An Extension of Dominance Analysis to Canonical Correlation Analysis

Dominance analysis (Budescu, 1993 Budescu, D. V. 1993. Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression.. Psychological Bulletin, 114: 542–551. Crossref], Web of Science ®] , Google Scholar]) offers a general framework for determination of relative importance of predictors in univariate and multivariate multiple regression models. This approach relies on pairwise comparisons of the contribution of predictors in all relevant subset models. In this article we extend dominance analysis to canonical correlation analysis to explore the relative importance of the variables in both sets. The proposed extension provides (a) a decomposition of the models' fit into components associated with the individual variables; (b) the ability to compare the relative importance of variables from the two sets; (c) the ability to perform multistage analyses, involving all canonical variates; and (d) a bootstrapping inference procedure. The approach is illustrated with an empirical data example involving parenting styles and youth outcomes and its unique features are highlighted and discussed.