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Algebraic exact inference for rater agreement models

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  • Fabio Rapallo

    (University of Genova)

Abstract

In recent years, a method for sampling from conditional distributions for categorical data has been presented by Diaconis and Sturmfels. Their algorithm is based on the algebraic theory of toric ideals which are used to create so called “Markov Bases”. The Diaconis-Sturmfels algorithm leads to a non-asymptotic Monte Carlo Markov Chain algorithm for exact inference on some classes of models, such as log-linear models. In this paper we apply the Diaconis-Sturmfels algorithm to a set of models arising from the rater agreement problem with special attention to the multi-rater case. The relevant Markov bases are explicitly computed and some results for simplify the computation are presented. An extended example on a real data set shows the wide applicability of this methodology.

Suggested Citation

  • Fabio Rapallo, 2005. "Algebraic exact inference for rater agreement models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(1), pages 45-66, February.
    • Handle: RePEc:spr:stmapp:v:14:y:2005:i:1:d:10.1007_bf02511574
    DOI: 10.1007/BF02511574
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    References listed on IDEAS

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    1. J. Richard Landis & Gary G. Koch, 1975. "A review of statistical methods in the analysis of data arising from observer reliability studies (Part I)," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 29(3), pages 101-123, September.
    2. Fabio Rapallo, 2003. "Algebraic Markov Bases and MCMC for Two‐Way Contingency Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 385-397, June.
    3. Peter W. F. Smith & Jonathan J. Forster & John W. McDonald, 1996. "Monte Carlo Exact Tests for Square Contingency Tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(2), pages 309-321, March.
    4. J. Richard Landis & Gary G. Koch, 1975. "A review of statistical methods in the analysis of data arising from observer reliability studies (Part II)," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 29(4), pages 151-161, December.
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    Cited by:

    1. Fabio Rapallo, 2022. "Analysis of the Weighted Kappa and Its Maximum with Markov Moves," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1270-1289, December.
    2. Fabio Rapallo & Maria Piera Rogantin, 2007. "Markov chains on the reference set of contingency tables with upper bounds," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 35-51.
    3. Krampe, Anne & Kuhnt, Sonja, 2007. "Bowker's test for symmetry and modifications within the algebraic framework," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4124-4142, May.

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