Variable Selection for Regression Models

A simple method for subset selection of independent variables in regression models is proposed. We expand the usual regression equation to an equation that incorporates all possible subsets of predictors by adding indicator variables as parameters. The vector of indicator variables dictates which predictors to include. Several choices of priors can be employed for the unknown regression coeecients and the unknown indicator parameters. The posterior distribution of the indicator vector is approximated by means of the Markov chain Monte Carlo algorithm. We select subsets with high posterior probabilities. In addition to linear models, we consider generalized linear models.