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Iterative proportional scaling via decomposable submodels for contingency tables

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  • Endo, Yushi
  • Takemura, Akimichi

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.

Suggested Citation

  • Endo, Yushi & Takemura, Akimichi, 2009. "Iterative proportional scaling via decomposable submodels for contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 966-978, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:966-978
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    References listed on IDEAS

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    1. Malvestuto, F. M., 1989. "Computing the maximum-entropy extension of given discrete probability distributions," Computational Statistics & Data Analysis, Elsevier, vol. 8(3), pages 299-311, November.
    2. Badsberg, J. H. & Malvestuto, F. M., 2001. "An implementation of the iterative proportional fitting procedure by propagation trees," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 297-322, September.
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    Cited by:

    1. Xu, Ping-Feng & Sun, Jubo & Shan, Na, 2016. "Local computations of the iterative proportional scaling procedure for hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 17-23.
    2. Saadi, Ismaïl & Mustafa, Ahmed & Teller, Jacques & Farooq, Bilal & Cools, Mario, 2016. "Hidden Markov Model-based population synthesis," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 1-21.

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    2. Badsberg, J. H. & Malvestuto, F. M., 2001. "An implementation of the iterative proportional fitting procedure by propagation trees," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 297-322, September.
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