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Marginal log‐linear parameters and their collapsibility for categorical data

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  • Sayan Ghosh
  • P. Vellaisamy

Abstract

Collapsibility is a practical and useful technique for dimension reduction in multidimensional contingency tables. In this paper, we consider marginal log‐linear models for studying collapsibility and related aspects in such tables. These models generalize ordinary log‐linear and multivariate logistic models, besides several others. First, we obtain some characteristic properties of marginal log‐linear parameters. Then we define collapsibility and strict collapsibility of these parameters in a general sense. Several necessary and sufficient conditions for collapsibility and strict collapsibility are derived based on simple functions of only the cell probabilities, which are easily verifiable. These include results for an arbitrary set of marginal log‐linear parameters having some common effects. The connections of strict collapsibility to various forms of independence of the variables are explored. We analyze some real‐life datasets to illustrate the above results on collapsibility and strict collapsibility. Finally, we obtain a result relating parameters with the same effect, but different margins for an arbitrary table, and demonstrate smoothness of marginal log‐linear models under collapsibility conditions.

Suggested Citation

  • Sayan Ghosh & P. Vellaisamy, 2024. "Marginal log‐linear parameters and their collapsibility for categorical data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 523-543, August.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:3:p:523-543
    DOI: 10.1111/stan.12332
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    References listed on IDEAS

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    1. D. R. Cox & Nanny Wermuth, 2003. "A general condition for avoiding effect reversal after marginalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 937-941, November.
    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.
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