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Objective Bayesian comparison of order-constrained models in contingency tables

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  • Roberta Paroli

    () (Università Cattolica del Sacro Cuore)

  • Guido Consonni

    () (Università Cattolica del Sacro Cuore)

Abstract

In social and biomedical sciences, testing in contingency tables often involves order restrictions on cell probabilities parameters. We develop objective Bayes methods for order-constrained testing and model comparison when observations arise under product binomial or multinomial sampling. Specifically, we consider tests for monotone order of the parameters against equality of all parameters. Our strategy combines in a unified way both the intrinsic prior methodology and the encompassing prior approach in order to compute Bayes factors and posterior model probabilities. Performance of our method is evaluated on several simulation studies and real datasets.

Suggested Citation

  • Roberta Paroli & Guido Consonni, 2020. "Objective Bayesian comparison of order-constrained models in contingency tables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 139-165, March.
  • Handle: RePEc:spr:testjl:v:29:y:2020:i:1:d:10.1007_s11749-019-00650-w
    DOI: 10.1007/s11749-019-00650-w
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    References listed on IDEAS

    as
    1. Consonni, Guido & La Rocca, Luca, 2008. "Tests Based on Intrinsic Priors for the Equality of Two Correlated Proportions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1260-1269.
    2. Valen E. Johnson & Richard D. Payne & Tianying Wang & Alex Asher & Soutrik Mandal, 2017. "On the Reproducibility of Psychological Science," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 1-10, January.
    3. Wetzels, Ruud & Grasman, Raoul P.P.P. & Wagenmakers, Eric-Jan, 2010. "An encompassing prior generalization of the Savage-Dickey density ratio," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2094-2102, September.
    4. Guido Consonni & Elias Moreno & Sergio Venturini, 2010. "Testing Hardy-Weinberg Equilibrium: an Objective Bayesian Analysis," Quaderni di Dipartimento 121, University of Pavia, Department of Economics and Quantitative Methods.
    5. Klugkist, Irene & Hoijtink, Herbert, 2007. "The Bayes factor for inequality and about equality constrained models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6367-6379, August.
    6. Guido Consonni & Roberta Paroli, 2017. "Objective Bayesian Comparison of Constrained Analysis of Variance Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 589-609, September.
    7. Ronald L. Wasserstein & Nicole A. Lazar, 2016. "The ASA's Statement on p -Values: Context, Process, and Purpose," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 129-133, May.
    8. Mulder, Joris, 2014. "Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 448-463.
    9. Casella, George & Moreno, Elías, 2009. "Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1261-1271.
    10. G. Iliopoulos & M. Kateri & I. Ntzoufras, 2009. "Bayesian Model Comparison for the Order Restricted RC Association Model," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 561-587, December.
    11. M. J. Bayarri & G. García‐Donato, 2008. "Generalization of Jeffreys divergence‐based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003, November.
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