The Open Mathematics, Statistics and Probability Journal
2017, 08 : 27-38Published online 2017 October 16. DOI: 10.2174/1876527001708010027
Publisher ID: TOSPJ-8-27
RESEARCH ARTICLE
Bayesian Inference for Three Bivariate Beta Binomial Models
* Address correspondence to this author at the Department of Mathematics and Statistics, University of, Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4; Tel: 001-403-220-5210; E-mail: scollnik@ucalgary.ca
ABSTRACT
Background:
This paper considers three two-dimensional beta binomial models previously introduced in the literature. These were proposed as candidate models for modelling forms of correlated and overdispersed bivariate count data. However, the first model has a complicated form of bivariate probability mass function involving a generalized hypergeometric function and the remaining two do not have closed forms of probability mass functions and are not amenable to analysis using maximum likelihood. This limited their applicability.
Objective:
In this paper, we will discuss how the Bayesian analyses of these models may go forward using Markov chain Monte Carlo and data augmentation.
Results:
An illustrative example having to do with student achievement in two related university courses is included. Posterior and posterior predictive inferences and predictive information criteria are discussed.