Assessing Variable Importance for Best Subset Selection

One of the primary issues that arises in statistical modeling pertains to the assessment of the relative importance of each variable in the model. A variety of techniques have been proposed to quantify variable importance for regression models. However, in the context of best subset selection, fewer satisfactory methods are available. With this motivation, we here develop a variable importance measure expressly for this setting. We investigate and illustrate the properties of this measure, introduce algorithms for the efficient computation of its values, and propose a procedure for calculating p-values based on its sampling distributions. We present multiple simulation studies to examine the properties of the proposed methods, along with an application to demonstrate their practical utility.