Bqr {Brq}

Bayesian Quantile Regression

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

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.

Author(s)

Rahim Alhamzawi

Examples

# 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")