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

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")

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