A flexible Bayesian hierarchical quantile spatial model for areal data

Abstract

This article introduces a new class of nested models that extends the literature standard combination of spatial autoregressive model for areal data with parametric quantile regression by considering an asymmetric Laplace distribution for the random errors. In addition to being more flexible, the new proposed model can incorporate a hierarchical structure, allowing it to deal with clustered data. Such an approach produces a robust statistical method for modeling the quantiles of areal data distributed in a geographically hierarchical setting. The proposed non-hierarchical model is evaluated using a wellknown house pricing dataset and a simulation study. In addition, its hierarchical version is applied to a real dataset of math scores related to public high schools within the metropolitan area of Rio de Janeiro, Brazil.