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Relational models for contingency tables

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  • Klimova, Anna
  • Rudas, Tamás
  • Dobra, Adrian

Abstract

The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions for the existence of maximum likelihood estimates under these models are given, and it is shown that the usual equivalence between multinomial and Poisson likelihoods holds if and only if an overall effect is present in the model. If such an effect is not assumed, the model becomes a curved exponential family and a related mixed parameterization is given that relies on non-homogeneous odds ratios. Several examples are presented to illustrate the properties and use of such models.

Suggested Citation

  • Klimova, Anna & Rudas, Tamás & Dobra, Adrian, 2012. "Relational models for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 159-173, February.
    • Handle: RePEc:eee:jmvana:v:104:y:2012:i:1:p:159-173
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    References listed on IDEAS

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    1. Zelterman, Daniel & Youn, Ted I. K., 1992. "Indicator models in social mobility tables," Computational Statistics & Data Analysis, Elsevier, vol. 14(1), pages 39-53, June.
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    Cited by:

    1. Anna Klimova & Tamás Rudas, 2012. "Coordinate-free analysis of trends in British social mobility," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1681-1691, January.
    2. Klimova, Anna & Rudas, Tamás, 2016. "On the closure of relational models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 440-452.
    3. Anna Klimova & Tamás Rudas, 2015. "Iterative Scaling in Curved Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 832-847, September.
    4. Erzsébet Bukodi & John H. Goldthorpe & Jouni Kuha, 2017. "The pattern of social fluidity within the British class structure: a topological model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 841-862, June.
    5. Klimova, Anna & Rudas, Tamás, 2022. "Hierarchical Aitchison–Silvey models for incomplete binary sample spaces," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    6. Antonoio Forcina, 2019. "Estimation and testing of multiplicative models for frequency data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 807-822, October.

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    1. Anna Klimova & Tamás Rudas, 2012. "Coordinate-free analysis of trends in British social mobility," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1681-1691, January.
    2. Erzsébet Bukodi & John H. Goldthorpe & Jouni Kuha, 2017. "The pattern of social fluidity within the British class structure: a topological model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 841-862, June.

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