Parametric Modeling of Quantile Regression Coefficient Functions with Longitudinal Data

TL;DR

This paper introduces a novel parametric approach to modeling quantile regression coefficients for longitudinal data, using a two-level quantile function and penalized fixed-effects estimation, with theoretical and practical validation.

Contribution

It extends quantile regression coefficients modeling to longitudinal data with a new two-level model and a penalized fixed-effects estimator, improving over standard methods.

Findings

The method provides consistent estimators under certain conditions.

Simulation studies demonstrate improved performance over existing methods.

Application to real data illustrates practical utility.

Abstract

In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the QRCM paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on $\ell_1$ and $\ell_2$ penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.