# Brq1: Bayesian Quantile Regression In Brq: Bayesian Analysis of Quantile Regression Models

## Description

This function implements the idea of Bayesian quantile regression employing a likelihood function that is based on the asymmetric Laplace distribution (Yu and Moyeed, 2001). The asymmetric Laplace error distribution is written as scale mixtures of normal distributions as in Reed and Yu (2009).

## Usage

 `1` ```Bqr(x,y, tau =0.5, 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. `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 18 19 20 21 22 23 24 25 26``` ```# Example 1 n <- 100 x <- runif(n=n,min=0,max=5) y <- 1 + 1.5*x + .5*x*rnorm(n) Brq(y~x,tau=0.5,runs=2000, burn=500) fit=Brq(y~x,tau=0.5,runs=2000, burn=500) DIC(fit) # Example 2 n <- 100 x <- runif(n=n,min=0,max=5) y <- 1 + 1.5*x+ .5*x*rnorm(n) plot(x,y, main="Scatterplot and Quantile Regression Fit", xlab="x", cex=.5, col="gray") for (i in 1:5) { if (i==1) p = .05 if (i==2) p = .25 if (i==3) p = .50 if (i==4) p = .75 if (i==5) p = .95 fit = Brq(y~x,tau=p,runs=1500, burn=500) # Note: runs =11000 and burn =1000 abline(a=mean(fit\$coef[1]),b=mean(fit\$coef[2]),lty=i,col=i) } abline( lm(y~x),lty=1,lwd=2,col=6) legend(x=-0.30,y=max(y)+0.5,legend=c(.05,.25,.50,.75,.95,"OLS"),lty=c(1,2,3,4,5,1), lwd=c(1,1,1,1,1,2),col=c(1:6),title="Quantile") ```

Brq documentation built on July 1, 2020, 7:07 p.m.