Variable importance in regression models

Regression analysis is one of the most-used statistical methods. Often part of the research question is the identification of the most important regressors or an importance ranking of the regressors. Most regression models are not specifically suited for answering the variable importance question, so that many different proposals have been made. This article reviews in detail the various variable importance metrics for the linear model, particularly emphasizing variance decomposition metrics. All linear modelmetrics are illustrated by an example analysis. For nonlinear parametric models, several principles from linear models have been adapted, and machine-learning methods have their own set of variable importance methods. These are also briefly covered. Although there are many variable importance metrics, there is still no convincing theoretical basis for them, and they all have a heuristic touch. Nevertheless, some metrics are considered useful for a crude assessment in the absence of a good subject matter theory. (C) 2015 Wiley Periodicals, Inc.