Quantile regression in linear mixed models: a stochastic approximation EM approach.
Quantile regression in linear mixed models: a stochastic approximation EM approach.
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DOI：
10.4310/sii.2017.v10.n3.a10
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发表时间：
2017
影响因子：
0.8
通讯作者：
Bandyopadhyay D
中科院分区：
文献类型：
--
作者：
Galarza CE;Lachos VH;Bandyopadhyay D
本文提出了一种基于似然的方法来分析基于非对称拉普拉斯分布的连续纵向数据的分位数回归模型。与传统的均值回归方法相比，QR可以表征结果变量的整个条件分布，并且对异常值和错误分布的存在更鲁棒。利用ALD的良好的分层表示，我们的经典方法遵循EM（SAEM）算法的随机近似，在推导固定效应和方差分量的精确最大似然估计。我们评估的有限样本性能的算法和ML估计的渐近性质，通过实证实验和应用到两个真实的生活数据集。我们的实证结果清楚地表明，SAEM估计在标准误差和均方误差方面优于通过Geraci和Bottai（2014）方法的高斯求积和非光滑优化例程的组合获得的估计。所提出的SAEM算法在R包qrLMM（）中实现。
This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stochastic Approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the Geraci and Bottai (2014) approach in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the R package qrLMM().