Brq (version 2.0)

BTrq: Bayesian Tobit Quantile Regression

Description

This function implements the idea of Bayesian tobit quantile regression using a likelihood function that is based on the asymmetric Laplace distribution. The asymmetric Laplace error distribution is written as scale mixtures of normal distributions. In this function, a two-level hierarchical Bayesian model is used. Specifically, I put zero mean Gaussian priors on the regression coefficients with non informative Jeffreys prior distributions for the unknown variances.

Usage

BTrq(formula, tau =0.5, runs =11000, burn =1000)

Arguments

formula

Model formula.

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.

References

[1] Alhamzawi, R. (2014). Model selection in quantile regression models. Journal of Applied Statistics, 42, 445-458.

Examples

# NOT RUN {
# 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=BTrq(y~x,tau=tau, 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")}
# }