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Component Models for Three-Way Data: An Alternating Least Squares Algorithm with Optimal Scaling Features

Published online by Cambridge University Press:  01 January 2025

Richard Sands  and
Forrest W. Young
Richard Sands
Affiliation:
University of North Carolina at Chapel Hill
Forrest W. Young*
Affiliation:
University of North Carolina at Chapel Hill
*
Reprints and programs may be obtained from Forrest Young, Psychometric Laboratory, Davie Hall 013-A, University of North Carolina, Chapel Hill, NC 27514
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Abstract

A review of the existing techniques for the analysis of three-way data revealed that none were appropriate to the wide variety of data usually encountered in psychological research, and few were capable of both isolating common information and systematically describing individual differences. An alternating least squares algorithm was proposed to fit both an individual difference model and a replications component model to three-way data which may be defined at the nominal, ordinal, interval, ratio, or mixed measurement level; which may be discrete or continuous; and which may be unconditional, matrix conditional, or row conditional. This algorithm was evaluated by a Monte Carlo study. Recovery of the original information was excellent when the correct measurement characteristics were assumed. Furthermore, the algorithm was robust to the presence of random error. In addition, the algorithm was used to fit the individual difference model to a real, binary, subject conditional data set. The findings from this application were consistent with previous research in the area of implicit personality theory and uncovered interesting systematic individual differences in the perception of political figures and roles.

Keywords

individual differencesmeasurement level
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 39 - 67
Copyright
Copyright © 1980 The Psychometric Society

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Footnotes

This paper is part of a Thesis performed by Richard Sands under the direction of Forrest Young at the L. L. Thurstone Psychometric Laboratory, University of North Carolina at Chapel Hill. Thanks are extended to Drs. Charles Schmidt and Andrea Sedlak for the use of their political role data set.

References

Reference Notes

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