Variable importance analysis: A comprehensive review

Measuring variable importance for computational models or measured data is an important task in many applications. It has drawn our attention that the variable importance analysis (VIA) techniques were developed independently in many disciplines. We are strongly aware of the necessity to aggregate all the good practices in each discipline, and compare the relative merits of each method, so as to instruct the practitioners to choose the optimal methods to meet different analysis purposes, and to guide current research on VIA. To this end, all the good practices, including seven groups of methods, i.e., the difference-based variable importance measures (VIMs), parametric regression and related VIMs, nonparametric regression techniques, hypothesis test techniques, variance-based VIMs, moment-independent VIMs and graphic VIMs, are reviewed and compared with a numerical test example set in two situations (independent and dependent cases). For ease of use, the recommendations are provided for different types of applications, and packages as well as software for implementing these VIA techniques are collected. Prospects for future study of VIA techniques are also proposed.