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

TL;DR

This paper introduces a Bayesian quantile regression approach for mixed discrete-continuous data with zeros, providing insights into censoring probabilities and conditional quantiles, demonstrated through simulations and real-world applications.

Contribution

It develops a novel Bayesian quantile regression model for zero-inflated data, incorporating censoring information and using MCMC for posterior inference, with applications to econometrics and expenditure analysis.

Findings

Effective modeling of zero-inflated data with censored observations

Accurate estimation of censoring probabilities and quantiles

Successful application to real datasets from Britain and Brazil

Abstract

In this work we show a Bayesian quantile regression method to response variables with mixed discrete-continuous distribution with a point mass at zero, where these observations are believed to be left censored or true zeros. We combine the information provided by the quantile regression analysis to present a more complete description of the probability of being censored given that the observed value is equal to zero, while also studying the conditional quantiles of the continuous part. We build up an Markov Chain Monte Carlo method from related models in the literature to obtain samples from the posterior distribution. We demonstrate the suitability of the model to analyze this censoring probability with a simulated example and two applications with real data. The first is a well known dataset from the econometrics literature about women labor in Britain and the second considers the statistical analysis of expenditures with durable goods, considering information from Brazil.