Modelos de regressão binária espacial bayesiana para dados desbalanceados

Abstract

Binary regression models are excellent modeling approaches for dichotomous data, allowing us to relate the probability of the event of interest to the available covariates. In this type of scenario, it is common to encounter data imbalance, that is, a proportion of zeros (or ones) significantly different from ones (or zeros), which makes symmetric link functions poor alternatives when fitting the model. In this work, we propose a class of binary regression models fitted with asymmetric link functions, namely: the power and reverse power link functions. Additionally, we incorporate spatial random effects into our regression, thereby assuming that the binary data can be spatially referenced. The resulting binary regression becomes a special type of Bayesian hierarchical model whose spatial structure is modeled through a more flexible prior distribution than the standard CAR (Conditional Autoregressive) model: the G-Wishart prior distribution. Through a motivational dataset, we present an extension of the proposed spatial binary regression model. For both models, we provide simulation studies and applications to real data, as well as a Bayesian analysis for the detection of influential points. Parameter estimation is fully Bayesian, with a focus on maximizing computational efficiency during the estimation process. The performance of the models proposed herein will be assessed and compared using Bayesian diagnostic metrics and predictive quality measures. The performance of our algorithm will be evaluated through computational simulations and applications to real-world datasets. Finally, as a preliminary and motivational perspective, we present a simulation study using the DAGAR spatial model.