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A Bayesian Alternative to Least Squares and Equal Weighting Coefficients in Regression

Published online by Cambridge University Press:  01 January 2025

James E. Laughlin
James E. Laughlin*
Affiliation:
University of South Carolina
*
Requests for reprints should be sent to James E. Laughlin, Department of Psychology, University, of South Carolina, Columbia, South Carolina, 29208.
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Abstract

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. Some interesting connections between this Bayesian procedure and several other methods for estimating optimal weighting coefficients are discussed. In addition, results are presented of a Monte Carlo investigation which compared the effectiveness of the Bayesian procedure relative to least squares, equal weight, ridge, and Bayesian exchangeability estimations.

Keywords

Bayesian exchangeabilityridge regressionbiased estimation
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 3 , September 1979 , pp. 271 - 288
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

†

In fairness to Wainer it should be noted here that he tempered his view on the use of equal weights in a later paper [Wainer, 1978]. It is certainly not my intent by including this quote to single out Wainer as the spokesman for equal weights (as the references cited above should indicate). It's just that he offers us such distinctive prose that it bears reprinting.

References

Reference Notes

Fischer, G. W. Four methods for assessing multi-attribute utilities: An experimental validation. Engineering Psychology Laboratory University of Michigan, 1972.CrossRefGoogle Scholar
Laughlin, J. E. Equal weighting coefficients as an alternative to least squares in regression, 1978, Columbia: Department of Psychology, University of South Carolina.Google Scholar
Ramsay, J. O. & Novick, M. R. PLU Robust Bayesian decision theory: Point estimation. Unpublished manuscript. McGill University, 1977.Google Scholar

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