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The K-INDSCAL Model for Heterogeneous Three-Way Dissimilarity Data

Published online by Cambridge University Press:  01 January 2025

Laura Bocci and
Maurizio Vichi
Laura Bocci*
Affiliation:
Sapienza University of Rome
Maurizio Vichi
Affiliation:
Sapienza University of Rome
*
Requests for reprints should be sent to Laura Bocci, Department of Communication and Social Research, Sapienza University of Rome, Via Salaria, 113, 00198 Rome, Italy. E-mail: laura.bocci@uniroma1.it
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Abstract

A weighted Euclidean distance model for analyzing three-way dissimilarity data (stimuli by stimuli by subjects) for heterogeneous subjects is proposed. First, it is shown that INDSCAL may fail to identify a common space representative of the observed data structure in presence of heterogeneity. A new model that removes the rotational invariance of the classical multidimensional scaling problem and specifies K common homogeneous spaces is proposed. The model, called mixture INDSCAL in K classes, or briefly K-INDSCAL, still includes individual saliencies. However, the large number of parameters in K-INDSCAL may produce instability of the estimates and therefore a parsimonious model will also be discussed. The parameters of the model are estimated in a least-squares fitting context and an efficient coordinate descent algorithm is given. The usefulness of K-INDSCAL is demonstrated by both artificial and real data analyses.

Keywords

three-way dissimilarity dataINDSCALheterogeneous dissimilarities datamixture of INDSCAL models

Information

Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 4 , October 2011, pp. 691 - 714
Copyright
Copyright © 2011 The Psychometric Society

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