Efficient Longitudinal Function-on-Function Regression

TL;DR

This paper introduces a fast, reliable method for longitudinal function-on-function regression, enabling accurate inference with reduced computational effort, demonstrated through simulations and a physical activity study.

Contribution

It presents a novel three-step approach for efficient longitudinal function-on-function regression with valid inference, implemented in an R package.

Findings

Accurate estimation and valid inference demonstrated in simulations.

Significant increases in morning physical activity observed in a real study.

Method reduces computational burden compared to existing approaches.

Abstract

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies demonstrate that the proposed method achieves accurate estimation and valid inference, while substantially reducing computational burden compared to existing approaches. Methods are motivated by a physical activity intervention trial in older adults where high-dimensional wearable data were collected longitudinally across multiple visits. Our applications reveal significant increases in physical activity in the morning using interpersonal intervention strategies, but not intrapersonal strategies. The proposed methods are implemented in an R package.