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Default Bayesian model determination methods for generalised linear mixed models

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  • Overstall, Antony M.
  • Forster, Jonathan J.

Abstract

A default strategy for fully Bayesian model determination for generalised linear mixed models (GLMMs) is considered which addresses the two key issues of default prior specification and computation. In particular, the concept of unit-information priors is extended to the parameters of a GLMM. A combination of Markov chain Monte Carlo (MCMC) and Laplace approximations is used to compute approximations to the posterior model probabilities to find a subset of models with high posterior model probability. Bridge sampling is then used on the models in this subset to approximate the posterior model probabilities more accurately. The strategy is applied to four examples.

Suggested Citation

  • Overstall, Antony M. & Forster, Jonathan J., 2010. "Default Bayesian model determination methods for generalised linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3269-3288, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3269-3288
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    References listed on IDEAS

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    1. Sturtz, Sibylle & Ligges, Uwe & Gelman, Andrew, 2005. "R2WinBUGS: A Package for Running WinBUGS from R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i03).
    2. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    1. 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.
    2. Barigou, Karim & Goffard, Pierre-Olivier & Loisel, Stéphane & Salhi, Yahia, 2023. "Bayesian model averaging for mortality forecasting using leave-future-out validation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 674-690.
    3. Quentin F. Gronau & Eric-Jan Wagenmakers & Daniel W. Heck & Dora Matzke, 2019. "A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge Sampling," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 261-284, March.
    4. Trung Hai Nguyen & Van N T La & Kyle Burke & David D L Minh, 2022. "Bayesian regression and model selection for isothermal titration calorimetry with enantiomeric mixtures," PLOS ONE, Public Library of Science, vol. 17(9), pages 1-22, September.

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