BALqr {Brq} | R Documentation |

## 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)
```

*Brq*version 3.0 Index]