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A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity

Published online by Cambridge University Press:  01 January 2025

Joonwook Park ,
Wayne S. DeSarbo  and
John Liechty
Joonwook Park*
Affiliation:
Southern Methodist University
Wayne S. DeSarbo
Affiliation:
Pennsylvania State University
John Liechty
Affiliation:
Pennsylvania State University
*
Requests for reprints should be sent to Joonwook Park, Cox School of Business, Southern Methodist University, 303 Fincher Building, Dallas, TX 75275, USA. E-mail: [email protected]
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Abstract

Multidimensional scaling (MDS) models for the analysis of dominance data have been developed in the psychometric and classification literature to simultaneously capture subjects’ preference heterogeneity and the underlying dimensional structure for a set of designated stimuli in a parsimonious manner. There are two major types of latent utility models for such MDS models that have been traditionally used to represent subjects’ underlying utility functions: the scalar product or vector model and the ideal point or unfolding model. Although both models have been widely applied in various social science applications, implicit in the assumption of such MDS methods is that all subjects are homogeneous with respect to their underlying utility function; i.e., they all follow a vector model or an ideal point model. We extend these traditional approaches by presenting a Bayesian MDS model that combines both the vector model and the ideal point model in a generalized framework for modeling metric dominance data. This new Bayesian MDS methodology explicitly allows for mixtures of the vector and the ideal point models thereby accounting for both preference heterogeneity and structural heterogeneity. We use a marketing application regarding physicians’ prescription behavior of antidepressant drugs to estimate and compare a variety of spatial models.

Keywords

Bayesian multidimensional scalingstructural heterogeneitypreference heterogeneitymultidimensional unfolding modelmultidimensional vector modelpharmaceutical marketing
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 3 , September 2008 , pp. 451 - 472
Copyright
Copyright © 2008 The Psychometric Society

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Footnotes

The authors thank Arvind Rangaswamy, Duncan K.H. Fong, and Joseph Schafer for their constructive comments on an earlier version of this manuscript. The helpful suggestions of the Editor, the AE, and two anonymous reviewers are also gratefully acknowledged.

Electronic Supplementary Material The online version of this article (http://dx.doi.org/10.1007/s11336-008-9064-1) contains supplementary material, which is available to authorized users.

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