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

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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.

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Authors and Affiliations

  1. Marketing Department, Smeal College of Business, Pennsylvania State University, University Park, PA, 16802, USA

    Wayne S. DeSarbo & John Liechty

  2. Cox School of Business, Southern Methodist University, 303 Fincher Building, Dallas, TX, 75275, USA

    Joonwook Park

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  1. Joonwook Park
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  2. Wayne S. DeSarbo
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  3. John Liechty
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Correspondence to Joonwook Park.

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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.

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Park, J., DeSarbo, W.S. & Liechty, J. A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity. Psychometrika 73, 451–472 (2008). https://doi.org/10.1007/s11336-008-9064-1

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  • DOI: https://doi.org/10.1007/s11336-008-9064-1

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