SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University


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Contributions: Abstract

Multivariate dominance analysis

David Budescu
University of Illinois
USA
Razia Azen
University of of Wisconsin at Milwaukee
USA

Dominance analysis was proposed by Budescu (1993) as a general methodology for comparing the relative importance of predictors in multiple regression. Dominance analysis determines the dominance of one predictor over another by comparing their unique contributions to R2 across all relevant subset models. Azen & Budescu (2003) refined this approach by defining a hierarchy of levels of dominance (complete, conditional and general) that differ in their strictness, and by using bootstrap re-sampling methodology to assess the stability of the results. These papers demonstrate a variety of new insights into the patterns of relative importance in a set of predictors than can be extracted from dominance analysis.

In this paper we propose multivariate dominance analysis for multivariate multiple regression models, involving q criteria and p predictors (q £ p). This technique would allow researchers to compare the relative contribution of predictors while accounting for the relationship between criteria. Building upon previous work by Cramer and Nicewander (1979) and by van den Burg and Lewis (1988) we propose a set of desiderata for an appropriate multivariate definition of R2 for this purpose. They are boundedness of the measure, its invariance under linear transformations, monotonic relation to the number of predictors, and appropriate sensitivity to the inter-criteria correlations. An analysis of several possible measures reveals that only two to satisfy all the requirements are identified:

R2xy
=
1-|Syy|
|Syy|x|
,   and
P2yx
=
1-tr(S-1yySyy|x)/q.

We illustrate the applications of the multivariate dominance analysis and analyze its relation with the univariate dominance analyses (of the q criteria separately). Finally, we compare results of multivariate dominance analyses based on the two measures and provide recommendations for choosing the most appropriate one.