Marginal Homogeneity of Multidimensional Contingency Tables

Tests of marginal homogeneity in a two-way contingency table given by [1], [3], and [13] do not seem to lend themselves easily to extension to the problem of $m$-way marginal homogeneity in an $N$-way $r \times r \times \cdots \times r$ contingency table, $m < N$. The principle of minimum discrimination information estimation and the associated minimum discrimination information statistic applied in [5] to the problem of marginal homogeneity in an $r \times r$ contingency table can be easily extended to the case of a multidimensional contingency table. Estimates of the cell entries under the hypotheses of $m$-way marginal homogeneity are given. Relationships among the tests of homogeneity for $m$-way, $m = 1, 2, \cdots, N - 1$, marginals are given by an analysis of information. Numerical results are given for two sample $3 \times 3 \times 3$ tables, and two $5 \times 5$ tables.