Statistical Modelling 18 (1) (2018), 73–93
Bayesian quantile regression analysis for continuous data with a discrete component at zero
Bruno Santos
Department of Statistics,
Institute of Mathematics and Statistics,
Federal University of Bahia,
Brazil
e-mail: brunorsantos@ufba.br
Heleno Bolfarine
Department of Statistics,
Institute of Mathematics and Statistics,
University of São Paulo,
Brazil
Abstract:
In this work, we propose 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 a 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 analyse 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 labour in Britain, and the second considers the statistical analysis of expenditures with durable goods, considering information from Brazil.
Keywords:
asymmetric Laplace distribution; Bayesian quantile regression; Durable goods; left censoring; two-part model.
Downloads:
Example data and code found in the pdf file
here.
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