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Longitudinal functional additive model with continuous proportional outcomes for physical activity data
Author(s) -
Li Haocheng,
Keadle Sarah Kozey,
Kipnis Victor,
Carroll Raymond J.
Publication year - 2016
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.121
Subject(s) - variance (accounting) , functional data analysis , functional principal component analysis , statistics , random effects model , mathematics , regression , principal component analysis , regression analysis , econometrics , computer science , medicine , economics , accounting , meta analysis
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.