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Context-specific independencies in hierarchical multinomial marginal models

Author

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  • Federica Nicolussi

    (University of Milano)

  • Manuela Cazzaro

    (University of Milano Bicocca)

Abstract

This paper focuses on studying the relationships among a set of categorical (ordinal) variables collected in a contingency table. Besides the marginal and conditional (in)dependencies, thoroughly analyzed in the literature, we consider the context-specific independencies holding only in a subspace of the outcome space of the conditioning variables. To this purpose we consider the hierarchical multinomial marginal models and we provide several original results about the representation of context-specific independencies through these models. The theoretical results are supported by an application concerning the innovation degree of Italian enterprises.

Suggested Citation

  • Federica Nicolussi & Manuela Cazzaro, 2020. "Context-specific independencies in hierarchical multinomial marginal models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 767-786, December.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-019-00503-8
    DOI: 10.1007/s10260-019-00503-8
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    References listed on IDEAS

    as
    1. Colombi, R. & Forcina, A., 2014. "A class of smooth models satisfying marginal and context specific conditional independencies," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 75-85.
    2. 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.
    3. Henrik Nyman & Johan Pensar & Timo Koski & Jukka Corander, 2016. "Context-specific independence in graphical log-linear models," Computational Statistics, Springer, vol. 31(4), pages 1493-1512, December.
    4. Manuela Cazzaro & Roberto Colombi, 2008. "Modelling two way contingency tables with recursive logits and odds ratios," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(4), pages 435-453, October.
    5. Manuela Cazzaro & Roberto Colombi, 2014. "Marginal Nested Interactions for Contingency Tables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2799-2814, July.
    6. Colombi, Roberto & Giordano, Sabrina & Cazzaro, Manuela, 2014. "hmmm: An R Package for Hierarchical Multinomial Marginal Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i11).
    7. Tamás Rudas & Wicher P. Bergsma & Renáta Németh, 2010. "Marginal log-linear parameterization of conditional independence models," Biometrika, Biometrika Trust, vol. 97(4), pages 1006-1012.
    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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