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

Psychometrika, Vol. 73, No. 3, pp. 451-472, 2008

Posted: 16 Jun 2016

See all articles by Joonwook Park

Joonwook Park

University of Kentucky - Marketing and Supply Chain

Wayne S. DeSarbo

Pennsylvania State University

John Liechty

Pennsylvania State University, University Park

Date Written: Septeber 2008

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 scaling, structural heterogeneity, preference heterogeneity, multidimensional unfolding model, multidimensional vector model, pharmaceutical marketing

Suggested Citation

Park, Joonwook and DeSarbo, Wayne S. and Liechty, John, A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity (Septeber 2008). Psychometrika, Vol. 73, No. 3, pp. 451-472, 2008, Available at SSRN: https://ssrn.com/abstract=2795720

Joonwook Park

University of Kentucky - Marketing and Supply Chain ( email )

United States

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

John Liechty

Pennsylvania State University, University Park ( email )

University Park
State College, PA 16802
United States

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