A Computer Intensive Approach to the Analysis of Sparse Multidemensional Contingency Tables
David Edwards · 1984
An approach to the analysis of sparse multidimensional contingency tables by means of simple exact tests is described. The tests are essentially equivalent to tests for the conditional independence of two factors given the third in a 3-way table, and software for this purpose can be used. The tests are initially applied to the whole table, and then to appropriate marginal tables, using collapsibility properties in provisionally accepted models. Results proved by Sundberg (1975) imply that the models accessible by such a procedure are precisely the decomposable models. A simple direct proof of this result using graph theory is given here, together with an illustrative example. Enumeration of the conditional distributions in totality is often infeasible, and monte carlo methods must be used. Hopefully the procedure leads to testing in sufficiently deep marginals at some stage that asymptotic approximations can thenceforth be used.