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Abstract:
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We develop methods for variable selection when modeling the association between a functional response and functional predictors that are observed on the same domain. 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, heart rate, location, posture, attitude, 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 simulated- and real-data analyses.
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