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 article, we describe how the $\mathit{qrcm}$ 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 ${\mathcal{l}}_1$ and ${\mathcal{l}}_2$ 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.

摘要

在普通分位数回归中，一次估计不同阶的分位数。另一种方法，称为分位数回归系数建模( qrcm )，是将分位数回归系数建模为分位数阶的参数函数。在本文中，我们将描述如何$\mathit{qrcm}$范式可以应用于纵向数据。我们引入了一个两级分位数函数，其中使用两个不同的分位数回归模型来描述受试者内反应的（条件）分布和个体效应的分布。我们提出了一种新型的惩罚固定效应估计器，并讨论了它相对于基于${\mathcal{升}}_1$ 和 ${\mathcal{升}}_2$处罚。我们提供模型可识别性条件，导出渐近特性，描述拟合优度度量和模型选择标准，呈现模拟结果并讨论应用。所提出的方法已在 R 包 qrcm 中实现。