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Psychometrika

, Volume 45, Issue 1, pp 39–67 | Cite as

Component models for three-way data: An alternating least squares algorithm with optimal scaling features

  • Richard Sands
  • Forrest W. Young
Article

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.

Key words

individual differences measurement level 

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Reference notes

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Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • Richard Sands
    • 1
  • Forrest W. Young
    • 1
  1. 1.Psychometric LaboratoryUniversity of North CarolinaChapel Hill

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