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

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)

Example output

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

tau:[1] 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: [e-mail]      #
#                      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 July 1, 2020, 7:07 p.m.