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Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling

Author

Listed:
  • Kensuke Okada

    (Senshu University)

  • Shin-ichi Mayekawa

    (Tokyo Institute of Technology)

Abstract

In Bayesian analysis of multidimensional scaling model with MCMC algorithm, we encounter the indeterminacy of rotation, reflection and translation of the parameter matrix of interest. This type of indeterminacy may be seen in other multivariate latent variable models as well. In this paper, we propose to address this indeterminacy problem with a novel, offline post-processing method that is easily implemented using easy-to-use Markov chain Monte Carlo (MCMC) software. Specifically, we propose a post-processing method based on the generalized extended Procrustes analysis to address this problem. The proposed method is compared with four existing methods to deal with indeterminacy thorough analyses of artificial as well as real datasets. The proposed method achieved at least as good a performance as the best existing method. The benefit of the offline processing approach in the era of easy-to-use MCMC software is discussed.

Suggested Citation

  • Kensuke Okada & Shin-ichi Mayekawa, 2018. "Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling," Computational Statistics, Springer, vol. 33(3), pages 1457-1473, September.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-017-0759-6
    DOI: 10.1007/s00180-017-0759-6
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    References listed on IDEAS

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    1. 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.
    2. repec:dau:papers:123456789/6069 is not listed on IDEAS
    3. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
    4. Peter Schönemann & Robert Carroll, 1970. "Fitting one matrix to another under choice of a central dilation and a rigid motion," Psychometrika, Springer;The Psychometric Society, vol. 35(2), pages 245-255, June.
    5. Li, Yong & Yu, Jun, 2012. "Bayesian hypothesis testing in latent variable models," Journal of Econometrics, Elsevier, vol. 166(2), pages 237-246.
    6. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    7. Michael C Hout & Stephen D Goldinger & Kyle J Brady, 2014. "MM-MDS: A Multidimensional Scaling Database with Similarity Ratings for 240 Object Categories from the Massive Memory Picture Database," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-11, November.
    8. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
    9. Bakker, Ryan & Poole, Keith T., 2013. "Bayesian Metric Multidimensional Scaling," Political Analysis, Cambridge University Press, vol. 21(1), pages 125-140, January.
    10. Joonwook Park & Wayne DeSarbo & John Liechty, 2008. "A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 451-472, September.
    11. Papastamoulis, Panagiotis, 2016. "label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(c01).
    12. Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    13. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
    14. J. Ramsay, 1977. "Maximum likelihood estimation in multidimensional scaling," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 241-266, June.
    15. Jos Berge, 1977. "Orthogonal procrustes rotation for two or more matrices," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 267-276, June.
    16. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
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