# Objective Bayesian Comparison of Constrained Analysis of Variance Models

## Author

Listed:
• 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, ElÃ­as, 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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## Citations

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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.

### Keywords

ANOVA; Bayes factor; Bayesian model choice; hypothesis testing; inequality constraint; intrinsic prior;

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