  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.
