Generalized Multilevel Functional Regression.

Publication Type:

Journal Article


Journal of the American Statistical Association, Volume 104, Issue 488, p.1550-1561 (2009)


2009, Center-Authored Paper, Public Health Sciences Division


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 (GLMMs). 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 (SHHS), 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 data sets. Supplemental materials for this article are available online.