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External Analysis with Three-Mode Principal Component Models

Published online by Cambridge University Press:  01 January 2025

Willem A. van der Kloot  and
Pieter M. Kroonenberg
Willem A. van der Kloot*
Affiliation:
Leiden University
Pieter M. Kroonenberg*
Affiliation:
Department of Education, Leiden University
*
Requests for reprints should be sent to Willem A. van der Kloot, Department of Psychology, Hooigracht 15, 2312 KM Leiden, THE NETHERLANDS.
Correspondence regarding the TUCKALS programs should be addressed to Pieter M. Kroonenberg, Department of Education, Postbus 9507, 2300 RA Leiden, THE NETHERLANDS.
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Abstract

Through external analysis of two-mode data one attempts to map the elements of one mode (e.g., attributes) as vectors in a fixed space of the elements of the other mode (e.g., stimuli). This type of analysis is extended to three-mode data, for instance, when the ratings are made by more individuals. It is described how alternating least squares algorithms for three-mode principal component analysis (PCA) are adapted to enable external analysis, and it is demonstrated that these techniques are useful for exploring differences in the individuals' mappings of the attribute vectors in the fixed stimulus space. Conditions are described under which individual differences may be ignored. External three-mode PCA is illustrated with data from a person perception experiment, designed after two studies by Rosenberg and his associates whose results were used as external information.

Keywords

multidimensional scalingindividual differencesthree-mode factor analysisperson perception
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 479 - 494
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

We gratefully acknowledge the assistance of Piet Brouwer in implementing the external analysis options in the TUCKALS programs.

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