Bayesian Quantile Regression Models for Complex Survey Data Under Informative Sampling

Abstract The interest in considering the relation among random variables in quantiles instead of the mean has emerged in various fields, and data collected from complex survey designs are of fundamental importance to different areas. Despite the extensive literature on survey data analysis and quantile regression models, research papers exploring quantile regression estimation accounting for an informative design have primarily been restricted to a frequentist framework. In this paper, we introduce different Bayesian methods relying on the survey-weighted estimator and the estimating equations. A model-based simulation study evaluates the proposed methods compared to alternative approaches and a naïve model fitting ignoring the informative sampling design under different scenarios. In addition, we illustrate and conduct a prior sensitivity analysis in a design-based simulation study that uses data from Prova Brasil 2011.