Generalized multilevel function-on-scalar regression and principal component analysis

被引:103
作者
Goldsmith, Jeff [1 ]
Zipunnikov, Vadim [2 ]
Schrack, Jennifer [3 ,4 ]
机构
[1] Columbia Univ, Mailman Sch Publ Hlth, Dept Biostat, New York, NY 10027 USA
[2] Johns Hopkins Univ, Dept Biostat, Bloomberg Sch Publ Hlth, Baltimore, MD 21205 USA
[3] Johns Hopkins Univ, Bloomberg Sch Publ Hlth, Dept Epidemiol, Baltimore, MD USA
[4] NIA, Longitudinal Studies Sect, Translat Gerontol Branch, NIH, Bethesda, MD 20892 USA
关键词
Accelerometry; Bayesian inference; Generalized functional data; Hamiltonian Monte Carlo; Penalized splines; PHYSICAL-ACTIVITY; LONGITUDINAL DATA; MODELS; ACCELEROMETER; PATTERNS; BINARY; PCA;
D O I
10.1111/biom.12278
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
This manuscript considers regression models for generalized, multilevel functional responses: functions are generalized in that they follow an exponential family distribution and multilevel in that they are clustered within groups or subjects. This data structure is increasingly common across scientific domains and is exemplified by our motivating example, in which binary curves indicating physical activity or inactivity are observed for nearly 600 subjects over 5 days. We use a generalized linear model to incorporate scalar covariates into the mean structure, and decompose subject-specific and subject-day-specific deviations using multilevel functional principal components analysis. Thus, functional fixed effects are estimated while accounting for within-function and within-subject correlations, and major directions of variability within and between subjects are identified. Fixed effect coefficient functions and principal component basis functions are estimated using penalized splines; model parameters are estimated in a Bayesian framework using Stan, a programming language that implements a Hamiltonian Monte Carlo sampler. Simulations designed to mimic the application have good estimation and inferential properties with reasonable computation times for moderate datasets, in both cross-sectional and multilevel scenarios; code is publicly available. In the application we identify effects of age and BMI on the time-specific change in probability of being active over a 24-hour period; in addition, the principal components analysis identifies the patterns of activity that distinguish subjects and days within subjects.
引用
收藏
页码:344 / 353
页数:10
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