Bayesian Tobit quantile regression usingg-prior distribution with ridge parameter

Abstract

A Bayesian approach is proposed for coefficient estimation in Tobit quantile regression model. The proposed approach is based on placing a g-prior distribution depends on the quantile level on the regression coefficients. The prior is generalized by introducing a ridge parameter to address important challenges that may arise with censored data, such as multicollinearity and overfitting problems. Then, a stochastic search variable selection approach is proposed for Tobit quantile regression model based on g-prior. An expression for the hyperparameter g is proposed to calibrate the modified g-prior with a ridge parameter to the corresponding g-prior. Some possible extensions of the proposed approach are discussed, including the continuous and binary responses in quantile regression. The methods are illustrated using several simulation studies and a microarray study. The simulation studies and the microarray study indicate that the proposed approach performs well.

The comparison of censored quantile regression methods in prognosis factors of breast cancer survival

“…It is necessary task to measure the goodness of survival models. Although for the model diagnostics of quantile regression with complete data some tools, such as the worm plot, have been proposed, for censored quantile regression is still greatly underdeveloped 43 , 44 . Designing effective model diagnostic tools for censored quantile regression warrants more in-depth research.…”

A novel Bayesian method for variable selection and estimation in binary quantile regression

“…Alhamzawi and Yu [20] developed a quantile-dependent prior for the regression coefficients in the Tobit QR model and showed that this prior specification enhanced the accuracy of posterior inference. However, the use of the quantile-dependent prior comes at the cost of higher computational complexity for conducting posterior inference, since the conditional posteriors of a subset of parameters remain intractable.…”

“…Therefore, in this article, we offer a novel three-stage computational scheme to approximate the exact joint posterior of the parameters that facilitated faster computation in the aforementioned setting. More specifically, we begin with an expectation-maximization (EM) algorithm to enable sampling from the marginal posterior of the parameters that turn out to be the computational bottleneck and then utilize the approximate conjugacy of the prior in Alhamzawi and Yu [20] to derive a composition sampler for the remaining parameters. To our knowledge, little work has been developed in binary QR models under this prior setting.…”

Bayesian quantile regression analysis for continuous data with a discrete component at zero

“…Kobayashi (2016) presented Bayesian Tobit quantile regression models with endogenous variables. Alhamzawi and Yu (2015) considered the estimation of Tobit quantile regression models using a g-prior distribution with a ridge parameter for more flexibility when dealing with censored data. And as an illustration of Tobit quantile regression models, Yue and Hong (2012) explained medical expenditures in panel survey data using this approach.…”