Bayesian analysis and diagnostic of overdispersion models for binomial data

In the present paper, we focus our attention on the multiplicative binomial model, the double binomial model and the beta-binomial model considering the Bayesian perspective, modeling both the probability of success and the dispersion parameters. A Bayesian methodology is considered for estimation and diagnostic under these three overdispersed binomial regression models. A teratology data set is analyzed using the considered methodology. We present a simulation study, based on data sets generated mimicking the characteristics of the teratology data to assess the quality of Bayesian estimates and to assess the performance of the considered Bayesian diagnostic tools under each regression model. An extended study based on simulated data is also performed to compare the logit and probit link functions in a setting of overdispersed binomial data. We also consider simulated data sets to illustrate how to detect overdispersion using posterior predictive checks.