Set Correlation As A General Multivariate Data-Analytic Method

Because of its flexibility and generality, beyond its capacity to handle the standard multivariate methods as special cases, set correlation offers some useful novel data-analytic techniques, among which are illustrated a hierarchical analysis of common and unique aspects of a battery, multivariate contrasts among outcomes, the multivariate analysis of partial variance, and contingency table analysis.

Abstract

Set correlation is a multivariate generalization of multiple regression/correlation analysis that features the employment of overall measures of association interpretable as proportions of variance and the use of set-partialled sets of variables, e.g. D·C with B·A. Partialling is a powerful device that may be used for statistical control and for representing non-linear and conditional (interactive) relationships, contrast functions, and the uniqueness of a variable or subset of variables. Generally, it offers a means for specifying functional components of sets. Since information in virtually any form can be represented as a set, partialled if necessary, the extension of partialling to sets of dependent variables makes it possible, within a single framework, to study relationships that are currently handled by diverse methods. Because of its flexibility and generality, beyond its capacity to handle the standard multivariate methods as special cases, set correlation offers some useful novel data-analytic techniques, among which are illustrated a hierarchical analysis of common and unique aspects of a battery, multivariate contrasts among outcomes, the multivariate analysis of partial variance, and contingency table analysis.