Variable Selection in Functional Linear Concurrent Regression

Abstract: We propose a novel method for variable selection in functional linear concurrent regression. Our research is motivated by a fisheries footprint study where the goal is to identify important time-varying socio-structural drivers influencing patterns of seafood consumption, and hence fisheries footprint, over time, as well as estimating their dynamic effects. We develop a variable selection method in functional linear concurrent regression extending the classically used scalar on scalar variable selection methods like LASSO, SCAD, and MCP. We show in functional linear concurrent regression the variable selection problem can be addressed as a group LASSO, and their natural extension; group SCAD or a group MCP problem. Through simulations, we illustrate our method, particularly with group SCAD or group MCP penalty, can pick out the relevant variables with high accuracy and has minuscule false positive and false negative rate even when data is observed sparsely, is contaminated with noise and the error process is highly non-stationary. We also demonstrate two real data applications of our method in studies of dietary calcium absorption and fisheries footprint in the selection of influential time-varying covariates.