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

M. Baragatti and D. Pommeret

Computational Statistics & Data Analysis, 2012, vol. 56, issue 6, 1920-1934

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.

Keywords: Bayesian Lasso; Generalized linear mixed model; Metropolis-within-Gibbs algorithm; Probit mixed regression model; Ridge parameter; Stochastic search variable selection; Zellner prior (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:6:p:1920-1934

DOI: 10.1016/j.csda.2011.11.017

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