Ridge parameter for g-prior distribution in Probit mixed model
Résumé
In the Bayesian variable selection framework, a common prior distribution for the regression coefficients is the g-prior of Zellner (1986). However, there are two standard cases in which the associated covariance matrix does not exist, and the conventional prior of Zellner can not 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 we propose a prior distribution derived from the prior of Zellner, by introducing a ridge parameter. The prior obtained is a flexible and simple adaptation of the g-prior. This adaptation is a compromise between the conditional independent case of the coefficient regressors and the automatic scaling advantage offered by the g-prior. A full variable selection method using this prior is developed for probit mixed models, with a Metropolis-within-Gibbs algorithm using the grouping technique of Liu (1994). The method is then applied to both simulated and real datasets.
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