Iterative proportional scaling via decomposable submodels for contingency tables

Authors:
Yushi Endo;Akimichi Takemura
Affiliations:
Graduate School of Information Science and Technology, University of Tokyo, Japan;Graduate School of Information Science and Technology, University of Tokyo, Japan
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

We propose iterative proportional scaling (IPS) via decomposable submodels for maximizing the likelihood function of a hierarchical model for contingency tables. In ordinary IPS the proportional scaling is performed by cycling through the members of the generating class of a hierarchical model. We propose the adjustment of more marginals at each step. This is accomplished by expressing the generating class as a union of decomposable submodels and cycling through the decomposable models. We prove the convergence of our proposed procedure, if the amount of scaling is adjusted properly at each step. We also analyze the proposed algorithms around the maximum likelihood estimate (MLE) in detail. The faster convergence of our proposed procedure is illustrated by numerical examples.