title: Longitudinal functional additive model with continuous proportional outcomes for physical activity data.
abstract: Motivated by physical activity data obtained from the BodyMedia FIT device (www.bodymedia.com), we take a functional data approach for longitudinal studies with continuous proportional outcomes. The functional structure depends on three factors. In our three-factor model, the regression structures are specified as curves measured at various factor-points with random effects that have a correlation structure. The random curve for the continuous factor is summarized using a few important principal components. The difficulties in handling the continuous proportion variables are solved by using a quasilikelihood type approximation. We develop an efficient algorithm to fit the model, which involves the selection of the number of principal components. The method is evaluated empirically by a simulation study. This approach is applied to the BodyMedia data with 935 males and 84 consecutive days of observation, for a total of 78, 540 observations. We show that sleep efficiency increases with increasing physical activity, while its variance decreases at the same time.
authors.affiliation: Departments of Oncology and Community Health Sciences, University of Calgary, Calgary, AB, T2N 1N4, Canada.
authors.forename: Haocheng
authors.initials: H
authors.lastname: Li
authors.affiliation: Kinesiology Department, California Polytechnic State University, San Luis Obispo, CA, U.S.A.
authors.forename: Sarah
authors.initials: S
authors.lastname: Kozey-Keadle
authors.affiliation: Biometry Research Group, DCP, National Cancer Institute, Bethesda, MD, U.S.A.
authors.forename: Victor
authors.initials: V
authors.lastname: Kipnis
authors.affiliation: Department of Statistics, Texas A&M University, College Station, TX, U.S.A. and Department of Mathematics and Statistics, University of Technology Sydney, Broadway, NSW, 2007, Australia.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
keywords: BodyMedia FIT device; continuous proportions; functional data; mixed-effects model; physical activity; sleep efficiency