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A Latent Class Multidimensional Scaling Model for Two-Way One-Mode Continuous Rating Dissimilarity Data

Published online by Cambridge University Press:  01 January 2025

J. Fernando Vera ,
Rodrigo Macías  and
Willem J. Heiser
J. Fernando Vera*
Affiliation:
University of Granada
Rodrigo Macías
Affiliation:
University of Granada
Willem J. Heiser
Affiliation:
Leiden University
*
Requests for reprints should be sent to J. Fernando Vera, Department of Statistics and O.R., Faculty of Sciences, University of Granada, 18071 Granada, Spain. E-mail: jfvera@ugr.es
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Abstract

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework. In each iteration, the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix, and the rest of parameters, are estimated in a simulated annealing based algorithm. A model selection strategy is used to test the number of latent classes and the dimensionality of the problem. Both simulated and classical dissimilarity data are analyzed to illustrate the model.

Keywords

multidimensional scalingclusteringlatent class analysisfinite mixture modelmaximum likelihoodsimulated annealingiterative majorizationMonte Carlo simulation
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 2 , June 2009 , pp. 297 - 315
Copyright
Copyright © 2008 The Psychometric Society

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