Bayesian quantile regression for hierarchical linear models

References

• Lindley DV, Smith AFM. Bayes estimates for the linear model. J R Statist Soc. 1972;B(34):1–41.
   Google Scholar
• Shiffrin RM, Lee MD, Kim W. A survey of model evaluation approaches with a tutorial on hierarchical Bayesian methods. Cogn Sci. 2008;32:1248–1284. doi: 10.1080/03640210802414826
   PubMed Web of Science ®Google Scholar
• Choi T, Schervish MJ, Schmitt KA. Bayesian hierarchical analysis for multiple health endpoints in a toxicity study. Int Biometric Soc. 2010;15(3):290–307.
   Google Scholar
• Laird NM, Ware H. Random-effects models for longitudinal data. Biometrics. 1982;38:963–974. doi: 10.2307/2529876
   PubMed Web of Science ®Google Scholar
• Gamerman D. Efficient sampling from the posterior distribution in generalized linear mixed models. Stat Comput. 1997;7:57–68. doi: 10.1023/A:1018509429360
   Web of Science ®Google Scholar
• Escobar MD. Nonparametric Bayesian methods in hierarchical model. J Statist Plan Inference. 1995;43:97–106. doi: 10.1016/0378-3758(94)00011-J
   Web of Science ®Google Scholar
• Koenker R, Bassett G. Regression quantiles. Econometrical. 1978;46(1):33–50. doi: 10.2307/1913643
   Web of Science ®Google Scholar
• Koenker R, Bassett G. Robust tests for heteroscedasticity based on regression quantiles. Econometrica. 1982;50:43–61. doi: 10.2307/1912528
   Web of Science ®Google Scholar
• Bassett GW, Koenker R. An empirical quantile function for linear models with iid errors. J Amer Statist Assoc. 1982;77:407–415.
   Web of Science ®Google Scholar
• Bassett G, Koenker R. Strong consistency of regression quantiles and related empirical processes. Econom Theory. 1986;2:191–201. doi: 10.1017/S0266466600011488
   Google Scholar
• Koenker R, D'Orey V. Computing regression quantiles. Appl Stat. 1987;36:383–393. doi: 10.2307/2347802
   Web of Science ®Google Scholar
• Koenker R, D'Orey V. Remark AS R92: A remark on Algorithm AS 229: computing dual regression quantiles and regression rank scores. Appl Stat. 1993;43:410–414. doi: 10.2307/2986030
   Web of Science ®Google Scholar
• Koenker R, Machado JAF. Goodness of fit and related inference processes for quantile regression. J Amer Statist Assoc. 1999;94(448):1296–1310. doi: 10.1080/01621459.1999.10473882
   Web of Science ®Google Scholar
• Yu K, Moyeed RA. Bayesian quantile regression. Stat Probab Lett. 2001;54(4):437–447. doi: 10.1016/S0167-7152(01)00124-9
   Web of Science ®Google Scholar
• Yu K, Stander J. Bayesian analysis of a Tobit quantile regression model. J Econ. 2007;137:260–276. doi: 10.1016/j.jeconom.2005.10.002
   Web of Science ®Google Scholar
• Tsionas EG. Bayesian quantile inference. J Statist Comput Simul. 2003;73(9):659–674. doi: 10.1080/0094965031000064463
   Web of Science ®Google Scholar
• Kottas A, Gelfand AE. Bayesian semiparametric median regression modelling. J Amer Statist Assoc. 2001;97(460):1020–1033.
   Google Scholar
• Kottas A, Krnjajic M. Bayesian semiparametric modelling in quantile regression. Scand J Stat. 2009;36(2):297–319. doi: 10.1111/j.1467-9469.2008.00626.x
   Web of Science ®Google Scholar
• Yu K, Zhang J. A three-parameter asymmetric Laplace distribution and its extension. Commun Stat: Theory Methods. 2005;34(9–10):1636–1640.
   Web of Science ®Google Scholar
• Chen L, Yu K. Automatic Bayesian quantile regression curve fitting. Stat Comput. 2009;19:271–281. doi: 10.1007/s11222-008-9091-x
   Web of Science ®Google Scholar
• Tian MZ, Chen GM. Hierarchical linear regression models for conditional quantiles. Sci China: Ser A Math. 2006;49(12):1800–1815. doi: 10.1007/s11425-006-2023-3
   Google Scholar
• Tian MZ, Tang ML, Chan PS. Semiparametric quantile modelling of hierarchical Data. Acta Math Sin. 2009;25(4):597–616. doi: 10.1007/s10114-008-7220-2
   Web of Science ®Google Scholar
• George EL, McCulloch RE. Variable selection via Gibbs sampling. J Amer Statist Assoc. 1993;88:881–889. doi: 10.1080/01621459.1993.10476353
   Web of Science ®Google Scholar
• George EL, McCulloch RE. Approaches for Bayesian variable selection. Statist Sin. 1997;7:339–373.
   Web of Science ®Google Scholar
• Wang XY, Song XF. Measure market risk based on Bayesian quantile regression model with an application. J Syst Manage. 2009;18(1):40–48.
   Google Scholar
• Alhamzawi R, Yu K. Variable selection in quantile regression via Gibbs sampling. J Appl Stat. 2012;39(4):799–813. doi: 10.1080/02664763.2011.620082
   Web of Science ®Google Scholar
• Alhamzawi R, Yu K, Vinciotti V, Tucker A. Prior elicitation for mixed quantile regression with an allometric model. Environmetrics. 2011;22:911–920. doi: 10.1002/env.1118
   Web of Science ®Google Scholar