Building a large hierarchical log-linear model by applying a graphical model method

Abstract

We address an issue of model-searching based on a collection of marginal models under an assumption that the model is graphically decomposable. A main theme which is instrumental throughout the thesis is that decomposability is preserved between a model and its submodel and that a particular type of separators in the graph of model is found in a decomposable graphical model and in a collection of its submodels. These separators, which are called minimal connector sin the thesis, are a guideline for model combination. A theory for the guideline is laid out to the effect that we may use the minimal connectors for drawing a blueprint based on which a combined model is formed. This theoretic result is then carried over to a more larger set of hierarchical log-linear models by applying the concept of interaction graph. The result of thethesis is applied to real data for building a hierarchical log-linear model that can not be handled as a single model.