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, <i>X</i>. However, the model validation for <i>X</i> 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 paper. 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.

摘要：贝塔二项模型（beta-binomial model）已被广泛用作一种解析易处理的替代模型，用以刻画具有组内相关性的二项随机变量<italic>X</italic>的过度离散特性。然而，针对<italic>X</italic>的该模型验证研究却鲜有开展。由于贝塔二项概率质量函数存在多种不同形态，本文针对经分类的各类形态逐一开展模型验证分析。此外，为衡量最大似然估计（maximum likelihood estimator, MLE）的偏倚出现时机与偏倚程度，本文分别基于贝塔二项模型方法与矩估计法估计量（method of moments estimator, MME），针对各类形态计算并展示了均方误差（mean square error, MSE）。