title: Variable Selection in Function-on-Scalar Regression.
abstract: For regression models with functional responses and scalar predictors, it is common for the number of predictors to be large. Despite this, few methods for variable selection exist for function-on-scalar models, and none account for the inherent correlation of residual curves in such models. By expanding the coefficient functions using aB-spline basis, we pose the function-on-scalar model as a multivariate regression problem. Spline coefficients are grouped within coefficient function, and group-minimax concave penalty (MCP) is used for variable selection. We adapt techniques from generalized least squares to account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance; simulation results indicate that this iterative algorithm often performs as well as pre-whitening using the true covariance, and substantially outperforms methods that neglect the covariance structure. We apply our method to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control, and find that our method provides lower prediction errors than competing methods.
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University.
authors.forename: Yakuan
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University.
authors.forename: Jeff
authors.initials: J
authors.lastname: Goldsmith
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University.
authors.forename: Todd
authors.initials: T
authors.lastname: Ogden
keywords: Group MCP; Kinematic Data; Pre-whitening; Splines