The Collapsibility And The Decomposition Of Likelihood Ratio Tests In Multidimensional Tables

The coUapsibility of the likelihood ratio test for a multidimensional contingency table is considered .Further sufficient conditions for coUapsibility is found in terms of the graphs of two tested graphical models. Also,using the decomposition of the graphs of two graphical models, we can get some useful results about the decomposition of the likelihood ratio test statistic. In this paper, the test statistic can be decomposed into several special smaller parts and each part is a statistic about a marginal contingency table;under the null hypothesis each part is an asymptotical x~2 random variable and these parts are asymptotical independent.