BLqr {Brq}

Bayesian Lasso quantile regression

Description

This function implements the idea of Bayesian Lasso quantile regression using a likelihood function that is based on the asymmetric Laplace distribution (Rahim, 2016). The asymmetric Laplace error distribution is written as a scale mixture of normal distributions as in Reed and Yu (2009). This function implements the Bayesian lasso for linear quantile regression models by assigning scale mixture of normal (SMN) priors on the parameters and independent exponential priors on their variances. We propose an alternative Bayesian analysis of the Bayesian lasso problem reported in Li, et al. (2010). A Gibbs sampling algorithm for the Bayesian Lasso quantile regression is constructed by sampling the parameters from their full conditional distributions.

Usage

BLqr(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, 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.

[3] Li, Q., Xi, R. and Lin, N. (2010). Bayesian regularized quantile regression. Bayesian Analysis, 5(3): 533-56.

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="BLqr",runs=5000, burn=1000)
summary(fit)
model(fit)