Reply to “A Comment on a New Measure of Predictor Variable Importance in Multiple Regression”

Jackson provides a clear statement of a basic (and noncontroversial) limitation of all measures in multiple regression-namely, there is no unambiguous measure of importance in the case of correlated predictor variables. Darlington (1968) presented this same caveat more than a decade ago and some of our own publications have emphasized it as well (Green and Tull, 1978; Green with Carroll, 1978). Amemiya (1976) came to this same conclusion in his econometric investigation of regressor selection. It was not the intent of our article to suggest that 82 is immune to this limitation; if our discussion implied this conclusion, it is important that Jackson has set the record straight. However, it is one thing to say that all of the commonly used measures (except the simple validity measure, but it has its own limitations) are vulnerable to changes in the number and nature of correlated predictors. It is quite another matter to assume, because of this, that all such measures are equally useful for summarizing predictor variable importance. Indeed, Darlington goes on to discuss the various pros and cons of many measures, despite their common ambiguity in the face of correlated predictors. All we meant to show about 2 is that it appears-on the basis of limited research to date-to have some attractive properties, assuming, as is often the case, that the researcher is required to say something to the client about predictor importance, even in the case of correlated predictors. In addition to always being non-negative and summing to R2, the 82 measure provides a more or less symmetric allocation of shared variance in the situation of correlated predictors. This was the main point of the article. An illustration of the properties of 62 is in order.