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The Simultaneous Prediction of Any Number of Criteria by the Use of a Unique Set of Weights

Published online by Cambridge University Press:  01 January 2025

Albert K. Kurtz
Albert K. Kurtz*
Affiliation:
Life Insurance Sales Research Bureau, Hartford, Conn.
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Abstract

When several criteria are available, it is ordinarily necessary (1) to select one of them as the criterion, (2) to use several and thus arrive at several different sets of weights, or (3) to combine them into a single measure. A formula is derived for the determination of a unique set of weights. The use of these weights will produce the highest possible average coefficient of correlation between the various criteria and two (or more) weighted independent variables. If desired, the criteria may be assigned any predetermined weights. The weights then derived for the independent variables are such that the weighted average of the correlation coefficients between the various criteria and the independent variable composite will be a maximum. In the use of these formulas, no assumptions are necessary regarding the interrelationships existing among the criteria and it is not necessary to compute the intercorrelations among the criteria. A numerical example is included.

Type
Original Paper
Information
Psychometrika , Volume 2 , Issue 2 , June 1937 , pp. 95 - 101
Copyright
Copyright © 1937 The Psychometric Society

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References

* Except for changes in notation, this is the same formula as that given by Thurstone, L. L. (A scoring method for mental tests. Psychol. Bull., 1919, 16, no. 7.) and by Kelley, T. L. (Statistical method. New York: The Macmillan Company, 1924. Formula 150.)

* Hotelling, Harold: “The most predictable criterion.” Journal of Educational Psychology, February, 1935, 26, 139-142.

† Horst, Paul: “Obtaining a composite measure from a number of different measures of the same attribute,” Psychometrika, March, 1936, 1, 53-60.

‡ Edgerton, Harold A. and Kolbe, Laverne E.: “The method of minimum variation for the combination of criteria,” Psychometrika, September, 1936, 1, 183-187.