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A new general class of RC association models: Estimation and main properties

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  • Forcina, Antonio
  • Kateri, Maria

Abstract

The paper introduces a new class of row-column (RC) association models for contingency tables by allowing the user to select both the scale on which interactions are measured as in Kateri and Papaioannou (1994) and the type of logit (local, global, continuation) suitable for the row and column classification variables as in Bartolucci and Forcina (2002). These choices determine the matrix of interactions which is subjected to rank constraints. Examples are provided where the new models fit substantially better than traditional ones; an intuitive explanation for this behavior is outlined and supported by numerical investigations. An extension of the optimality property in Kateri and Papaioannou (1994) is derived, leading to a general representation theorem and reconstruction formulas for the joint probabilities. These results are the key to show that, given marginal logits, the generalized interactions introduced in this paper determine uniquely the bivariate distribution; in addition, for each pair of logit types, we establish which kind of positive association is implied by our extended interactions being non negative. Quick model selection within this wide class can be performed by an efficient algorithm for computing maximum likelihood estimates which allows for additional linear constraints both on marginal logits and interactions.

Suggested Citation

  • Forcina, Antonio & Kateri, Maria, 2021. "A new general class of RC association models: Estimation and main properties," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000191
    DOI: 10.1016/j.jmva.2021.104741
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    References listed on IDEAS

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    1. Bartolucci F. & Forcina A., 2002. "Extended RC Association Models Allowing for Order Restrictions and Marginal Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1192-1199, December.
    2. Anders Ekholm & John W. McDonald & Peter W. F. Smith, 2000. "Association Models for a Multivariate Binary Response," Biometrics, The International Biometric Society, vol. 56(3), pages 712-718, September.
    3. 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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    Cited by:

    1. Kateri, Maria & Nikolov, Nikolay I., 2022. "A generalized Mallows model based on ϕ-divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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