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Prior elicitation, variable selection and Bayesian computation for logistic regression models

Author

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  • M.‐H. Chen
  • J. G. Ibrahim
  • C. Yiannoutsos

Abstract

Bayesian selection of variables is often difficult to carry out because of the challenge in specifying prior distributions for the regression parameters for all possible models, specifying a prior distribution on the model space and computations. We address these three issues for the logistic regression model. For the first, we propose an informative prior distribution for variable selection. Several theoretical and computational properties of the prior are derived and illustrated with several examples. For the second, we propose a method for specifying an informative prior on the model space, and for the third we propose novel methods for computing the marginal distribution of the data. The new computational algorithms only require Gibbs samples from the full model to facilitate the computation of the prior and posterior model probabilities for all possible models. Several properties of the algorithms are also derived. The prior specification for the first challenge focuses on the observables in that the elicitation is based on a prior prediction y0 for the response vector and a quantity a0 quantifying the uncertainty in y0. Then, y0 and a0 are used to specify a prior for the regression coefficients semi‐automatically. Examples using real data are given to demonstrate the methodology.

Suggested Citation

  • M.‐H. Chen & J. G. Ibrahim & C. Yiannoutsos, 1999. "Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 223-242.
  • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:223-242
    DOI: 10.1111/1467-9868.00173
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    Cited by:

    1. He, Xin & Mao, Xiaojun & Wang, Zhonglei, 2024. "Nonparametric augmented probability weighting with sparsity," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    2. Min-Hua Jen & Alex Bottle & Graham Kirkwood & Ron Johnston & Paul Aylin, 2011. "The performance of automated case-mix adjustment regression model building methods in a health outcome prediction setting," Health Care Management Science, Springer, vol. 14(3), pages 267-278, September.
    3. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    4. Chen, Ming-Hui & Shao, Qi-Man, 1999. "Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 277-296, November.
    5. Chen, Min & Wang, Xinlei, 2011. "Approximate predictive densities and their applications in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1570-1580, April.
    6. Leonardo Egidi & Ioannis Ntzoufras, 2020. "A Bayesian quest for finding a unified model for predicting volleyball games," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1307-1336, November.
    7. Ho-Hsiang Wu & Marco A. R. Ferreira & Mohamed Elkhouly & Tieming Ji, 2020. "Hyper Nonlocal Priors for Variable Selection in Generalized Linear Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 147-185, February.
    8. McCandless Lawrence C & Douglas Ian J. & Evans Stephen J. & Smeeth Liam, 2010. "Cutting Feedback in Bayesian Regression Adjustment for the Propensity Score," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-24, March.
    9. Shi, Guiling & Lim, Chae Young & Maiti, Tapabrata, 2019. "Bayesian model selection for generalized linear models using non-local priors," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 285-296.
    10. Ming-Hui Chen & Qi-Man Shao, 2002. "Partition-Weighted Monte Carlo Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 338-354, June.
    11. Imaduddin Ahmed & Priti Parikh & Parfait Munezero & Graham Sianjase & D’Maris Coffman, 2023. "The impact of power outages on households in Zambia," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 40(3), pages 835-867, October.

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