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Locating the Extrema of Fungible Regression Weights

Published online by Cambridge University Press:  01 January 2025

Niels G. Waller  and
Jeff A. Jones
Niels G. Waller*
Affiliation:
University of Minnesota
Jeff A. Jones
Affiliation:
University of Minnesota
*
Requests for reprints should be sent to Niels G. Waller, Department of Psychology, University of Minnesota, N218 Elliott Hall, 75 East River Road, Minneapolis, MN, 55455, USA. E-mail: nwaller@umn.edu
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Abstract

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of “fungible weights” (Waller, Psychometrica, in press) that yields identical SSE (sum of squared errors) and R2 values. When the R2 using the alternate weights is a fixed value, fungible weights (ai) that yield the maximum or minimum cosine with an OLS weight vector (b) are called “fungible extrema.” We describe two methods for locating fungible extrema and we report R code (R Development Core Team, 2007) for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, Commun. Stat. Simul. Comput. 14:441–448, 1985).

Keywords

multiple regressionalternate weightsfungible weightsparameter sensitivity
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 4 , December 2009 , pp. 589 - 602
Copyright
Copyright © 2009 The Psychometric Society

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