Longitudinal Functional Models with Structured Penalties

TL;DR

This paper develops a new method for estimating time-varying relationships in longitudinal data using structured penalties, combining penalized regression with mixed models, and demonstrates its effectiveness through simulations and real HIV neurocognitive data.

Contribution

It introduces a novel estimation framework for longitudinal functional regression models with structured penalties, linking penalized least squares to mixed models.

Findings

Effective estimation of time-varying coefficients demonstrated in simulations.

Application to HIV neurocognitive data reveals meaningful associations.

Method outperforms traditional approaches in capturing dynamic relationships.

Abstract

This paper addresses estimation in a longitudinal regression model for association between a scalar outcome and a set of longitudinally-collected functional covariates or predictor curves. The framework consists of estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions but having time-varying coefficients. The estimation procedure exploits the equivalence between penalized least squares estimation and a linear mixed model representation. The process is empirically evaluated with several simulations and it is applied to analyze the neurocognitive impairment of HIV patients and its association with longitudinally-collected magnetic resonance spectroscopy curves.