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Marginal parameterizations of discrete models defined by a set of conditional independencies

Author

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  • Forcina, A.
  • Lupparelli, M.
  • Marchetti, G.M.

Abstract

It is well-known that a conditional independence statement for discrete variables is equivalent to constraining to zero a suitable set of log-linear interactions. In this paper we show that this is also equivalent to zero constraints on suitable sets of marginal log-linear interactions, that can be formulated within a class of smooth marginal log-linear models. This result allows much more flexibility than known until now in combining several conditional independencies into a smooth marginal model. This result is the basis for a procedure that can search for such a marginal parameterization, so that, if one exists, the model is smooth.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2519-2527
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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. Yuchung J. Wang, 2004. "Compatibility among marginal densities," Biometrika, Biometrika Trust, vol. 91(1), pages 234-239, March.
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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. Forcina, Antonio, 2012. "Smoothness of conditional independence models for discrete data," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 49-56.
    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. Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.

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