RECURSIVE PROCEDURES FOR HIERARCHICAL LOGLINEAR MODELS ON HIGH-DIMENSIONAL CONTINGENCY TABLES

Recursive procedures proposed in this paper can find the maximum likelihood estimates (MLEs) for hierarchical loglinear models more efficiently than the iterative proportional fitting procedure (IPFP), the expectation-maximization (EM) algorithm and the Newton-Raphson method, especially for higher dimensional contingency tables. For a given loglinear model, at first, the recursive procedures separate it recursively into a class of models of marginal tables with the lowest possible dimensions, secondly find the MLEs for the respective lower dimensional models, and finally the proposed procedures obtain the MLEs for the original higher dimensional model from the MLEs of these lower dimensional models. For the lower dimensional models unable to be separated further, the recursive procedures find the MLEs by using the IPFP, the EM algorithm or the Newton-Raphson method.