Abstract: We have developed an enhanced spike and slab model for variable selection in linear regression models via restricted final prediction error (FPE) criteria; classic examples of which are AIC and BIC. Based on our proposed Bayesian hierarchical model, a Gibbs sampler is developed to sample models. The special structure of the prior enforces a unique mapping between sampling a model and calculating constrained ordinary least squares estimates for that model, which helps to formulate the restricted FPE criteria. Empirical comparisons are done to the lasso, adaptive lasso and relaxed lasso; followed by a real life data example.
Abstract: We have developed a tool for model space exploration and variable selec tion in linear regression models based on a simple spike and slab model (Dey, 2012). The model chosen is the best model with minimum final prediction error (FPE) values among all other models. This is implemented via the R package modelSampler. However, model selection based on FPE criteria is dubious and question able as FPE criteria can be sensitive to perturbations in the data. This R package can be used for empirical assessment of the stability of FPE criteria. A stable model selection is accomplished by using a bootstrap wrapper that calls the primary function of the package several times on the bootstrapped data. The heart of the method is the notion of model averaging for sta ble variable selection and to study the behavior of variables over the entire model space, a concept invaluable in high dimensional situations.