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Objective Bayesian Comparison of Constrained Analysis of Variance Models

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  • Guido Consonni

    () (Università Cattolica del Sacro Cuore)

  • Roberta Paroli

    (Università Cattolica del Sacro Cuore)

Abstract

In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $$\{ \mu _1, \mu _2, \mu _3\}$$ { μ 1 , μ 2 , μ 3 } through an analysis of variance (ANOVA), a model may specify that $$\mu _1

Suggested Citation

  • 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.
  • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-016-9516-y
    DOI: 10.1007/s11336-016-9516-y
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    References listed on IDEAS

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    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. Herbert Hoijtink, 2013. "Objective Bayes Factors for Inequality Constrained Hypotheses," International Statistical Review, International Statistical Institute, vol. 81(2), pages 207-229, August.
    3. Bartolucci, Francesco & Scaccia, Luisa & Farcomeni, Alessio, 2012. "Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4067-4080.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    10. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    11. Davide Altomare & Guido Consonni & Luca La Rocca, 2013. "Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non-Local Priors," Biometrics, The International Biometric Society, vol. 69(2), pages 478-487, June.
    12. C. M. Carvalho & J. G. Scott, 2009. "Objective Bayesian model selection in Gaussian graphical models," Biometrika, Biometrika Trust, vol. 96(3), pages 497-512.
    13. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    14. Floryt Van Wesel & Herbert Hoijtink & Irene Klugkist, 2011. "Choosing Priors for Constrained Analysis of Variance: Methods Based on Training Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 666-690, December.
    15. 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.
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    Cited by:

    1. 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.

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