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Bayesian structured variable selection in linear regression models

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  • Min Wang
  • Xiaoqian Sun
  • Tao Lu

Abstract

In this paper we consider the Bayesian approach to the problem of variable selection in normal linear regression models with related predictors. We adopt a generalized singular $$g$$ g -prior distribution for the unknown model parameters and the beta-prime prior for the scaling factor $$g$$ g , which results in a closed-form expression of the marginal posterior distribution without integral representation. A special prior on the model space is then advocated to reflect and maintain the hierarchical or structural relationships among predictors. It is shown that under some nominal assumptions, the proposed approach is consistent in terms of model selection and prediction. Simulation studies show that our proposed approach has a good performance for structured variable selection in linear regression models. Finally, a real-data example is analyzed for illustrative purposes. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Min Wang & Xiaoqian Sun & Tao Lu, 2015. "Bayesian structured variable selection in linear regression models," Computational Statistics, Springer, vol. 30(1), pages 205-229, March.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:1:p:205-229
    DOI: 10.1007/s00180-014-0529-7
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    References listed on IDEAS

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    7. 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.
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    Cited by:

    1. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    2. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    4. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.

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