We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors. Here, we focus on three-way binary tables and show that, even in such a simple case, the situation is quite different than for two-way tables. Many more constraints are needed to ensure a unique solution to the problem. Therefore, the uniqueness of the transformed table is subject to arbitrary choices of the practitioner. We illustrate the theory through some examples, and conclude with a discussion on the topic and future research directions.

翻译：我们研究将多路列联表转换为具有相同依赖结构的均匀边际等价表的问题。该问题与离散随机向量Copula建模的最新进展相关。本文聚焦于三维二元列联表，并证明即便在这种简单情形下，其情况也与二维列联表存在本质差异。要确保该问题存在唯一解，需施加更多约束条件。因此，转换后表格的唯一性取决于实践者的主观选择。我们通过若干实例阐明相关理论，最后就该主题及未来研究方向展开讨论。