Subgroup analysis for the functional linear model

TL;DR

This paper introduces a penalization-based method for subgroup analysis in functional linear models, enabling identification of heterogeneous coefficient functions across unknown subgroups, with proven theoretical properties and superior performance in simulations and real data.

Contribution

It develops a novel penalized fusion approach for simultaneous subgroup detection and coefficient estimation in functional linear models, addressing the challenge of unknown subgroup structures.

Findings

The method accurately identifies subgroup structures.

It outperforms competing methods in simulations.

Application to air quality data yields new insights.

Abstract

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.