Brq (version 2.0)

BALrq: 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 (Yu and Moyeed, 2001). The asymmetric Laplace error distribution is written as scale mixtures of normal distributions as in Reed and Yu (2009). The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coeffficients (Alhamzawi et al., 2012).

Usage

BALrq(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, 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.

[3] Yu, K. and Moyeed, R.A. (2001). Bayesian Quantile Regression. Statistics & Probability Letters, 54, 437--447. URL: http://www.sciencedirect.com/science/article/pii/S0167715201001249.

See Also

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

Examples

# NOT RUN {
# 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 = BALrq(y~0+x,tau=0.5,runs=5000, burn=1000)
# Note: runs =11000 and burn =1000
fit$coef

# }