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A class of smooth models satisfying marginal and context specific conditional independencies

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  • Colombi, R.
  • Forcina, A.

Abstract

We study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional independence models which are known to be non-smooth belong to this class. We introduce a new marginal log-linear parameterization and show that smoothness may be restored by restricting one or more independence statements to hold conditionally to a restricted subset of the configurations of the conditioning variables. Our results are based on a specific reconstruction algorithm from log-linear parameters to probabilities and fixed point theory. Several examples are examined and a general rule for determining the implied conditional independence restrictions is outlined.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:75-85
    DOI: 10.1016/j.jmva.2014.01.001
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    References listed on IDEAS

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    1. Forcina, Antonio, 2012. "Smoothness of conditional independence models for discrete data," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 49-56.
    2. Forcina, A. & Lupparelli, M. & Marchetti, G.M., 2010. "Marginal parameterizations of discrete models defined by a set of conditional independencies," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2519-2527, November.
    3. 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.
    4. Søren Højsgaard, 2004. "Statistical Inference in Context Specific Interaction Models for Contingency Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 143-158, March.
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    Cited by:

    1. 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.
    2. Forcina, Antonio, 2023. "Marginal log-linear models and mediation analysis," Statistics & Probability Letters, Elsevier, vol. 194(C).
    3. 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.

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