TY - JOUR
T1 - A bayesian vector multidimensional scaling procedure for the analysis of ordered preference data
AU - Fong, Duncan K.H.
AU - Desarbo, Wayne S.
AU - Park, Joonwook
AU - Scott, Crystal J.
N1 - Funding Information:
Duncan K. H. Fong is Professor of Marketing and Statistics (E-mail: [email protected]), Wayne S. DeSarbo is the Smeal Distinguished Research Professor of Marketing (E-mail: [email protected]), Marketing Department, Smeal College of Business, Pennsylvania State University, University Park, PA 16802. Joonwook Park is Assistant Professor of Marketing, Cox School of Business, Southern Methodist University, Dallas, TX 75275 (E-mail: [email protected]). Crystal J. Scott is Assistant Professor of Marketing, School of Management, University of Michigan–Dearborn, Dearborn, MI 48126 (E-mail: [email protected]). Duncan K. H. Fong’s work was sponsored in part by a research grant from the Smeal College. The authors wish to acknowledge and thank the Editor, an Associate Editor, and three anonymous reviewers for their constructive comments.
PY - 2010/6
Y1 - 2010/6
N2 - 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.
AB - 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.
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U2 - 10.1198/jasa.2009.ap08105
DO - 10.1198/jasa.2009.ap08105
M3 - Article
AN - SCOPUS:78649433078
SN - 0162-1459
VL - 105
SP - 482
EP - 492
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 490
ER -