Longitudinal Dynamic Functional Regression

TL;DR

This paper introduces a flexible, parsimonious framework for modeling the association between scalar outcomes and functional predictors over time in longitudinal studies, enhancing prediction accuracy and trajectory reconstruction.

Contribution

It develops a novel time-varying functional regression model using orthogonal basis functions, improving prediction and interpretability in longitudinal functional data analysis.

Findings

Excellent prediction accuracy demonstrated in simulations

Efficient computational performance achieved

Successful application to animal science data on sow feed intake

Abstract

This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study time-varying regression that leads to superior prediction properties and allows to reconstruct full trajectories of the response. The idea is to model the time-varying functional predictors using orthogonal basis functions and expand the time-varying regression coefficient using the same basis. Numerical investigation through simulation studies and data analysis show excellent performance in terms of accurate prediction and efficient computations, when compared with existing alternatives. The methods are inspired and applied to an animal science application, where of interest is to study the association between the feed intake of lactating sows and the minute-by-minute {temperature} throughout the 21st days of their lactation period. R code and an R illustration are provided at http://www4.stat.ncsu.edu/~staicu/software