Robust Modeling for Continuous Bounded Spatial Data

Abstract This paper develops two parametric median-based spatial regression models for geostatistical data defined on a bounded support. Specifically, these models resemble spatial generalized linear mixed models (SGLMMs), wherein the response variable is modeled using Kumaraswamy and Johnson-t distributions. The proposed models are more robust than the usual spatial beta regression model against the presence of asymmetries and extreme observations. A fully Bayesian analysis is employed to make inferences using the Metropolis-Hastings-within-Gibbs (MHG) sampling algorithm. Simulation studies and two applications to real-life mathematical Olympics data from Brazil and forest canopy cover data from the Zagros forests in Iran demonstrate that our proposals significantly outperform competitors in terms of predictive accuracy and precision of estimates.