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Markov bases for typical block effect models of two-way contingency tables

Author

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  • Ogawa, Mitsunori
  • Takemura, Akimichi

Abstract

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via the Markov chain Monte Carlo method. In this paper, we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are typical block-wise effect models of two-way contingency tables, and perform conditional tests with some real data sets.

Suggested Citation

  • Ogawa, Mitsunori & Takemura, Akimichi, 2012. "Markov bases for typical block effect models of two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 219-229.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:219-229
    DOI: 10.1016/j.jmva.2012.06.007
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    References listed on IDEAS

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    1. Hara, Hisayuki & Takemura, Akimichi & Yoshida, Ruriko, 2009. "A Markov basis for conditional test of common diagonal effect in quasi-independence model for square contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1006-1014, February.
    2. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
    3. Akimichi Takemura & Satoshi Aoki, 2004. "Some characterizations of minimal Markov basis for sampling from discrete conditional distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 1-17, March.
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