Bayesian Model Selection in Order-Restricted Two-Way ANOVA Mixed Models

In this article, we propose several Bayesian model selection procedures, based on the spike and slab priors, to select significant variables while accounting for some restrictions on them. We concentrate on the following methods: Kuo and Mallick, stochastic search variable selection (SSVS), Ishwaran and Rao (NMIG). Bayesian computation is straightforward via simple Gibbs sampling algorithm. The methods are illustrated using simulated data and an application to the blood lead levels data. Results indicate that the proposed approaches perform very well in various situations.