Bayesian Quantile Regression Methods in Handling Non-normal and Heterogeneous Error Term

摘要

Background and Objective: Quantile regression is a developing statistical tool which is used to explain the relationship between response and predictor variables. Quantile approach has ability to model the data which non-normal distributed and non-constant variance assumption. This study presented the ability of the quantile and Bayesian quantile method in overcoming the problem of violation of normality and homogenous assumption for error terms and compare the results. Materials and Methods: This research implemented the simulation study to explore the performance of the asymmetric Laplace distribution for working likelihood in posterior estimation process. Markov Chain Monte Carlo method using Gibbs sampling algorithm was then applied to estimate the parameter in quantile regression model. This study designed distributions for error term; normal, non-normal and heterogeneous variability, then compare the bias and Monte Carlo standard error as the results of classical quantile and Bayesian quantile method. Convergency of parameter estimated were also checked. Results: Bayesian quantile estimation method resulted lower biases and lower Monte Carlo standard error than the classical quantile method for all selected conditions of error term. Conclusion: This study proved that Bayesian quantile regression method produced better proposed model then classical quantile method in the case of non-normal and heterogenous error term.