The structure of the strict collapsibility model in a three-dimensional contingency table is investigated with the goal of developing more powerful tests. After showing that strict collapsibility can be written as a finite union of distinct models, an intersection union test is proposed which is at least as powerful asymptotically as the likelihood ratio test. Intersection union tests for strong collapsibility and marginal independence are also suggested.
"Intersection Union Tests for Strict Collapsibility in Three-Dimensional Contingency Tables." Ann. Statist. 17 (4) 1693 - 1708, December, 1989. https://doi.org/10.1214/aos/1176347388