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A study of variable selection using g-prior distribution with ridge parameter

Author

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  • Baragatti, M.
  • Pommeret, D.

Abstract

In the Bayesian stochastic search variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner. However there are two standard cases where the associated covariance matrix does not exist and the conventional prior of Zellner cannot be used: if the number of observations is lower than the number of variables (large p and small n paradigm), or if some variables are linear combinations of others. In such situations, a prior distribution derived from the prior of Zellner can be considered by introducing a ridge parameter. This prior is a flexible and simple adaptation of the g-prior and its influence on the selection of variables is studied. A simple way to choose the associated hyper-parameters is proposed. The method is valid for any generalized linear mixed model and particular attention is paid to the study of probit mixed models when some variables are linear combinations of others. The method is applied to both simulated and real datasets obtained from Affymetrix microarray experiments. Results are compared to those obtained with the Bayesian Lasso.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1920-1934
    DOI: 10.1016/j.csda.2011.11.017
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. repec:dau:papers:123456789/857 is not listed on IDEAS
    4. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    5. Kwon, Deukwoo & Landi, Maria Teresa & Vannucci, Marina & Issaq, Haleem J. & Prieto, DaRue & Pfeiffer, Ruth M., 2011. "An efficient stochastic search for Bayesian variable selection with high-dimensional correlated predictors," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2807-2818, October.
    6. 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.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Berrett, Candace & Calder, Catherine A., 2012. "Data augmentation strategies for the Bayesian spatial probit regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 478-490.
    9. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    10. repec:dau:papers:123456789/1906 is not listed on IDEAS
    11. van Dyk, David A. & Park, Taeyoung, 2008. "Partially Collapsed Gibbs Samplers: Theory and Methods," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 790-796, June.
    12. Gupta, Mayetri & Ibrahim, Joseph G., 2007. "Variable Selection in Regression Mixture Modeling for the Discovery of Gene Regulatory Networks," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 867-880, September.
    13. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. Lee, Kuo-Jung & Chen, Ray-Bing & Wu, Ying Nian, 2016. "Bayesian variable selection for finite mixture model of linear regressions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 1-16.
    2. Aijun Yang & Xuejun Jiang & Lianjie Shu & Jinguan Lin, 2017. "Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis," Computational Statistics, Springer, vol. 32(1), pages 127-143, March.
    3. 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.
    4. 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).
    5. Latouche, Pierre & Mattei, Pierre-Alexandre & Bouveyron, Charles & Chiquet, Julien, 2016. "Combining a relaxed EM algorithm with Occam’s razor for Bayesian variable selection in high-dimensional regression," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 177-190.

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