# Btqr3: Bayesian adaptive Lasso tobit quantile regression In Brq: Bayesian Analysis of Quantile Regression Models

## 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

 `1` ```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.`

Rahim Alhamzawi

## References

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

 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 11 12 13``` ```# 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) ```

### Example output

```Call:
Brq.formula(formula = y ~ 0 + x, tau = 0.5, method = "BALtqr",
runs = 5000, burn = 1000)

tau: 0.5

Estimate  L.CredIntv U.CredIntv
x1  4.93690310  4.71431522  5.1821386
x2  0.13148970 -0.07817097  0.3535027
x3 -0.07767333 -0.30322891  0.1349979
x4 -0.03623259 -0.25835844  0.2084069
x5  0.04443654 -0.14828332  0.2463726
x6 -0.07384801 -0.25991133  0.1303745
x7  0.07040778 -0.13837449  0.2882326
x8  0.05826576 -0.12109430  0.2677376
=====  Model selection based on credible intervals ======
#                                                       #
#               Author: Rahim Alhamzawi                 #
#               Contact: [email protected]      #
#                      July, 2018                       #
#                                                       #
=========================================================
Estimate
x1 4.936903
x2 0.000000
x3 0.000000
x4 0.000000
x5 0.000000
x6 0.000000
x7 0.000000
x8 0.000000
```

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