Btqr {Brq}

Bayesian tobit quantile regression

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

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.

Author(s)

Rahim Alhamzawi

Examples

# 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")}