Abstract
Bayesian regression quantile has received much attention in recent literature. The objective of this paper is to illustrate Brq, a new software package in R. Brq allows for the Bayesian coefficient estimation and variable selection in regression quantile (RQ) and support Tobit and binary RQ. In addition, this package implements the Bayesian Tobit and binary RQ with lasso and adaptive lasso penalties. Further modeling functions for summarising the results, drawing trace plots, posterior histograms, autocorrelation plots, and plotting quantiles are included.
Similar content being viewed by others
References
Algamal, Z.Y., Alhamzawi, R., Ali, H.T.M.: Gene selection for microarray gene expression classification using bayesian lasso quantile regression. Comput. Biol. Med. 97, 145–152 (2018)
Alhamzawi, R., Ali, H.T.M.: Bayesian tobit quantile regression with penalty. Commun. Stat. Simul. Comput. 47(6), 1739–1750 (2018)
Alhamzawi, R., Yu, K.: Bayesian tobit quantile regression using g-prior distribution with ridge parameter. J. Stat. Comput. Simul. 85(14), 2903–2918 (2015)
Alhamzawi, R., Yu, K., Benoit, D.F.: Bayesian adaptive lasso quantile regression. Stat. Model. 12(3), 279–297 (2012)
Alhamzawi, R., Yu, K., Vinciotti, V., Tucker, A.: Prior elicitation for mixed quantile regression with an allometric model. Environmetrics 22(7), 911–920 (2011)
Alhamzawi, R.J.T.: Prior elicitation and variable selection for bayesian quantile regression. Ph. D. thesis, Brunel University, School of Information Systems, Computing and Mathematics (2013)
Benoit, D.F., Van den Poel, D.: Binary quantile regression: a Bayesian approach based on the asymmetric laplace distribution. J. Appl. Econ. 27(7), 1174–1188 (2012)
Brownlee, K.A.: Statistical Theory and Methodology in Science and Engineering, vol. 150. Wiley, New York (1965)
Davino, C., Furno, M., Vistocco, D.: Quantile Regression: Theory and Applications. Wiley, Amsterdam (2013)
Farcomeni, A.: Quantile regression for longitudinal data based on latent Markov subject-specific parameters. Stat. Comput. 22(1), 141–152 (2012)
Geraci, M., et al.: Linear quantile mixed models: the lqmm package for laplace quantile regression. J. Stat. Softw. 57(13), 1–29 (2014)
Geraci, M., Bottai, M.: Quantile regression for longitudinal data using the asymmetric laplace distribution. Biostatistics 8(1), 140–154 (2006)
Hao, L., Naiman, D.Q.: Quantile regression. quantitative applications in the social sciences(2007)
Hashem, H., Vinciotti, V., Alhamzawi, R., Yu, K.: Quantile regression with group lasso for classification. Adv. Data Anal. Classif. 10(3), 375–390 (2016)
Isaacs, D., Altman, D., Tidmarsh, C., Valman, H., Webster, A.: Serum immunoglobulin concentrations in preschool children measured by laser nephelometry: reference ranges for igg, iga, igm. J. Clin. Pathol. 36(10), 1193–1196 (1983)
Koenker, R., Bassett, v.: Regression quantiles. Econometr. J. Econ. Soc. 33–50 (1978)
Koenker, R., Hallock, K.F.: Quantile regression. J. Econ. Perspect. 15(4), 143–156 (2001)
Koenker, R., Machado, J.A.: Goodness of fit and related inference processes for quantile regression. J. Am. Stat. Assoc. 94(448), 1296–1310 (1999)
Koenker, R.W., D’Orey, V.: Algorithm as 229: computing regression quantiles. J. R. Stat. Soc.: Ser. C (Appl. Stat.) 36(3), 383–393 (1987)
Kozumi, H., Kobayashi, G.: Gibbs sampling methods for bayesian quantile regression. J. Stat. Comput. Simul. 81(11), 1565–1578 (2011)
Li, Q., Xi, R., Lin, N., et al.: Bayesian regularized quantile regression. Bayesian Anal. 5(3), 533–556 (2010)
Manski, C.F.: Maximum score estimation of the stochastic utility model of choice. J. Econ. 3(3), 205–228 (1975)
Manski, C.F.: Asymptotic properties of the maximum score estimator. J. Econ. 27, 313–333 (1985)
Marino, M.F., Alfó, M.: Latent drop-out based transitions in linear quantile hidden markov models for longitudinal responses with attrition. Adv. Data Anal. Classif. 9(4), 483–502 (2015)
Marino, M.F., Tzavidis, N., Alfò, M.: Mixed hidden markov quantile regression models for longitudinal data with possibly incomplete sequences. Stat. Methods Med. Res. 27(7), 2231–2246 (2018)
Neelon, B., Li, F., Burgette, L.F., Benjamin Neelon, S.E.: A spatiotemporal quantile regression model for emergency department expenditures. Stat. Med. 34(17), 2559–2575 (2015)
Manski, C.F.: Asymptotic properties of the maximum score estimator. J. Econ. 27, 313–333 (1985)
Manski, C.F.: Asymptotic properties of the maximum score estimator. J. Econ. 27, 313–333 (1985)
Portnoy, S., Lin, G.: Asymptotics for censored regression quantiles. J. Nonparametr. Stat. 22(1), 115–130 (2010)
Powell, J.L.: Censored regression quantiles. J. Econometr. 32(1), 143–155 (1986)
Reed, C., Yu, K.: A partially collapsed gibbs sampler for bayesian quantile regression. Technical report, Department of Mathematical Sciences, Brunel University (2009)
Stamey, T. A., Kabalin, J. N., McNeal, J. E., Johnstone, I. M., Freiha, F., Redwine, E. A., Yang, N.: Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate. II. Radical prostatectomy treated patients. J. Urol. 141(5), 1076–1083 (1989)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B (Methodol.) 267–288 (1996)
Yu, K., Dang, W., Zhu, H., Al Hamzawi, R.: Comment on article by Spokoiny, Wang and Härdle. J. Stat. Plan. Inference 7(143), 1140–1144 (2013)
Yu, K., Lu, Z., Stander, J.: Quantile regression: applications and current research areas. J. R. Stat. Soc. Ser. D (Stat.) 52(3), 331–350 (2003)
Yu, K., Moyeed, R.A.: Bayesian quantile regression. Stat. Probab. Lett. 54(4), 437–447 (2001)
Yu, K., Stander, J.: Bayesian analysis of a tobit quantile regression model. J. Econometr. 137(1), 260–276 (2007)
Yue, Y.R., Rue, H.: Bayesian inference for additive mixed quantile regression models. Comput. Stat. Data Anal. 55(1), 84–96 (2011)
Zou, H.: The adaptive lasso and its oracle properties. J. Am. Stat. Assoc. 101(476), 1418–1429 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Alhamzawi, R., Ali, H.T.M. Brq: an R package for Bayesian quantile regression. METRON 78, 313–328 (2020). https://doi.org/10.1007/s40300-020-00190-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40300-020-00190-6