Modelos de regressão gama unitária e extensões sob a abordagem Bayesiana

Abstract

Regression models for data with bounded support, particularly within the unit interval, are widely used in the literature to model percentages, proportions, or rates. Recently, these models have garnered significant attention from the statistical community. Among the existing proposals, notable models include beta regression, simplex models, Kumaraswamy models, Johnson Sb models, and more recently, unit Weibull models, among others. In this work, we focus on the unit Gamma regression model and its extensions from a Bayesian perspective, which offers several advantages over classical inference, such as eliminating the need for asymptotic results, particularly in complex models. Within the context of this model, we propose a comprehensive framework for parameter estimation, model fit assessment, model comparison, and influence analysis. This is achieved using the Bayesian approach through stochastic simulation algorithms based on Markov Chain Monte Carlo (MCMC) methods.