Quasi-Bayesian Approach to a Nonlinear Random Effects Quantile Regression Model

• Activity Number: 579
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Mi-Ok Kim*+
• Companies: Cincinnati Children's Hospital Medical Center
• Keywords: Semiparametric ; Quantile Regression ; Clustered Data ; Empirical Likelihood

Abstract

We consider a non-linear random effects quantile regression analysis of clustered data and propose a quasi-Bayesian approach using empirical likelihood. The random regression coefficients are assumed independent with a common mean, following parametrically specified distributions. We formulate the estimation of the random coefficients as an estimating equations problem and use empirical likelihood to incorporate the parametric likelihood of the random coefficients. A likelihood-like statistical criterion function is yield. We use this -like statistical criterion function as the likelihood and Markov Chain Monte Carlo (MCMC) samplers in the Bayesian framework. We propose the resulting quasi- posterior mean as an estimator. We illustrate the methodology with a real data example of the Cystic Fibrosis (CF) Foundation Patient Registry data. Age related lung function decline is of research interest and random effects quantile regression methodology enables quantile specific rates of decline conditioning on age, accommodating variation across CF centers.