# Brq3: Bayesian adaptive Lasso quantile regression In Brq: Bayesian Analysis of Quantile Regression Models

## 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

 `1` ```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.

Rahim Alhamzawi

## References

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

 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# 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) ```

Brq documentation built on May 2, 2019, 4:12 a.m.