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Abstract
To analyze data collected from surveys where subjects are asked to rate multiple stimuli, multidimensional scaling (MDS), broadly defined, is commonly used to produce a joint space map of subjects and stimuli in a reduced dimensionality in order to gain insights into the inter-relationships between these row and column entities. In this paper, we propose a two-way Bayesian vector MDS procedure incorporating dimension reparameterization with a variable selection option to determine the dimensionality and simultaneously identify the significant covariates that help interpret the derived dimensions in the joint space map. We discuss how we solve identifiability problems in a Bayesian context that are associated with the two-way vector MDS model, and demonstrate through a simulation study how our proposed model outperforms a popular benchmark model. In addition, an empirical application dealing with consumers' ratings of large sport utility vehicles is presented to illustrate the proposed methodology. We are able to obtain interpretable and managerially insightful results from our proposed model with variable selection in comparison to the benchmark model. |