Generalized Multilevel Functional Regression.

Journal of the American Statistical Association
Ciprian M CrainiceanuChong-Zhi Di

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 (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.

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Citations

Aug 7, 2010·Journal of the American Statistical Association·Yehua LiRaymond J Carroll
Jan 1, 2011·Journal of the American Statistical Association·Ciprian M CrainiceanuNaresh M Punjabi
Mar 1, 2012·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Jeff GoldsmithDaniel Reich
Jan 1, 2011·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Vadim ZipunnikovCiprian Crainiceanu
May 30, 2015·Journal of Statistical Planning and Inference·Ana-Maria StaicuRaymond J Carroll
Sep 12, 2013·Cognitive, Affective & Behavioral Neuroscience·H ShouC M Crainiceanu
Feb 24, 2016·Statistics and Computing·Luo XiaoCiprian Crainiceanu
Aug 3, 2012·Statistics in Medicine·Ciprian M CrainiceanuNaresh Punjabi
Jun 9, 2012·Journal of the Royal Statistical Society. Series C, Applied Statistics·Jeff GoldsmithDaniel Reich
Nov 5, 2011·Biometrics·Ana-Maria StaicuDavid Ruppert
Jul 30, 2011·NeuroImage·Vadim ZipunnikovCiprian Crainiceanu
Feb 6, 2014·Journal of the American Statistical Association·Huaihou ChenH Alex Choi
May 8, 2018·Statistics in Medicine·Clemontina A DavenportVeerabhadran Baladandayuthapani
Dec 3, 2013·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Dawn B WoodardDavid Ruppert
May 30, 2014·Stat·Chongzhi DiWolfgang S Jank
Oct 17, 2017·Biostatistics·So Young ParkCiprian M Crainiceanu
Jan 11, 2017·Biometrics·Kyle HasenstabDamla Şentürk
Mar 16, 2017·Biometrics·Yu-Ru SuLi Hsu
Sep 19, 2017·International Statistical Review = Revue Internationale De Statistique·Philip T ReissR Todd Ogden
Jun 6, 2020·NeuroImage·Marco PalmaUNKNOWN Alzheimer’s Disease Neuroimaging Initiative
Nov 29, 2014·The Annals of Applied Statistics·Tian GeTimothy D Johnson
Jan 1, 2010·Electronic Journal of Statistics·Sonja GrevenDaniel Reich

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