Division of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
Institute for Biomedical Research and Innovation (IRIB), National Research Council (CNR), Palermo, Italy.
Stat Methods Med Res. 2020 Dec;29(12):3757-3769. doi: 10.1177/0962280220941159. Epub 2020 Jul 19.
Quantile regression is widely used to estimate conditional quantiles of an outcome variable of interest given covariates. This method can estimate one quantile at a time without imposing any constraints on the quantile process other than the linear combination of covariates and parameters specified by the regression model. While this is a flexible modeling tool, it generally yields erratic estimates of conditional quantiles and regression coefficients. Recently, parametric models for the regression coefficients have been proposed that can help balance bias and sampling variability. So far, however, only models that are linear in the parameters and covariates have been explored. This paper presents the general case of nonlinear parametric quantile models. These can be nonlinear with respect to the parameters, the covariates, or both. Some important features and asymptotic properties of the proposed estimator are described, and its finite-sample behavior is assessed in a simulation study. Nonlinear parametric quantile models are applied to estimate extreme quantiles of longitudinal measures of respiratory mechanics in asthmatic children from an epidemiological study and to evaluate a dose-response relationship in a toxicological laboratory experiment.
分位数回归广泛用于估计给定协变量的感兴趣的因变量的条件分位数。这种方法可以一次估计一个分位数，而不会对分位数过程施加任何限制，除了回归模型指定的协变量和参数的线性组合。虽然这是一个灵活的建模工具，但它通常会产生条件分位数和回归系数的不稳定估计。最近，已经提出了回归系数的参数模型，这些模型可以帮助平衡偏差和抽样变异性。然而，到目前为止，仅探索了参数和协变量线性的模型。本文提出了非线性参数分位数模型的一般情况。这些模型可以是参数、协变量或两者的非线性。描述了所提出的估计器的一些重要特征和渐近性质，并在模拟研究中评估了其有限样本行为。非线性参数分位数模型被应用于从一项流行病学研究中估计哮喘儿童呼吸力学的纵向测量的极端分位数，并在毒理学实验室实验中评估剂量反应关系。
