Variable Selection in Function-on-Scalar Regression

• Activity Number: 31
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yakuan Chen* and Jeff Goldsmith and Todd Ogden
• Companies: Columbia University and Columbia University and Columbia University
• Keywords: function-on-scalar regression ; variable selection ; correlated errors

Abstract

The problem of variable selection often arises in the context of models with functional responses and scalar predictors. In comparison with traditional regression models, this setting is complicated by the dimensionality of the response and coefficient curves and by the correlation structure of the residuals. By expanding the coefficient functions using a B-spline basis, we pose the function-on-scalar model as a multivariate multiple 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 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. 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.