METRON https://doi.org/10.1007/s40300-020-00190-6 Brq: an R package for Bayesian quantile regression Rahim Alhamzawi 1 · Haithem Taha Mohammad Ali 2 Received: 27 February 2020 / Accepted: 26 September 2020 © Sapienza Università di Roma 2020 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. Keywords Bayesian quantile · Lasso · Adaptive lasso · Prior elicitation · Tobit 1 Introduction Regression quantile (RQ), introduced by Koenker and Bassett [16], models the conditional quantiles of the outcome of interest as a function of the predictors. Since its introduction, RQ has been a topic of great theoretical concern as well as large applications in many research areas such as econometrics, marketing, medicine, ecology, and survival analysis [9,13,26]. Suppose that we have a sample of observations {(x i , y i ); i = 1, 2,..., n}, where y i denotes the response variable and x i denotes the k -dimensional vector of covariates. The linear RQ model for the τ th quantile level, τ ∈ (0, 1), is y i = x ′ i β τ + ε i , where β τ is a vector of coefficients dependent on τ and ε i ’s are independent with their τ th quantile level equal to zero. For simplicity of notation, we will omit the subscript τ from β τ in the remainder of the paper. In the classical literature, the error density is often left unspecified and the unknow vector β is estimated by solving [16] min β n  i =1 ρ τ ( y i − x ′ i β). (1) B Rahim Alhamzawi rahim.alhamzawi@qu.edu.iq 1 Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al Diwaniyah, Iraq 2 Department of Economics, Nawroz University, Duhok, Iraq 123