Variable importance scores

Abstract: Scoring of variables for importance in predicting a response is an ill-defined concept. Several methods have been proposed but little is known of their performance. This paper fills the gap with a comparative evaluation of eleven methods and an updated one based on the GUIDE algorithm. For data without missing values, eight of the methods are shown to be biased in that they give higher or lower scores to different types of variables, even when all are independent of the response. Of the remaining four methods, only two are applicable to data with missing values, with GUIDE the only unbiased one. GUIDE achieves unbiasedness by using a self-calibrating step that is applicable to other methods for score de-biasing. GUIDE also yields a threshold for distinguishing important from unimportant variables at 95 and 99 percent confidence levels; the technique is applicable to other methods as well. Finally, the paper studies the relationship of the scores to predictive power in three data sets. It is found that the scores of many methods are more consistent with marginal predictive power than conditional predictive power.