# Btqr1: Bayesian tobit quantile regression In Brq: Bayesian Analysis of Quantile Regression Models

## Description

This function implements the idea of Bayesian tobit quantile regression employing a likelihood function that is based on the asymmetric Laplace distribution (Yu and Stander, 2007). The asymmetric Laplace error distribution is written as scale mixtures of normal distributions as in Reed and Yu (2009).

## Usage

 `1` ```Btqr(x,y, tau = 0.5, left = 0, runs = 11000, burn = 1000, thin=1) ```

## Arguments

 `x` `Matrix of predictors.` `y` `Vector of dependent variable. ` `tau` `The quantile of interest. Must be between 0 and 1.` `left` ` Left censored point.` `runs` `Length of desired Gibbs sampler output.` `burn` `Number of Gibbs sampler iterations before output is saved.` `thin` `thinning parameter of MCMC draws.`

Rahim Alhamzawi

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```# Example set.seed(12345) x <- abs(rnorm(100)) y <- -0.5 + x +(.25 + .25*x)*rnorm(100) plot(x,y, type="n") h <-(y > 0) points(x[h],y[h],cex=.9,pch=16) points(x[!h],y[!h],cex=.9,pch=1) y <- pmax(0,y) for(tau in (2:8)/9){ fit=Brq(y~x,tau=tau, method="Btqr", left=0, runs=1000, burn=500)\$coef # Note: runs =11000 and burn =1000 Xs=sort(x) Xc=cbind(1,sort(x)) Xcf=Xc%*%c(fit) Xcfp=pmax(0,Xcf) lines(Xs,Xcfp,col="red")} ```

### Example output ```
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Brq documentation built on May 2, 2019, 4:12 a.m.