Bayesian composite quantile regression for linear mixed-effects models

Bayesian Spatio-Temporal Modeling for the Inpatient Hospital Costs of Alcohol-Related Disorders

“…This suggests that ST‐WCQR is robust to heterogeneous effects and non‐normal errors. The superiority of the composite method over the conventional mean regression and the single quantile‐based counterparts for the asymmetric errors and heterogeneous data is consistent with results in the previous studies for the classical linear regression (Alhamzawi, 2016; Huang & Chen, 2015; Zhao et al, 2016) and longitudinal analysis (Tian et al, 2017, 2021). It is not surprising to find that ST‐WCQR has higher estimation efficiency than the single quantile‐based STQR and STMR, especially for the random intercepts.…”

“…To allow for different amounts of contribution from quantile regression curves to coefficient estimation, quantile‐specific weights are employed in (). When these weights are equal, ST‐WCQR reduces to the spatio‐temporal CQR that generally leads to less efficiency and less robustness (Bradic et al, 2011; Huang & Chen, 2015; Jiang et al, 2014; Sun et al, 2013; Tian et al, 2017). In addition, ST‐WCQR also serves as a unified approach for both mean regression and quantile regression since the ST‐WCQR with $$$ L=1 $$$ reduces to the quantile regression.…”

“…This paper provides a solution from a Bayesian perspective. Suppose that $$$ {y}_{ijk} $$$ follows a pseudo composite asymmetric Laplace distribution $$$ \mathrm{PCALD}\left(\boldsymbol{\mu}, \boldsymbol{\sigma}, \boldsymbol{\tau} \right) $$$ (Tian et al, 2017) with probability density function given by $$$ f\left(y|\boldsymbol{\mu}, \boldsymbol{\sigma}, \boldsymbol{\tau} \right)\propto {\prod}_{l=1}^L\frac{1}{\sigma_l}\exp \left\{-{\rho}_{\tau_l}\left(\frac{y-{\mu}_l}{\sigma_l}\right)\right\}, $$$ where $$$ {\mu}_l={\alpha}_l+m\left(\boldsymbol{x}\right) $$$, $$$ \boldsymbol{\mu} ={\left({\mu}_1,\dots, {\mu}_L\right)}^{\top } $$$ is a vector of location parameters, $$$ \boldsymbol{\sigma} ={\left({\sigma}_1,\dots, {\sigma}_L\right)}^{\top } $$$ is a vector of scale parameters, and $$$ \boldsymbol{\tau} ={\left({\tau}_1,\dots, {\tau}_L\right)}^{\top }...$…”

“…For sparse linear models, Huang and Chen (2015) proposed a Bayesian CQR with lasso penalty, which is further developed by Alhamzawi (2016) and Zhao et al (2016) using other sparsity inducing priors for better performance, especially under the case of heterogeneous errors. Tian et al (2017) propose a pseudo composite asymmetric Laplace distribution to conduct Bayesian CQR for longitudinal analysis. For semi‐parametric varying‐coefficient partially linear models, Kai et al (2011) studied the substantial efficiency gain of the proposed CQR estimators for non‐normal errors over the LS and single quantile‐based techniques.…”

Identification of Wiener Model with Internal Noise Using a Cubic Spline Approximation-Bayesian Composite Quantile Regression Algorithm

“…e Bayesian CQR (BCQR) algorithm used in this paper does not depend on the actual distribution of data, but on the likelihood function formed by the ALD [27]. e essence of BCQR is that the estimated parameter is regarded as a random variable, and the sampling distribution of parameter can be obtained by repeated sampling.…”