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

Nathaniel E. Helwig

doi:10.1007/s11336-013-9331-7

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

Nathaniel E. Helwig

Psychology (Twin Cities)

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	725-739
Number of pages	15
Journal	Psychometrika
Volume	78
Issue number	4
DOIs	https://doi.org/10.1007/s11336-013-9331-7
State	Published - Oct 2013

Bibliographical note

Funding Information:
The author would like to thank Sungjin Hong for helpful comments regarding an early draft of this paper, and the associate editor for helpful comments throughout the review process. This work was funded by the Campus Research Board at the University of Illinois (grant #11243) and the NSF (grant #DMS-1055815).

Keywords

Parafac2
Parafac2 sign indeterminacy
Parafac2 uniqueness
SCA
SCA uniqueness
simultaneous component analysis

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10.1007/s11336-013-9331-7

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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.",

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note = "Funding Information: The author would like to thank Sungjin Hong for helpful comments regarding an early draft of this paper, and the associate editor for helpful comments throughout the review process. This work was funded by the Campus Research Board at the University of Illinois (grant #11243) and the NSF (grant #DMS-1055815).",

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AB - 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.

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

Abstract

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