IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v29y2020i4d10.1007_s10260-019-00503-8.html
   My bibliography  Save this article

Context-specific independencies in hierarchical multinomial marginal models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-019-00503-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-019-00503-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    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.
    Full references (including those not matched with items on IDEAS)

    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. Colombi, Roberto, 2020. "Selection tests for possibly misspecified hierarchical multinomial marginal models," Econometrics and Statistics, Elsevier, vol. 16(C), pages 136-147.
    2. 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.
    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. 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.
    6. Colombi, R. & Giordano, S., 2015. "Multiple hidden Markov models for categorical time series," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 19-30.
    7. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    8. Forcina, Antonio, 2023. "Marginal log-linear models and mediation analysis," Statistics & Probability Letters, Elsevier, vol. 194(C).
    9. R. Colombi & A. Forcina, 2016. "Testing order restrictions in contingency tables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 73-90, January.
    10. Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.
    11. Federico Castelletti & Guido Consonni & Luca Rocca, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 261-267, June.
    12. 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.
    13. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    14. 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.
    15. 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.
    16. Alan Agresti & Sabrina Giordano & Anna Gottard, 2022. "A Review of Score-Test-Based Inference for Categorical Data," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 31-48, September.
    17. Klimova, Anna & Rudas, Tamás, 2022. "Hierarchical Aitchison–Silvey models for incomplete binary sample spaces," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    18. Forcina, Antonio, 2017. "A Fisher-scoring algorithm for fitting latent class models with individual covariates," Econometrics and Statistics, Elsevier, vol. 3(C), pages 132-140.

    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:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-019-00503-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.