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Degenerate solutions obtained from several variants of factor analysis
Author(s) -
Zijlstra Bonne J. H.,
Kiers Henk A. L.
Publication year - 2002
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.764
Subject(s) - degenerate energy levels , multiplicative function , component (thermodynamics) , mathematics , component analysis , property (philosophy) , statistical physics , mathematical analysis , physics , thermodynamics , statistics , quantum mechanics , philosophy , epistemology
Abstract Considerable research has been performed concerning degenerate solutions from the Parafac model. However, degenerate solutions have also been reported to occur with the shifted multiplicative model and a model for component analysis of multitrait multimethod matrices. Furthermore, we obtained similarly degenerate solutions for the directly fitted Parafac‐2 model, the indirectly fitted Parafac‐2 model and a constrained variant of the Tucker‐3 model. Comparing degenerate solutions reported in the literature with the degenerate solutions we obtained ourselves, we learned that for all the above‐mentioned models there are two‐factor degenerate solutions sharing the same properties. We distinguish three common features. Furthermore, the above‐mentioned models have in common that they are all variants of factor analysis producing component matrices with components that are rotationally unique. Underscoring the significance of this property, we show that all models for two‐way and three‐way factor analysis not resulting in solutions with rotationally unique components cannot produce degenerate solutions. Copyright © 2002 John Wiley & Sons, Ltd.