Weighted quantile regression for longitudinal data

TL;DR

This paper introduces a novel quantile regression model tailored for longitudinal data, accounting for within-subject correlation to improve inference efficiency and providing consistent, asymptotically normal estimates.

Contribution

It develops a new quantile regression approach for longitudinal data that incorporates correlation structure and uses smoothed estimating functions for better convergence.

Findings

Simulation studies show improved estimation accuracy.

Application to real data demonstrates practical utility.

Method achieves consistent and asymptotically normal estimates.

Abstract

Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view of the statistical landscape. In this paper we propose a new quantile regression model for longitudinal data. The proposed approach incorporates the correlation structure between repeated measures to enhance the efficiency of the inference. In order to use the Newton-Raphson iteration method to obtain convergent estimates, the estimating functions are redefined as smoothed functions which are differentiable with respect to regression parameters. Our proposed method for quantile regression provides consistent estimates with asymptotically normal distributions. Simulation studies are carried out to evaluate the performance of the proposed method. As an illustration, the proposed method was applied to a real-life data that contains self-reported labor pain for women in two groups.