BALtqr {Brq}

Bayesian adaptive Lasso tobit quantile regression

Description

This function implements the idea of Bayesian adaptive Lasso tobit 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 normal distributions as in Reed and Yu (2009). The proposed method (BALtqr) extends the Bayesian Lasso tobit quantile regression by allowing different penalization parameters for different regression coeffficients (Alhamzawi et al., 2013).

Usage

BALtqr(x,y, tau = 0.5, left = 0,  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.

left

Left censored point.

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. (2013). Tobit Quantile Regression with the adaptive Lasso penalty. The Fourth International Arab Conference of Statistics, 450 ISSN (1681 6870).

[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)
y=pmax(0, y)

fit = Brq(y~0+x,tau=0.5, method="BALtqr",runs=5000, burn=1000)
summary(fit)
model(fit)