The validation of a beta-binomial model for overdispersed binomial data

ABSTRACT

The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable, X. However, the model validation for X has been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this article. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased.

KEYWORDS:

• Beta-binomial distribution
• Intra-correlated binary data
• Model adequacy
• Overdispersion

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F10
• Secondary 62F99

Acknowledgment

The authors express many thanks to Dr. Craig Beam for allowing the use of the screening mammogram data.