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Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

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  • Bartolucci, Francesco
  • Scaccia, Luisa
  • Farcomeni, Alessio

Abstract

A Bayesian approach is developed for selecting the model that is most supported by the data within a class of marginal models for categorical variables, which are formulated through equality and/or inequality constraints on generalized logits (local, global, continuation, or reverse continuation), generalized log-odds ratios, and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is specified following the encompassing prior approach. Then, model selection is performed by using Bayes factors estimated through an importance sampling method. The approach is illustrated by three applications based on different datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also performed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4067-4080
    DOI: 10.1016/j.csda.2012.04.006
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Bartolucci F. & Forcina A. & Dardanoni V., 2001. "Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1497-1505, December.
    4. Irene Klugkist & Bernet Kato & Herbert Hoijtink, 2005. "Bayesian model selection using encompassing priors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 57-69, February.
    5. Bartolucci, F. & Scaccia, L., 2004. "Testing for positive association in contingency tables with fixed margins," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 195-210, August.
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    Cited by:

    1. Gordon Anderson, Alessio Farcomeni, Maria Grazia Pittau and Roberto Zelli, 2019. "Multidimensional Nation Wellbeing, More Equal yet More Polarized: An Analysis of the Progress of Human Development Since 1990," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 44(1), pages 1-22, March.
    2. Linda J. Young & M. Kateri & A. Agresti, 2013. "Bayesian inference about odds ratio structure in ordinal contingency tables," Environmetrics, John Wiley & Sons, Ltd., vol. 24(5), pages 281-288, August.
    3. Ntzoufras, Ioannis & Tarantola, Claudia, 2013. "Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 161-177.
    4. Boitani, Andrea & Punzo, Chiara, 2019. "Banks’ leverage behaviour in a two-agent new Keynesian model," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 347-359.
    5. Lorenza Rossi & Emilio Zanetti Chini, 2016. "Firms’ Dynamics and Business Cycle: New Disaggregated Data," DEM Working Papers Series 123, University of Pavia, Department of Economics and Management.
    6. Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.
    7. Alan Agresti, 2014. "Two Bayesian/frequentist challenges for categorical data analyses," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 125-132, August.
    8. 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.
    9. Ioannis Ntzoufras & Claudia Tarantola & Monia Lupparelli, 2018. "Probability Based Independence Sampler for Bayesian Quantitative Learning in Graphical Log-Linear Marginal Models," DEM Working Papers Series 149, University of Pavia, Department of Economics and Management.

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