Open Access
August 2015 Bayesian analysis and diagnostic of overdispersion models for binomial data
Carolina C. M. Paraíba, Carlos A. R. Diniz, Rubiane M. Pires
Braz. J. Probab. Stat. 29(3): 608-639 (August 2015). DOI: 10.1214/14-BJPS236


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.


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Carolina C. M. Paraíba. Carlos A. R. Diniz. Rubiane M. Pires. "Bayesian analysis and diagnostic of overdispersion models for binomial data." Braz. J. Probab. Stat. 29 (3) 608 - 639, August 2015.


Received: 1 May 2012; Accepted: 1 January 2014; Published: August 2015
First available in Project Euclid: 11 June 2015

zbMATH: 1326.62061
MathSciNet: MR3355750
Digital Object Identifier: 10.1214/14-BJPS236

Keywords: Bayesian analysis , beta-binomial , diagnostic , double binomial , multiplicative binomial , overdispersion

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 3 • August 2015
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