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Monotonic Weighted Power Transformations to Additivity

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay
J. O. Ramsay*
Affiliation:
McGill University
*
Requests for reprints should be sent to J. O. Ramsay, Department of Psychology, McGill University, Montreal, Canada.
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Abstract

A class of monotonic transformations which generalize the power transformation is fit to the independent and dependent variables in multiple regression so that the resulting additive relationship is optimized. This is achieved by minimizing a quadratic fitting criterion with linear inequality constraints on the parameters. A quadratic programming technique which works reliably and quickly in this application is outlined. Some examples of the analysis of artificial and real data are offered.

Keywords

monotonictransformationsLaplace transformadditivitymultiple regressionpower transformation
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 1 , March 1977 , pp. 83 - 109
Copyright
Copyright © 1977 The Psychometric Society

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Footnotes

This work was supported by National Research Council of Canada Grant APA 320 to the author.

References

Reference Note

Ward, L. L. Is uncorrelating the residuals worth it? Unpublished masters thesis, McGill University, 1973.Google Scholar

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