IDEAS home Printed from https://ideas.repec.org/p/pav/wpaper/172.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q172.pdf
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lorenza Rossi & Emilio Zanetti Chini, 2016. "Firms’ Dynamics and Business Cycle: New Disaggregated Data," DEM Working Papers Series 123, University of Pavia, Department of Economics and Management.
    2. Monia Lupparelli & Giovanni M. Marchetti & Wicher P. Bergsma, 2009. "Parameterizations and Fitting of Bi‐directed Graph Models to Categorical Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 559-576, September.
    3. Boitani, Andrea & Punzo, Chiara, 2019. "Banks’ leverage behaviour in a two-agent new Keynesian model," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 347-359.
    4. Ioannis Ntzoufras & Claudia Tarantola & Monia Lupparelli, 2018. "Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models," DEM Working Papers Series 149, University of Pavia, Department of Economics and Management.
    5. 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.
    6. Robin J. Evans & Thomas S. Richardson, 2013. "Marginal log-linear parameters for graphical Markov models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 743-768, September.
    7. 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.
    8. Alberto Roverato, 2015. "Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 627-648, June.
    9. Kayvan Sadeghi & Alessandro Rinaldo, 2020. "Hierarchical models for independence structures of networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 439-457, August.
    10. Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    11. Silvana Tiedemann & Jorge Sanchez Canales & Felix Schur & Raffaele Sgarlato & Lion Hirth & Oliver Ruhnau & Jonas Peters, 2024. "Identifying Elasticities in Autocorrelated Time Series Using Causal Graphs," Papers 2409.15530, arXiv.org.
    12. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    13. Roberto Colombi & Sabrina Giordano, 2013. "Monotone dependence in graphical models for multivariate Markov chains," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 873-885, October.
    14. Monia Lupparelli & Alberto Roverato, 2017. "Log-mean linear regression models for binary responses with an application to multimorbidity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 227-252, February.
    15. Christian Gische & Manuel C. Voelkle, 2022. "Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 868-901, September.
    16. Robin J. Evans, 2016. "Graphs for Margins of Bayesian Networks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 625-648, September.
    17. Eichler, M. & Didelez, V., 2009. "On Granger-causality and the effect of interventions in time series," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pav:wpaper:172. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Paolo Bonomolo (email available below). General contact details of provider: https://edirc.repec.org/data/dppavit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.