A new zero-and/or-one augmented beta rectangular regression model is introduced in this work, which is based on a new parameterization of the rectangular beta distribution. Maximum likelihood estimation is performed by using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for discrete part). Also, we develop techniques of model t assessment, by using the randomized quantile residuals and model selection, considering criteria, such as AIC and BIC.We conducted several simulation studies, considering some situations of practical interest, in order to evaluate the parameter recovery of the proposed model and estimation method, the impact of transforming the observed zeros and ones with the use of non-augmented models and the behavior of the model selection criteria. A psychometric real data set was analyzed to illustrate the performance of the new approach considering the model studied.
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