Variable selection in nonlinear function-on-scalar regression.

Abstract

W e develop a new method for variable selection in a nonlinear additive function-on-scalar regression model. Existing methods for variable selection in function-on-scalar regression have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. W e propose a computationally efficient approach for variable selection in existing linear function-on-scalar regression using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in function-on-scalar regression, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in function-on-scalar regression even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003-2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle and health characteristics of the participants.