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Some Clarifications of the TUCKALS2 Algorithm Applied to the IDIOSCAL Problem

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge ,
Paul A. Bekker  and
Henk A. L. Kiers
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Paul A. Bekker
Affiliation:
University of Groningen
Henk A. L. Kiers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

Kroonenberg and de Leeuw have suggested fitting the IDIOSCAL model by the TUCKALS2 algorithm for three-way components analysis. In theory, this is problematic because TUCKALS2 produces two possibly different coordinate matrices, that are useless for IDIOSCAL unless they are equal. Kroonenberg has claimed that, when IDIOSCAL is fitted by TUCKALS2, the resulting coordinate matrices will be identical. In the present paper, this claim is proven valid when the data matrices are semidefinite. However, counterexamples for indefinite matrices are also constructed, by examining the global minimum in the case where the data matrices have the same eigenvectors. Similar counterexamples have been considered by ten Berge and Kiers in the related context of CANDECOMP/PARAFAC to fit the INDSCAL model.

Keywords

IDIOSCALTUCKALS2CANDECOMPPARAFAC
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 2 , June 1994 , pp. 193 - 201
Copyright
Copyright © 1994 The Psychometric Society

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