Bayesian modeling and prior sensitivity analysis for zero-one augmented beta regression models with an application to psychometric data. (English) Zbl 1445.62171

Nogarotto, Danilo Covaes; Azevedo, Caio Lucidius Naberezny; Bazán, Jorge Luis

Braz. J. Probab. Stat. 34, No. 2, 304-322 (2020).

Summary: The interest on the analysis of the zero-one augmented beta regression (ZOABR) model has been increasing over the last few years. In this work, we developed a Bayesian inference for the ZOABR model, providing some contributions, namely: we explored the use of Jeffreys-rule and independence Jeffreys prior for some of the parameters, performing a sensitivity study of prior choice, comparing the Bayesian estimates with the maximum likelihood ones and measuring the accuracy of the estimates under several scenarios of interest. The results indicate, in a general way, that: the Bayesian approach, under the Jeffreys-rule prior, was as accurate as the ML one. Also, different from other approaches, we use the predictive distribution of the response to implement Bayesian residuals. To further illustrate the advantages of our approach, we conduct an analysis of a real psychometric data set including a Bayesian residual analysis, where it is shown that misleading inference can be obtained when the data is transformed. That is, when the zeros and ones are transformed to suitable values and the usual beta regression model is considered, instead of the ZOABR model. Finally, future developments are discussed.

MSC:

62J05	Linear regression; mixed models
62F15	Bayesian inference
62P15	Applications of statistics to psychology

Keywords:

augmented beta regression; Bayesian inference; Jeffreys prior; MCMC methods; residual analysis

Software:

zoib; betareg; R; SAS

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