Un enfoque bayesiano para la regresión gamma unitaria mediante reparametrización en la media y los cuantiles

In recent years, considerable attention has been devoted to statistical models designed for continuous doubly bounded dependent variables, defined on a finite interval (a, b) with known limits satisfying −∞ < a < b < ∞. A predominant focus, however, has been on the special case in which the response is restricted to the standard unit interval, namely (0, 1). In this context, we introduce a new class of quantile regression models based on the unit-gamma distribution, along with a mean-based model. For inference, we adopt a Bayesian framework, employing Markov Chain Monte Carlo (MCMC) stochastic simulation algorithms. We conducted extensive simulations to verify the computational implementation and assess the properties of the Bayesian estimators. All analyses were carried out using the nimble package in R, which provides a flexible environment for building and fitting Bayesian hierarchical models. Our results suggest that the proposed Bayesian approach provides unbiased and consistent estimators for all model parameters. Additionally, we perform a detailed model fit assessment, comparing the proposed models with several established alternatives, and conduct an influence analysis to identify potential outliers or influential data points. Finally, we apply the proposed models to a real-world dataset, demonstrating their practical utility and systematically comparing their performance with that of existing models commonly used in the literature.