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Correlation Weights in Multiple Regression

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

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights (for any set of predictors) that yield the largest drop in R2 (the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, Rxx, and (2) the orientation of the correlation weights to the latent vectors of Rxx.

Keywords

multiple regressioncorrelation weightsalternate weightsparameter sensitivity

Information

Type
Theory and Methods
Information
Psychometrika , Volume 75 , Issue 1 , March 2010 , pp. 58 - 69
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

The authors would like to express their appreciation to Drs. Will Grove, Bob Pruzek, Scott Vrieze, and Steve Nydick for helpful comments on a draft of this article.

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