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Objective bayesian Hypothesis Testing in Binomial Regression Models with Integral Prior Distributions

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Author Info

  • Diego Salmeron

    (CIBERESP)

  • Juan Antonio Cano

    (Universidad de Murcia)

  • Christian Robert

    ()
    (Université Paris-Dauphine et CREST)

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    Abstract

    In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in epidemiological studies where one goal is to exhibit whether or not an exposure is a risk factor for developing a certain disease; the purpose of the current paper is to test the effect of specific exposure factors. We formulate the problem as a Bayesian model selection case and solve it using objective Bayes factors. To construct the reference prior distributions on the regression coefficients of the binomial regression models, we rely on the methodology of integral priors that is nearly automatic as it only requires the specification of estimation reference priors and it does not depend on tuning parameters or on hyperparameters within these priors

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-44.

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    Length: 17
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-44

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    Related research

    Keywords: Binomial regression model; Integral prior; Jeffreys prior; Markov chain; Objective Bayes factor;

    References

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    1. 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.
    2. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
    3. J. Cano & D. Salmerón & C. Robert, 2008. "Integral equation solutions as prior distributions for Bayesian model selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(3), pages 493-504, November.
    4. Chen, Ming-Hui & Ibrahim, Joseph G. & Kim, Sungduk, 2008. "Properties and Implementation of Jeffreys’s Prior in Binomial Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1659-1664.
    5. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    6. F. Javier Girãn & M. Lina Martínez & Elías Moreno & Francisco Torres, 2006. "Objective Testing Procedures in Linear Models: Calibration of the "p"-values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 765-784.
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