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Simultaneous Linear Prediction

Published online by Cambridge University Press:  01 January 2025

Jean J. Fortier
Jean J. Fortier*
Affiliation:
S.M.A. Inc., Montreal
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Abstract

Given a set of items (predictors) suppose one wishes to predict another set of items (predictands) in asimultaneous way. Such a situation may occur when the predictands are different measurable aspects of the same phenomenon. Alternatively one might wish to predict the success of an event (say a successfully performed task) which has many correlated or uncorrelated failure modes (say a set of possible mental or physical disabilities each of them by itself precluding the achievement of the said task.) In such a case a unidimensional prediction is of value only if prediction is simultaneous for all possible failure modes. A linear summarization of the predictors is suggested, which is unique and has “maximum” predictability value for all predictands simultaneously. Other summarizations or scores are found that give “maximum” explanation of residual measures on the predictands and that are uncorrelated. The set of those simultaneous linear predictions is compared to the set of the individual multiple regression predictions as used, for instance, in the same context by Horst [4] for each predictand given the original predictors. We suggest that this technique can be applied in particular to the summarization of a subset of items when the whole set of items constitutes the set of predictands.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 3 , September 1966 , pp. 369 - 381
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

This work was initiated at Stanford University under contract 2-1-065 with U. S. Office of Education and was partly revised at the Université de Montréal.

†

I wish to express my gratitude to Professor Herbert Solomon, Stanford University, for his unfailing assistance at all stages of my work.

References

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