Bayesian estimation, residual analysis and prior sensitivity study for zero-one augmented beta regression model with an application to psychometric data

Danilo Covaes Nogarotto
Caio L. N. Azevedo
Jorge Luiz Bazán

The interest on the analysis of the zero-one augmented beta regres sion (ZOABR) model has been increasing over the last years. In this paper we developed an extensive study on parameter recovery, prior sensitivity and the impact of some factors (scenarios of interest) comparing the Bayesian paradigm with the Maximum Likelihood (ML) approach. Jeffreys-rule, independence Jeffreys and improper priors were compared with usual choices. The results indicate, in a general way, that: the Bayesian approach, under the Jeffreys-rule prior, was as accurate as the ML one. In addition, as expected, the larger the sample size and the lower the variability of the data the more accurate are the parameter estimates. Also, we use the predictive distribution of the response to implement some available residual techniques (previously developed under the frequentist approach). To further illustrate the advantages of our approach, we conduct an analysis of a psychometric real data set including Bayesian residual analysis, where is showed that misleading inference can be obtained when the data is transformed. That is, when the observedzeros and ones are transformed to suitable values and the usual beta regression model is considered, instead using the ZOABR model. Finally, future developments are discussed.

augumented beta regression
Bayesian inference
MCMC methods
Jeffreys prior
residual analysis