IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v129y2019icp1-13.html
   My bibliography  Save this article

Bayesian multidimensional scaling procedure with variable selection

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301737
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.07.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jelnov, Pavel, 2019. "Comparison Dimensions and Similarity: Addressing Individual Heterogeneity," IZA Discussion Papers 12355, Institute of Labor Economics (IZA).
    2. Antonis A. Michis, 2021. "Wavelet Multidimensional Scaling Analysis of European Economic Sentiment Indicators," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 443-480, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Morales José F. & Song Tingting & Auerbach Arleen D. & Wittkowski Knut M., 2008. "Phenotyping Genetic Diseases Using an Extension of µ-Scores for Multivariate Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-20, June.
    3. Bijmolt, T.H.A. & Wedel, M., 1996. "A Monte Carlo Evaluation of Maximum Likelihood Multidimensional Scaling Methods," Research Memorandum 725, Tilburg University, School of Economics and Management.
    4. Venera Tomaselli, 1996. "Multivariate statistical techniques and sociological research," Quality & Quantity: International Journal of Methodology, Springer, vol. 30(3), pages 253-276, August.
    5. Bijmolt, T.H.A. & Wedel, M., 1996. "A Monte Carlo Evaluation of Maximum Likelihood Multidimensional Scaling Methods," Other publications TiSEM f72cc9d8-f370-43aa-a224-4, Tilburg University, School of Economics and Management.
    6. Xiaomeng Cao & Yuan Gao & Jingwei Cui & Shuangbiao Han & Lei Kang & Sha Song & Chengshan Wang, 2020. "Pore Characteristics of Lacustrine Shale Oil Reservoir in the Cretaceous Qingshankou Formation of the Songliao Basin, NE China," Energies, MDPI, vol. 13(8), pages 1-25, April.
    7. He, Jiayi & Shang, Pengjian & Xiong, Hui, 2018. "Multidimensional scaling analysis of financial time series based on modified cross-sample entropy methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 210-221.
    8. W. J. Krzanowski, 2006. "Sensitivity in Metric Scaling and Analysis of Distance," Biometrics, The International Biometric Society, vol. 62(1), pages 239-244, March.
    9. Gruenhage, Gina & Opper, Manfred & Barthelme, Simon, 2016. "Visualizing the effects of a changing distance on data using continuous embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 51-65.
    10. Roger Shepard, 1974. "Representation of structure in similarity data: Problems and prospects," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 373-421, December.
    11. Roger Girard & Norman Cliff, 1976. "A monte carlo evaluation of interactive multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(1), pages 43-64, March.
    12. J. Ramsay, 1969. "Some statistical considerations in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 34(2), pages 167-182, June.
    13. Massimiliano Agovino & Maria Ferrara & Antonio Garofalo, 2017. "The driving factors of separate waste collection in Italy: a multidimensional analysis at provincial level," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 19(6), pages 2297-2316, December.
    14. Jerzy Grobelny & Rafal Michalski & Gerhard-Wilhelm Weber, 2021. "Modeling human thinking about similarities by neuromatrices in the perspective of fuzzy logic," WORking papers in Management Science (WORMS) WORMS/21/09, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    15. Pepermans, Roland & Verleye, Gino, 1998. "A unified Europe? How euro-attitudes relate to psychological differences between countries," Journal of Economic Psychology, Elsevier, vol. 19(6), pages 681-699, December.
    16. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    17. Verniest, Fabien & Greulich, Sabine, 2019. "Methods for assessing the effects of environmental parameters on biological communities in long-term ecological studies - A literature review," Ecological Modelling, Elsevier, vol. 414(C).
    18. Charles Sherman, 1972. "Nonmetric multidimensional scaling: A monte carlo study of the basic parameters," Psychometrika, Springer;The Psychometric Society, vol. 37(3), pages 323-355, September.
    19. Bert Green, 1966. "The computer revolution in psychometrics," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 437-445, December.
    20. H. Micko, 1970. "A “halo”-model for multidimensional ratio scaling," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 199-227, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:129:y:2019:i:c:p:1-13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.