Model Prior Distribution for Variable Selection in Linear Regression Models

Abstract: In this work we discuss a novel model prior probability for variable selection in linear regression. The idea is to determine the prior mass in an objective sense, by considering the worth of each of the possible regression models, given the number of covariates under consideration. Through a simulation study, we show that the proposed prior outperforms the uniform prior and the Scott & Berger prior in a scenario of no prior knowledge about the size of the true regression models. We illustrate the use of the prior using two well-known data sets with, respectively, 15 and 4 covariates.