title: Multilevel sparse functional principal component analysis.
abstract: We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Diet al.2009) was proposed for such data when functions are densely recorded. Here we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between and within subject levels. We address inherent methodological differences in the sparse sampling context to: 1) estimate the covariance operators; 2) estimate the functional principal component scores; 3) predict the underlying curves. Through simulations the proposed method is able to discover dominating modes of variations and reconstruct underlying curves well even in sparse settings. Our approach is illustrated by two applications, the Sleep Heart Health Study and eBay auctions.
authors.affiliation: Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, M2-B500, Seattle, WA 98115, USA.
authors.forename: Chongzhi
authors.initials: C
authors.lastname: Di
authors.affiliation: Department of Biostatistics, Johns Hopkins University, 615 North Wolfe Street, Baltimore, MD 21205, USA.
authors.forename: Ciprian M
authors.initials: CM
authors.lastname: Crainiceanu
authors.affiliation: Department of Information Systems and Decision Sciences, University of South Florida, Tampa, FL 33620, USA.
authors.forename: Wolfgang S
authors.initials: WS
authors.lastname: Jank
keywords: functional principal component analysis; multilevel models; smoothing