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Bayesian multidimensional scaling procedure with variable selection

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  • Lin, L.
  • Fong, D.K.H.

Abstract

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.

Suggested Citation

  • Lin, L. & Fong, D.K.H., 2019. "Bayesian multidimensional scaling procedure with variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 1-13.
    • Handle: RePEc:eee:csdana:v:129:y:2019:i:c:p:1-13
    DOI: 10.1016/j.csda.2018.07.007
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    References listed on IDEAS

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    1. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2016. "Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem," Journal of Econometrics, Elsevier, vol. 192(1), pages 190-206.
    2. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. II," Psychometrika, Springer;The Psychometric Society, vol. 27(3), pages 219-246, September.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    5. Oh, Man-Suk, 2012. "A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 200-209.
    6. Duncan Fong & Wayne DeSarbo & Zhe Chen & Zhuying Xu, 2015. "A Bayesian Vector Multidimensional Scaling Procedure Incorporating Dimension Reparameterization with Variable Selection," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1043-1065, December.
    7. J. Kruskal, 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis," Psychometrika, Springer;The Psychometric Society, vol. 29(1), pages 1-27, March.
    8. Roger Shepard, 1962. "The analysis of proximities: Multidimensional scaling with an unknown distance function. I," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 125-140, June.
    9. Ian Spence & Stephan Lewandowsky, 1989. "Robust multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 501-513, September.
    10. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
    11. Fong, Duncan K. H. & DeSarbo, Wayne S. & Park, Joonwook & Scott, Crystal J., 2010. "A Bayesian Vector Multidimensional Scaling Procedure for the Analysis of Ordered Preference Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 482-492.
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