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Noncrossing structured additive multiple-output Bayesian quantile regression models

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Abstract

Quantile regression models are a powerful tool for studying different points of the conditional distribution of univariate response variables. Their multivariate counterpart extension though is not straightforward, starting with the definition of multivariate quantiles. We propose here a flexible Bayesian quantile regression model when the response variable is multivariate, where we are able to define a structured additive framework for all predictor variables. We build on previous ideas considering a directional approach to define the quantiles of a response variable with multiple outputs, and we define noncrossing quantiles in every directional quantile model. We define a Markov chain Monte Carlo (MCMC) procedure for model estimation, where the noncrossing property is obtained considering a Gaussian process design to model the correlation between several quantile regression models. We illustrate the results of these models using two datasets: one on dimensions of inequality in the population, such as income and health; the second on scores of students in the Brazilian High School National Exam, considering three dimensions for the response variable.

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Notes

  1. Here it was possible to answer the questionnaire based on the education of the man in charge of the person taking the examination. The same applies for mother education.

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Authors and Affiliations

  1. Universidade Federal do Espírito Santo, Vitória, Brazil

    Bruno Santos

  2. Georg-August-Universität Göttingen, Göttingen, Germany

    Thomas Kneib

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  1. Bruno Santos
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  2. Thomas Kneib
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Correspondence to Bruno Santos.

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Santos, B., Kneib, T. Noncrossing structured additive multiple-output Bayesian quantile regression models. Stat Comput 30, 855–869 (2020). https://doi.org/10.1007/s11222-020-09925-x

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