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

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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.

Original languageEnglish (US)
Pages (from-to)725-739
Number of pages15
JournalPsychometrika
Volume78
Issue number4
DOIs
StatePublished - Oct 1 2013

Keywords

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

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