  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.
