Some Remarks About Gibbs Variable Selection Performance

Gibbs variable selection is one of the Bayesian approaches to the variable selection problem in generalized linear models and, in particular, in linear regression. One of the advantages of this method is that it can be easily implemented in WinBUGS. The results obtained after Gibbs sampling convergence enable us to estimate, in a straightforward manner, the posterior model probabilities and the posterior variable inclusion probabilities. These probabilities allow us to identify the maximum a posteriori model and, if it exists, the median probability model, respectively. A simulation study was performed to study the importance of sample dimension and the number of predictors in the Gibbs variable selection performance in the scope of linear regression models. The results attained suggest that Gibbs variable selection is more demanding in terms of minimum sample sizes requirements than other well-known techniques.