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Bayesian Analysis of Graphical Models of Marginal Independence for Three Way Contingency Tables

Author

Listed:
  • Claudia Tarantola

    (Department of Economics and Business, University of Pavia)

  • Ioannis Ntzoufras

    (Department of Statistics, Athens University of Economics and Business)

Abstract

This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. Each marginal independence model corresponds to a particular factorization of the cell probabilities and a conjugate analysis based on Dirichlet prior can be performed. We illustrate a comprehensive Bayesian analysis of such models, involving suitable choices of prior parameters, estimation, model determination, as well as the allied computational issues. The posterior distributions of the marginal log-linear parameters is indirectly obtained using simple Monte Carlo schemes. The methodology is illustrated using two real data sets.

Suggested Citation

  • Claudia Tarantola & Ioannis Ntzoufras, 2012. "Bayesian Analysis of Graphical Models of Marginal Independence for Three Way Contingency Tables," Quaderni di Dipartimento 172, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:172
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q172.pdf
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    References listed on IDEAS

    as
    1. Tamás Rudas & Wicher P. Bergsma, 2004. "On applications of marginal models for categorical data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 15-37.
    2. Thomas Richardson, 2003. "Markov Properties for Acyclic Directed Mixed Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 145-157, March.
    3. Mathias Drton & Thomas S. Richardson, 2008. "Binary models for marginal independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 287-309, April.
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    Cited by:

    1. Ntzoufras, Ioannis & Tarantola, Claudia, 2013. "Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 161-177.
    2. Ioannis Ntzoufras & Claudia Tarantola, 2012. "Conjugate and Conditional Conjugate Bayesian Analysis of Discrete Graphical Models of Marginal Independence," Quaderni di Dipartimento 178, University of Pavia, Department of Economics and Quantitative Methods.

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    More about this item

    Keywords

    graphical models; marginal log-linear parameterization; Monte Carlo computation; order decomposability; power prior approach.;
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