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Stat Med. 2017 Jun 30;36(14):2237-2250. doi: 10.1002/sim.7254. Epub 2017 Feb 17.

Variable selection in the functional linear concurrent model.

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Department of Biostatistics, Columbia Mailman School of Public Health, Columbia University, New York, U.S.A.
Department of Medicine, Columbia University Medical Center, Columbia University, New York, U.S.A.
Department of Psychiatry and Behavioral Sciences, Stony Brook University, Stony Brook, U.S.A.


We propose methods for variable selection in the context of modeling the association between a functional response and concurrently observed functional predictors. This data structure, and the need for such methods, is exemplified by our motivating example: a study in which blood pressure values are observed throughout the day, together with measurements of physical activity, location, posture, affect or mood, and other quantities that may influence blood pressure. We estimate the coefficients of the concurrent functional linear model using variational Bayes and jointly model residual correlation using functional principal components analysis. Latent binary indicators partition coefficient functions into included and excluded sets, incorporating variable selection into the estimation framework. The proposed methods are evaluated in simulations and real-data analyses, and are implemented in a publicly available R package with supporting interactive graphics for visualization.


ambulatory blood pressure; functional data; intensive longitudinal data; spline smoothing; variational Bayes; wearable devices

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