Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for such clustered data but assumes that trials are independent and identically distributed. Extensions such as Dirichlet-multinomial and random-clumped multinomial can express positive association, where trials are more likely to result in a common category due to membership in a common cluster. This work considers a Conway-Maxwell-multinomial (CMM) distribution for modeling clustered categorical data exhibiting positively or negatively associated trials. The CMM distribution features a dispersion parameter which allows it to adapt to a range of association levels and includes several recognizable distributions as special cases. We explore properties of CMM, illustrate its flexible characteristics, identify a method to efficiently compute maximum likelihood (ML) estimates, present simulations of small sample properties under ML estimation, and demonstrate the model via several data analysis examples.

中文翻译：

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用于灵活建模聚类分类数据的 Conway-Maxwell 多项分布

分类数据通常被观察为由固定数量的试验产生的计数，其中每个试验包括从一组预先指定的类别中进行选择。多项分布用作此类聚类数据的标准模型，但假设试验是独立且同分布的。狄利克雷多项式和随机集束多项式等扩展可以表达正关联，其中由于属于共同集群的成员，试验更有可能产生共同类别。这项工作考虑了康威-麦克斯韦多项 (CMM) 分布，用于对显示正相关或负相关试验的聚类分类数据进行建模。CMM 分布具有一个分散参数，它允许它适应一系列关联级别，并包括几个可识别的分布作为特殊情况。我们探索 CMM 的特性，说明其灵活的特性，确定一种有效计算最大似然 (ML) 估计的方法，在 ML 估计下呈现小样本特性的模拟，并通过几个数据分析示例演示模型。