods for inference: (1) a two-stage frequentist approach; and (2) a joint Bayesian analysis. Our methods are motivated by and applied to the Sleep Heart Health Study, the largest community cohort study of sleep. However, our methods are general and easy to apply to a wide spectrum of emerging biological and medical datasets. Supplemental materials for this article are available online. Keywords: : Functional principal componentsSleep EEGSmoothing