Garren S T, Smith R L, Piegorsch W W
Department of Statistics, University of Virginia, Charlottesville 22903, USA.
Biometrics. 2000 Sep;56(3):947-50. doi: 10.1111/j.0006-341x.2000.947_1.x.
When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta-binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-fit test proposed by Brooks et al. (1997, Biometrics 53, 1097-1115) but find that it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.
当面对呈现超二项变异的比例数据时，数据分析师常常将贝塔二项分布视为比更常见的二项分布更合适的替代模型。一个典型的例子出现在实验动物毒理学实验中，一窝内胎儿的二元观测值往往相互关联。在这种情况下，检验贝塔二项模型的拟合优度可能是有意义的；然而，当窝大小之间存在很大差异时，这项工作就变得复杂了。我们研究了布鲁克斯等人（1997年，《生物统计学》53卷，1097 - 1115页）最近提出的一种拟合优度检验方法，但发现它缺乏区分贝塔二项模型和一些严重非贝塔二项模型的能力。他们文章中开发的其他检验方法和模型非常有用且有趣，但本文未对其进行研究。
