Brooks S P, Morgan B J, Ridout M S, Pack S E
School of Mathematics, University of Bristol, U.K.
Biometrics. 1997 Sep;53(3):1097-115.
Six data sets recording fetal control mortality in mouse litters are presented. The data are clearly overdispersed, and a standard approach would be to describe the data by means of a beta-binomial model or to use quasi-likelihood methods. For five of the examples, we show that beta-binomial model provides a reasonable description but that the fit can be significantly improved by using a mixture of a beta-binomial model with a binomial distribution. This mixture provides two alternative solutions, in one of which the binomial component indicates a high probability of death but is selected infrequently; this accounts for outlying litters with high mortality. The influence of the outliers on the beta-binomial fits is also demonstrated. The location and nature of the two main maxima to the likelihood are investigated through profile log-likelihoods. Comparisons are made with the performance of finite mixtures of binomial distributions.
本文展示了六个记录小鼠窝仔胎儿对照死亡率的数据集。数据明显过度离散，标准方法是通过贝塔二项式模型描述数据或使用拟似然方法。对于其中五个例子，我们表明贝塔二项式模型提供了合理的描述，但通过将贝塔二项式模型与二项分布混合使用，拟合效果可显著改善。这种混合提供了两种替代解决方案，其中一种二项式成分表明死亡概率高但很少被选中；这解释了死亡率高的异常窝仔情况。还展示了异常值对贝塔二项式拟合的影响。通过轮廓对数似然性研究了似然性两个主要最大值的位置和性质。并与二项分布有限混合的性能进行了比较。
