Consider building a log-linear model of 20 categorical variables, each of which is of three categories. Dealing with these variables all together is not feasible due to lack of memory capacity and weeks-long computing time. We have to deal with about 3.5 billion cells of contingency table. This thesis aims to propose a method and apply it to build a log-linear model for those variables. The method consists of firstly splitting the whole variable set into some subsets of manageable sizes, secondly building hierarchical log-linear models for those subsets of variables, and thirdly combining these marginal models into a model of the whole data set. A main theme in combining marginal models is that decomposability of probability distribution 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 connectors in 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 theoretic result of the thesis is applied to the data set of 20 variables, and the model-searching process is described in detail until a final model is reached.
위계적 선형 로그모형과 그래프 모형과의 결합은 복잡한 자료에 대한 간단하면서 직관적인 해석을 제공해준다. 하지만 다량의 자료를 분석하는 경우에는 상당한 시간이 필요하다. 이를 해결하기 위해 본 논문에서는 CART 알고리즘을 통한 전체 모형의 분할과 결합모형을 제안했다. 이 방법은 주어진 자료를 분할함으로써 더욱 쉽고 빠르게 모형을 찾는 방법을 보여주며 분할된 모형을 결합할 수 있는 조건을 제시한다. 또한 이러한 방법으로 결합된 모형이 좀더 간단한 결합 모형을 갖도록 축소하는 방법을 그래프 이론을 통하여 살펴 보았다. 마지막으로 실제 자료에 적용해 봄으로써 이 모형탐색 방법의 효율성을 확인했고 그에 따른 문제점을 제시했다.
