Brq (version 2.0)

BLTrq: Bayesian Lasso Tobit quantile regression

Description

This function implements the idea of Bayesian Lasso tobit quantile regression using a likelihood function that is based on the asymmetric Laplace distribution (Rahim, 2016). The asymmetric Laplace error distribution is written as scale mixtures of normal distributions as in Reed and Yu (2009). We specify zero mean Gaussian priors to the regression coefficients with an independent prior distributions for the unknown variances.

Usage

BLTrq(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. (2016). Bayesian variable selection in quantile regression using asymmetric Laplace distribution. Working paper.

[2] Reed, C. and Yu, K. (2009). A partially collapsed Gibbs sampler for Bayesian quantile regression. Technical Report. Department of Mathematical Sciences, Brunel University. URL: http://bura.brunel.ac.uk/bitstream/2438/3593/1/fulltext.pdf.

Examples

# NOT RUN {
set.seed(12345)
n <- 100
p=8
Beta=c(5, 0, 0, 0, 0, 0, 0, 0)
x <- matrix(rnorm(n=p*n),n)
y <-x%*%Beta+ rnorm(n)
y=pmax(y,0)
fit=BLTrq(y~0+x,tau=0.5, runs=5000, burn=1000)
# Note: runs =11000 and burn =1000
fit$coef
# }