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STRUCTURED ADDITIVE MULTIPLE-OUTPUT NONCROSSING BAYESIAN QUANTILE REGRESSION MODELS
In this work, we propose 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 (Guggisberg, 2017). We combine this approach with a proposal in the literature to define non-crossing quantiles in every directional quantile model (Rodrigues & Fan, 2017). We define a 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 German data from the Socio Economic Panel, where the interest lies in explaining more dimensions of inequality in the population, such as income and health, using the dependence between
these two variables.
Multiple-output response variable; Noncrossing Bayesian quantile regression; Inequality dimensions.
Modelos de Regressão
Bruno Santos, Thomas Kneib