In defense of Pratt's variable importance axioms: A response to Gromping

In a recent paper Gromping provided a wide-ranging review of metrics for assessing variable importance in regression analysis. There are, however, several flaws in Gromping's criticism of the well-known metric attributed to Pratt. Among the metrics she reviewed, Pratt's metric stands out because it is the only one that provides both a theoretically based definition of variable importance, and a simple method of estimation and inference. Our response is an effort to re-evaluate this unique metric. We give a simplified and abbreviated account of Pratt's original derivation, based on which we address the flaws in Gromping's presentation. We also discuss heuristic interpretations of Pratt's metric, and suggest a new approach for selecting one from among the many available metrics for assessing importance. This approach is intended to supplement that suggested by Gromping. Accordingly, the goal of this response is to help practitioners better understand and choose between available metrics for assessing variable importance. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis