bmds: FORTRAN program to implement the methods described in ”Bayesian Multidimensional Scaling and Choice of Dimension” by M-S. Oh and A. Raftery, JASA 2001. Multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects. We deal with two major problems in metric multidimensional scaling-configuration of objects and determination of the dimension of object configuration-within a Bayesian framework. A Markov chain Monte Carlo algorithm is proposed for object configuration, along with a simple Bayesian criterion, called MDSIC, for choosing their dimension. Simulation results are presented, as are real data. Our method provides better results than does classical multidimensional scaling and ALSCAL for object configuration, and MDSIC seems to work well for dimension choice in the examples considered.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Chevalier, Clément; Martius, Olivia; Ginsbourger, David: Modeling nonstationary extreme dependence with stationary max-stable processes and multidimensional scaling (2021)
  2. Holbrook, Andrew J.; Lemey, Philippe; Baele, Guy; Dellicour, Simon; Brockmann, Dirk; Rambaut, Andrew; Suchard, Marc A.: Massive parallelization boosts big Bayesian multidimensional scaling (2021)
  3. Michis, Antonis A.: Wavelet multidimensional scaling analysis of European economic sentiment indicators (2021)
  4. Yanchenko, Anna K.; Hoff, Peter D.: Hierarchical multidimensional scaling for the comparison of musical performance styles (2020)
  5. Jin, Ick Hoon; Jeon, Minjeong: A doubly latent space joint model for local item and person dependence in the analysis of item response data (2019)
  6. Lin, L.; Fong, D. K. H.: Bayesian multidimensional scaling procedure with variable selection (2019)
  7. Okada, Kensuke; Mayekawa, Shin-ichi: Post-processing of Markov chain Monte Carlo output in Bayesian latent variable models with application to multidimensional scaling (2018)
  8. Okada, Kensuke; Lee, Michael D.: A Bayesian approach to modeling group and individual differences in multidimensional scaling (2016)
  9. Fong, Duncan K. H.; DeSarbo, Wayne S.; Chen, Zhe; Xu, Zhuying: A Bayesian vector multidimensional scaling procedure incorporating dimension reparameterization with variable selection (2015)
  10. Zhang, Zhihua: The matrix ridge approximation: algorithms and applications (2014)
  11. Oh, Man-Suk: A simple and efficient Bayesian procedure for selecting dimensionality in multidimensional scaling (2012)
  12. Park, Joonwook; Rajagopal, Priyali; DeSarbo, Wayne S.: A new heterogeneous multidimensional unfolding procedure (2012)
  13. Park, Joonwook; DeSarbo, Wayne S.; Liechty, John: A hierarchical Bayesian multidimensional scaling methodology for accommodating both structural and preference heterogeneity (2008)
  14. Lipovetsky, Stan; Conklin, W. Michael: Singular value decomposition in additive, multiplicative, and logistic forms (2005)
  15. Leung, Pui Lam; Lau, Kin-nam: Estimating the city-block two-dimensional scaling model with simulated annealing (2004)
  16. Oh, Man-Suk; Raftery, Adrian E.: Bayesian multidimensional scaling and choice of dimension. (2001)