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Fungible Weights in Multiple Regression

Published online by Cambridge University Press:  01 January 2025

Niels G. Waller
Niels G. Waller*
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

Every set of alternate weights (i.e., nonleast squares weights) in a multiple regression analysis with three or more predictors is associated with an infinite class of weights. All members of a given class can be deemed fungible because they yield identical SSE (sum of squared errors) and R2 values. Equations for generating fungible weights are reviewed and an example is given that illustrates how fungible weights can be profitably used to evaluate parameter sensitivity in multiple regression.

Keywords

multiple regressionalternate weightsfungible weightsparameter sensitivity
Type
Original Paper
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 691 - 703
Copyright
Copyright © 2008 The Psychometric Society

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Footnotes

The author wishes to thank Drs. Robyn Dawes, William Grove, Markus Keel, Leslie Yonce, Joe Rausch, the editor, and three anonymous reviewers for helpful comments on earlier versions of this article.

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