BALqr {Brq}

Bayesian adaptive Lasso quantile regression

Description

This function implements the idea of Bayesian adaptive Lasso quantile regression employing a likelihood function that is based on the asymmetric Laplace distribution. The asymmetric Laplace error distribution is written as a scale mixture of normals as in Reed and Yu (2009). The proposed method (BALqr) extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coeffficients (Alhamzawi et al., 2012).

Usage

BALqr(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

References

[1] Alhamzawi, Rahim, Keming Yu, and Dries F. Benoit. (2012). Bayesian adaptive Lasso quantile regression. Statistical Modelling 12.3: 279-297.

[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

# Example 
n <- 150
p=8
Beta=c(5, 0, 0, 0, 0, 0, 0, 0)
x <- matrix(rnorm(n=p*n),n)
x=scale(x)
y <-x%*%Beta+rnorm(n)
y=y-mean(y)
fit = Brq(y~0+x,tau=0.5, method="BALqr",runs=5000, burn=1000)
summary(fit)