Bayesian multidimensional scaling procedure with variable selection

Multidimensional scaling methods are frequently used by researchers and practitioners to project high dimensional data into a low dimensional space. However, it is a challenge to integrate side information which is available along with the dissimilarities to perform such dimension reduction analysis. A novel Bayesian integrative multidimensional scaling procedure, namely Bayesian multidimensional scaling with variable selection, is proposed to incorporate external information on the objects into the analysis through the use of a latent multivariate regression structure. The proposed Bayesian procedure allows the incorporation of covariate information into the dimension reduction analysis through the use of a variable selection strategy. An efficient computational algorithm to implement the procedure is also developed. A series of simulation experiments and a real data analysis are conducted, and the proposed model is shown to outperform several benchmark models based on some measures commonly used in the literature.