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Context-specific independence in graphical log-linear models

Author

Listed:
  • Henrik Nyman

    (Åbo Akademi University)

  • Johan Pensar

    (Åbo Akademi University)

  • Timo Koski

    (KTH Royal Institute of Technology)

  • Jukka Corander

    (University of Helsinki)

Abstract

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-015-0606-6
    DOI: 10.1007/s00180-015-0606-6
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    References listed on IDEAS

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    1. Jukka Corander, 2003. "Labelled Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 493-508, September.
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    Cited by:

    1. 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.
    2. Klimova, Anna & Rudas, Tamás, 2022. "Hierarchical Aitchison–Silvey models for incomplete binary sample spaces," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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