Abstract

In this paper, we developed a full set of Bayesian inference tools, for zero-and/or-one augmented beta rectangular regression models to ana-lyze limited-augmented data, under a new parameterization. This parameter-ization: facilitates the development of both regression models and inferen-tial tools as well as make simplifies the respective computational implemen-tations. The proposed Bayesian tools were parameter estimation, model fit assessment, model comparison (information criteria), residual analysis and case influence diagnostics, developed through MCMC algorithms. In addi-tion, we adapted available methods of posterior predictive checking, using appropriate discrepancy measures. We conducted several simulation studies, considering some situations of practical interest, aiming to evaluate: prior sensitivity choice, parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones, along with the use of non-augmented models, and the behavior of the proposed model fit assessment and model comparison tools. A psychometric real data set was analyzed to illustrate the performance of the developed tools, illustrating the advantages of the developed analysis framework.