Bayesian inference for zero-and/or-one augmented beta rectangular regression models

Author(s)

Silva, Ana R. S. ^[1] ; Azevedo, Caio L. N. ^[1] ; Bazan, Jorge L. ^[2] ; Nobre, Juvencio S. ^[3]

Affiliation

^[1] Univ Estadual Campinas, Campinas - Brazil

^[2] Univ Sao Paulo, Sao Paulo - Brazil

^[3] Univ Fed Ceara, Fortaleza, Ceara - Brazil

• Document type: Journal article
• Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 35, n. 4, p. 749-771, NOV 2021.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 13/07850-0 - Zero-one heteroscedastic augmented rectangular beta regression models
• Grantee: Ana Roberta dos Santos Silva
• Support Opportunities: Scholarships in Brazil - Master