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The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component Analysis

Published online by Cambridge University Press:  01 January 2025

Nathaniel E. Helwig
Nathaniel E. Helwig*
Affiliation:
University of Illinois
*
Requests for reprints should be sent to Nathaniel E. Helwig, University of Illinois, Champaign, IL, USA. E-mail: nhelwig2@illinois.edu; NateHelving@gmail.com
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Abstract

Parafac2 is the most flexible Simultaneous Component Analysis (SCA) model that produces an essentially unique solution. In this paper, we discuss how Parafac2’s special sign indeterminacy affects applications of SCA, and we reveal how an external criterion variable can be used to ensure that estimated Parafac2 weights are meaningfully signed across the levels of the nesting mode. We present an example with real data from clinical psychology that illustrates the importance of Parafac2’s special sign indeterminacy, as well as the effectiveness of our proposed solution. We also discuss the implications of our results for general applications of SCA.

Keywords

Parafac2Parafac2 sign indeterminacyParafac2 uniquenesssimultaneous component analysisSCASCA uniqueness

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 4 , October 2013, pp. 725 - 739
Copyright
Copyright © 2013 The Psychometric Society

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