Hierarchical Quantile Regression

• Author / Creator

  Hassan, Imran

• Quantile regression supplements the ordinary least squares regression and provides a complete view of a relationship between a response variable and a set of covariates. The quantile regression model does not assume any particular error distribution. It is estimated by minimizing an asymmetric absolute error loss function. Bayesian inference of quantile regression is based on the likelihood function formed by independent asymmetric Laplace densities. The asymmetric Laplace distribution is a natural choice for the error distribution of the quantile regression model. However, the model based on the asymmetric Laplace distribution solely focuses on estimation and does not describe the underlying true model. Moreover, it assumes different models for estimating parameters for different quantile levels.
  In this project, we introduce a hierarchical quantile regression model that removes ambiguities of the quantile regression model based on the asymmetric Laplace distribution. The proposed hierarchical model treats the intercept and the slope of the linear quantile regression model as random effects. The model is estimated by the data cloning method which works in the Bayesian framework exploiting the computational advantage of the Markov Chain Monte Carlo (MCMC) algorithm, but gives the maximum likelihood estimates with standard errors.
  A simulation study with 50 repetitions has been performed to assess the parameter estimates. We have compared our results to the regular quantile regression estimates for different quantile levels.
  Our proposed hierarchical model gives a greater insight into the overall quantile regression picture. The model is easily extendable to accommodate more complex situations and provides room for further research.

• Subjects / Keywords

  • Asymmetric Laplace distribution
  • Bayesian statistics
  • Quantile regression
  • Markov Chain Monte Carlo
  • Hierarchical models
  • Data cloning

• Graduation date

  Fall 2014

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3KX1T

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.