Bayesian Inference for Zero-and/or-one Augmented Rectangular Beta Regression Models

Ana R.S. Santos
Caio L. N. Azevedo
Jorge L. Bazan
Juvêncio S. Nobre

In this paper, we developed a Bayesian inference for a zero-and/orone augmented rectangular beta regression model to analyze limitedaugmented data, under the presence of outliers. The proposed Bayesian tools were parameter estimation, model t assessment, model comparison, residual analysis and case in uence diagnostics, developed through
MCMC algorithms. In addition, we adapted available methods of posterior predictive checking using appropriate discrepancy measures.
Also, a comparison with the maximum likelihood estimation, previously proposed in the literature was performed, in terms of parameter recovery. We noticed that the results are quite similar, but the Bayesian approach is more easily implemented, including in uence diagnostics tools, besides also allowing incorporating prior information.
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, as well as the impact of transforming the observed zeros and ones along the use of non-augmented models. A psychometric real data set was analyzed to illustrate the
performance of the developed tools.

Augmented rectangular beta distribution; Bayesian inference; diagnostic
RP 12/2017