George E O, Bowman D
Department of Mathematical Sciences, University of Memphis, Tennessee 38152, USA.
Biometrics. 1995 Jun;51(2):512-23.
A full-likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability. The binomial and beta-binomial models are shown to occur as special cases correspondingly, respectively, to the choice of degenerate and beta-mixing distributions. For a finite exchangeable binary sequence of random variables, expressions for the joint distribution, moments, and correlations of all orders are derived. Maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster. In an application to developmental toxicology data analysis, the procedure introduced is compared with a beta-binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose.
提出了一种全似然程序，用于在可交换性假设下分析相关二元数据。结果表明，二项式模型和贝塔 - 二项式模型分别作为退化分布和贝塔混合分布选择的特殊情况出现。对于有限的可交换二元随机变量序列，推导了所有阶次的联合分布、矩和相关性的表达式。计算了所有阶次矩的最大似然估计，并用于估计相关性和聚类中反应数量的分布。在发育毒理学数据分析的应用中，将引入的程序与贝塔 - 二项式程序和广义估计方程程序进行了比较，其中平均反应和窝内相关性与剂量相关联。
