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

Author

Listed:
  • Diego Salmeron

    (CIBERESP)

  • Juan Antonio Cano

    (Universidad de Murcia)

  • Christian Robert

    (Université Paris-Dauphine et CREST)

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

Suggested Citation

  • Diego Salmeron & Juan Antonio Cano & Christian Robert, 2013. "Objective bayesian Hypothesis Testing in Binomial Regression Models with Integral Prior Distributions," Working Papers 2013-44, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2013-44
    as

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    References listed on IDEAS

    as
    1. F. Javier Girón & 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, December.
    2. 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.
    3. 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.
    4. 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.
    5. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    6. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    7. 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;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 493-504, November.
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