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A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data

Author

Listed:
  • David B. MacKay

    (Indiana University)

  • Joseph L. Zinnes

    (University of Illinois, Urbana)

Abstract

A probabilistic multidimensional scaling model that estimates both location and variance parameters for proximity and preference data is described and compared to a deterministic scaling model. Simulated and empirical choice data are used to compare models. Variance estimates from the probabilistic model are used to test a hypothesis about the homogeneity of stimulus perception under alternative modes of stimulus presentation.

Suggested Citation

  • David B. MacKay & Joseph L. Zinnes, 1986. "A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data," Marketing Science, INFORMS, vol. 5(4), pages 325-344.
    • Handle: RePEc:inm:ormksc:v:5:y:1986:i:4:p:325-344
    DOI: 10.1287/mksc.5.4.325
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    Citations

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    Cited by:

    1. Abe, Makoto, 1998. "Error structure and identification condition in maximum likelihood nonmetric multidimensional scaling," European Journal of Operational Research, Elsevier, vol. 111(2), pages 216-227, December.
    2. Dawn Iacobucci & Doug Grisaffe & Wayne DeSarbo, 2017. "Statistical perceptual maps: using confidence region ellipses to enhance the interpretations of brand positions in multidimensional scaling," Journal of Marketing Analytics, Palgrave Macmillan, vol. 5(3), pages 81-98, December.
    3. van de Velden, M. & de Beuckelaer, A. & Groenen, P.J.F. & Busing, F.M.T.A., 2011. "Nonmetric Unfolding of Marketing Data: Degeneracy and Stability," ERIM Report Series Research in Management ERS-2011-006-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    4. Elrod, Terry & Keane, Michael, 1995. "A Factor-Analytic Probit Model for Representing the Market Structure in Panel Data," MPRA Paper 52434, University Library of Munich, Germany.
    5. Gower, J.C. & Groenen, P.J.F. & van de Velden, M. & Vines, K., 2010. "Perceptual maps: the good, the bad and the ugly," ERIM Report Series Research in Management ERS-2010-011-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    6. Bowen, William M., 1995. "A Thurstonian comparison of the analytic hierarchy process and probabilistic multidimensional scaling through application to the nuclear waste site selection decision," Socio-Economic Planning Sciences, Elsevier, vol. 29(2), pages 151-163, June.

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