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A New Heterogeneous Multidimensional Unfolding Procedure

Published online by Cambridge University Press:  01 January 2025

Joonwook Park ,
Priyali Rajagopal  and
Wayne S. DeSarbo
Joonwook Park*
Affiliation:
Southern Methodist University
Priyali Rajagopal
Affiliation:
Southern Methodist University
Wayne S. DeSarbo
Affiliation:
Pennsylvania State University
*
Requests for reprints should be sent to Joonwook Park, Cox Business School, Southern Methodist University, Dallas, TX 75275, USA. E-mail: jpark@cox.smu.edu
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Abstract

A variety of joint space multidimensional scaling (MDS) methods have been utilized for the spatial analysis of two- or three-way dominance data involving subjects’ preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the underlying relevant dimensions, attributes, stimuli, and/or subjects’ utility structures in the same joint space representation. We demonstrate that care must be taken with respect to a key assumption in existent joint space MDS models such that all estimated dimensions are utilized by each and every subject in the sample, as this assumption can lead to serious distortions with respect to the derived joint spaces. We develop a new Bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three-way dominance data. A consumer psychology application regarding the preference for Over-the-Counter (OTC) analgesics is provided. We conclude by discussing the practical implications of the results, as well as directions for future research.

Keywords

multidimensional unfoldingdimension selectionBayesian multidimensional scalingconsumer psychologyheterogeneity
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 2 , April 2012 , pp. 263 - 287
Copyright
Copyright © 2012 The Psychometric Society

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