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Asymmetry models for square contingency tables: exact tests via algebraic statistics

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Abstract

Square contingency tables with the same row and column classification occur frequently in a wide range of statistical applications, e.g. whenever the members of a matched pair are classified on the same scale, which is usually ordinal. Such tables are analysed by choosing an appropriate loglinear model. We focus on the models of symmetry, triangular, diagonal and ordinal quasi symmetry. The fit of a specific model is tested by the chi-squared test or the likelihood-ratio test, where p-values are calculated from the asymptotic chi-square distribution of the test statistic or, if this seems unjustified, from the exact conditional distribution. Since the calculation of exact p-values is often not feasible, we propose alternatives based on algebraic statistics combined with MCMC methods.

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Authors and Affiliations

  1. Faculty of Statistics, TU Dortmund University, Dortmund, Germany

    Anne Krampe & Sonja Kuhnt

  2. Department of Statistics and Insurance Science, University of Piraeus, 185 34, Piraeus, Greece

    Maria Kateri

Authors
  1. Anne Krampe
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  2. Maria Kateri
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  3. Sonja Kuhnt
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Correspondence to Anne Krampe.

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Krampe, A., Kateri, M. & Kuhnt, S. Asymmetry models for square contingency tables: exact tests via algebraic statistics. Stat Comput 21, 55–67 (2011). https://doi.org/10.1007/s11222-009-9146-7

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  • DOI: https://doi.org/10.1007/s11222-009-9146-7

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