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Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

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  • MONIA LUPPARELLI
  • GIOVANNI M. MARCHETTI
  • WICHER P. BERGSMA

Abstract

We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation-independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:559-576
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    References listed on IDEAS

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    1. Bahjat F. Qaqish & Anastasia Ivanova, 2006. "Multivariate logistic models," Biometrika, Biometrika Trust, vol. 93(4), pages 1011-1017, December.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    4. Federica Nicolussi & Fulvia Mecatti, 2016. "A smooth subclass of graphical models for chain graph: towards measuring gender gaps," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 27-41, January.
    5. Federica Nicolussi & Fulvia Mecatti, 2016. "A smooth subclass of graphical models for chain graph: towards measuring gender gaps," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 27-41, January.
    6. Andrea Boitani & Chiara Punzo, 2018. "Banks’ leverage behaviour in a two-agent New Keynesian model," DEM Working Papers Series 150, University of Pavia, Department of Economics and Management.
    7. 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.
    8. 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.

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