A Bayesian Vector Multidimensional Scaling Procedure for the Analysis of Ordered Preference Data

Journal of the American Statistical Association, Volume 105, Issue 490, pages 482-492 (2010)

Posted: 17 Jun 2016

See all articles by Duncan K. H. Fong

Duncan K. H. Fong

Pennsylvania State University

Wayne S. DeSarbo

Pennsylvania State University

Joonwook Park

University of Kentucky - Marketing and Supply Chain

Crystal Scott

University of Michigan at Dearborn - School of Management

Date Written: 2010

Abstract

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing as required for many metric MDS procedures. Furthermore, the proposed Bayesian procedure allows external information in the form of an intractable posterior distribution derived from a related dataset to be incorporated as a prior in deriving the spatial representation of the preference data. An actual commercial application dealing with consumers’ intentions to buy new luxury sport utility vehicles are presented to illustrate the proposed methodology. Favorable comparisons are made with more traditional MDS approaches.

Keywords: Bayesian analysis, Multidimensional scaling, Preference analysis, Sports utility vehicles

Suggested Citation

Fong, Duncan K. H. and DeSarbo, Wayne S. and Park, Joonwook and Scott, Crystal, A Bayesian Vector Multidimensional Scaling Procedure for the Analysis of Ordered Preference Data (2010). Journal of the American Statistical Association, Volume 105, Issue 490, pages 482-492 (2010), Available at SSRN: https://ssrn.com/abstract=2796248

Duncan K. H. Fong

Pennsylvania State University ( email )

308 armsby
university park, PA 16802
United States

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Joonwook Park

University of Kentucky - Marketing and Supply Chain ( email )

United States

Crystal Scott

University of Michigan at Dearborn - School of Management ( email )

4901 Evergreen Road
Dearborn, MI 48128-1491
United States

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