(An) algorithm for log-linear modeling by using marginal models

Abstract

We address an issue of graphical modeling based on a collection of marginal models under an assumption that the model is graphically decomposable. In this paper, we build up an algorithm for combining marginal models. A main idea of the algorithm is that the relation between variables of marginal models, separation property, has to be preserved in the combined model structure. A separator, which is called prime separator in the paper, leads to a good method for model combination and the algorithm uses the prime separators to make out a result. This combining algorithm enables us to develop larger graphical models that cannot be handled as a single model. The algorithm is applied to six marginal models involving 40 variables and the goodness-of-fit test methods are introduced for measuring between the true model and the result model.