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

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and Marketing
• Author(s): Duncan K.H. Fong*+
• Companies: Penn State
• Keywords: Multidimensional Scaling ; Preference Analysis ; Bayesian Analysis

Abstract

We propose a Bayesian vector MDS model to analyze ordered preference data. 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. 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. Our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing. Also, the proposed Bayesian procedure allows external information in the form of a posterior distribution derived from a related data set to be incorporated as a prior in deriving the spatial representation of the preference data.