Comparing Predictors in Multivariate Regression Models: An Extension of Dominance Analysis

Dominance analysis (DA) is a method used to compare the relative importance of predictors in multiple regression. DA determines the dominance of one predictor over another by comparing their additional R² contributions across all subset models. In this article DA is extended to multivariate models by identifying a minimal set of criteria for an appropriate generalization of R² to the case of multiple response variables. The DA results obtained by univariate regression (with each criterion separately) are analytically compared with results obtained by multivariate DA and illustrated with an example. It is shown that univariate dominance does not necessarily imply multivariate dominance (and vice versa), and it is recommended that researchers who wish to account for the correlation among the response variables use multivariate DA to determine the relative importance of predictors.