Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation under non-normal error distribution. However, at least in principle, quantile regression (QR) is more robust in the presence of outliers/influential observations and misspecification of the error distributions when compared to the conventional mean regression approach. In this context, this paper develops a likelihood-based approach for estimating QR models with correlated continuous longitudinal data using the asymmetric Laplace distribution. Our approach relies on the stochastic approximation of the EM algorithm (SAEM algorithm), obtaining maximum likelihood estimates of the fixed effects and variance components in the case of nonlinear mixed effects (NLME) models. We evaluate the finite sample performance of the SAEM algorithm and asymptotic properties of the ML estimates through simulation experiments. Moreover, two real life datasets are used to illustrate our proposed method using the $$\texttt {qrNLMM}$$ qrNLMM package from $$\texttt {R}$$ R .

中文翻译：

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非线性混合效应模型的分位数回归：基于似然的观点

纵向数据经常使用正态混合效应模型进行分析。此外，传统的估计方法基于均值回归，导致非正态误差分布下的参数估计不稳健。然而，至少在原则上，与传统的平均回归方法相比，分位数回归 (QR) 在存在异常值/影响观察和错误分布的错误指定的情况下更加稳健。在这种情况下，本文开发了一种基于可能性的方法，用于使用非对称拉普拉斯分布估计具有相关连续纵向数据的 QR 模型。我们的方法依赖于 EM 算法（SAEM 算法）的随机近似，在非线性混合效应 (NLME) 模型的情况下，获得固定效应和方差分量的最大似然估计。我们通过模拟实验评估了 SAEM 算法的有限样本性能和 ML 估计的渐近特性。此外，使用来自 $$\texttt {R}$$ R 的 $$\texttt {qrNLMM}$$ qrNLMM 包，使用两个现实生活数据集来说明我们提出的方法。