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Unpublished Paper
Johns Hopkins University, Dept. of Biostatistics Working Papers
  • Ciprian M. Crainiceanu, Bloomberg School of Public Health, Department of Biostatistics, Johns Hopkins
  • Ana-Maria Staicu, Department of Mathematics, University of Bristol
  • Chongzhi Di, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health
Date of this Version

We introduce Generalized Multilevel Functional Linear Models (GMFLM), a novel statistical framework motivated by and applied to the Sleep Heart Health Study (SHHS), the largest community cohort study of sleep. The primary goal of SHHS is to study the association between sleep disrupted breathing (SDB) and adverse health effects. An exposure of primary interest is the sleep electroencephalogram (EEG), which was observed for thousands of individuals at two visits, roughly 5 years apart. This unique study design led to the development of models where the outcome, e.g. hypertension, is in an exponential family and the exposure, e.g. sleep EEG, is multilevel functional data. We show that GMFLMs are, in fact, generalized multilevel mixed effect models. Two consequences of this result are that: 1) the mixed effects inferential machinery can be used for GMFLM and 2) functional regression models can be extended naturally to include, for example, additional covariates, random effects and nonparametric components. We propose and compare two inferential methods based on the parsimonious decomposition of the functional space.

Citation Information
Ciprian M. Crainiceanu, Ana-Maria Staicu and Chongzhi Di. "GENERALIZED MULTILEVEL FUNCTIONAL REGRESSION" (2008)
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