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

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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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    2. 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.
    3. 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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    5. 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).

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