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Psychometrika

, Volume 62, Issue 3, pp 349–374 | Cite as

Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case

  • Henk A. L. Kiers
  • Jos M. F. ten Berge
  • Roberto Rocci
Article

Abstract

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the three modes of a three-way array; the 3MFA model also uses a three-way core array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3MFA model the components are not uniquely determined, and it seems hard to choose among all possible solutions. A particularly interesting feature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and PARAFAC that share the good properties of the 3MFA model and the PARAFAC model: They fit (almost) as well as the 3MFA model, they are relatively simple and they have the same uniqueness properties as the PARAFAC model.

Key words

three-way methods PARAFAC 

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Copyright information

© The Psychometric Society 1997

Authors and Affiliations

  • Henk A. L. Kiers
    • 1
  • Jos M. F. ten Berge
    • 1
  • Roberto Rocci
    • 2
  1. 1.University of GroningenThe Netherlands
  2. 2.University la SapienzaRome

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