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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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    1. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    2. P. J. Brown & M. Vannucci & T. Fearn, 1998. "Multivariate Bayesian variable selection and prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 627-641.
    3. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    4. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    5. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    6. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    7. Baragatti, M. & Pommeret, D., 2012. "A study of variable selection using g-prior distribution with ridge parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1920-1934.
    8. 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. 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.
    3. 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).
    4. 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.

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