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Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units

Published online by Cambridge University Press:  01 January 2025

Roberto Rocci  and
Maurizio Vichi
Roberto Rocci*
Affiliation:
University “Tor Vergata”
Maurizio Vichi
Affiliation:
University “La Sapienza”
*
Requests for reprints should be sent to Roberto Rocci, Dipartimento SEFeMEQ, Università' “Tor Vergata”, 00133 ROMA, ITALY; e-mail: roberto.rocci@uniroma2.it
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Abstract

A new methodology is proposed for the simultaneous reduction of units, variables, and occasions of a three-mode data set. Units are partitioned into a reduced number of classes, while, simultaneously, components for variables and occasions accounting for the largest common information for the classification are identified. The model is a constrained three-mode factor analysis and it can be seen as a generalization of the REDKM model proposed by De Soete and Carroll for two-mode data. The least squares fitting problem is mathematically formalized as a constrained problem in continuous and discrete variables. An iterative alternating least squares algorithm is proposed to give an efficient solution to this minimization problem in the crisp and fuzzy classification context. The performances of the proposed methodology are investigated by a simulation study comparing our model with other competing methodologies. Different procedures for starting the proposed algorithm have also been tested. A discussion of some interesting differences in the results follows. Finally, an application to real data illustrates the ability of the proposed model to provide substantive insights into the data complexities.

Keywords

classificationthree-way datasimultaneous modes reduction
Type
Theory and Methods
Information
Psychometrika , Volume 70 , Issue 4 , December 2005 , pp. 715 - 736
Copyright
Copyright © 2005 The Psychometric Society

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