Bqr {Brq} | R Documentation |
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")
[Package Brq version 3.0 Index]