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A New Multidimensional Scaling Methodology for the Analysis of Asymmetric Proximity Data in Marketing Research

Author

Listed:
  • Wayne S. Desarbo

    (University of Michigan)

  • Ajay K. Manrai

    (University of Delaware)

Abstract

This paper presents a new multidimensional scaling (MDS) methodology which operationalizes the Krumhansl (1978) distance-density model for the analysis of asymmetric proximity data. In Krumhansl's conceptualization, the symmetric Euclidean interbrand distances typically associated with the traditional MDS model are augmented by the spatial density around the brands in the derived space. This modification allows the distance-density model to accommodate many of the empirically observed violations of the metric axioms (such as asymmetry). An operationalization of the distance-density model is particularly attractive to marketers who often work with asymmetric brand switching data to investigate market structure and competition. We describe this new MDS procedure which is sufficiently flexible to fit a number of competing hypotheses of proximity. The algorithm employed for estimation is technically presented together with various program options. An analysis of an asymmetric brand switching matrix for automobiles is presented to illustrate the methodology. The results of this analysis are also compared with the solutions obtained from several of the currently available procedures for handling asymmetric proximity data. Finally, technical extensions to three-way analyses, hybrid models, etc., are discussed.

Suggested Citation

  • Wayne S. Desarbo & Ajay K. Manrai, 1992. "A New Multidimensional Scaling Methodology for the Analysis of Asymmetric Proximity Data in Marketing Research," Marketing Science, INFORMS, vol. 11(1), pages 1-20.
    • Handle: RePEc:inm:ormksc:v:11:y:1992:i:1:p:1-20
    DOI: 10.1287/mksc.11.1.1
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    Cited by:

    1. Cristina Tortora & Mireille Gettler Summa & Marina Marino & Francesco Palumbo, 2016. "Factor probabilistic distance clustering (FPDC): a new clustering method," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(4), pages 441-464, December.
    2. Rutger van Oest & Philip Hans Franses, 2003. "Which Brands gain Share from which Brands? Inference from Store-Level Scanner Data," Tinbergen Institute Discussion Papers 03-079/4, Tinbergen Institute.
    3. Ho, Ying & Chung, Yuho & Lau, Kin-nam, 2010. "Unfolding large-scale marketing data," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 119-132.
    4. Manrai, Ajay K., 1995. "Mathematical models of brand choice behavior," European Journal of Operational Research, Elsevier, vol. 82(1), pages 1-17, April.
    5. Chaturvedi, Anil & Carroll, J. D., 1998. "A perceptual mapping procedure for analysis of proximity data to determine common and unique product-market structures," European Journal of Operational Research, Elsevier, vol. 111(2), pages 268-284, December.
    6. Akinori Okada & Tadashi Imaizumi, 1997. "Asymmetric multidimensional scaling of two-mode three-way proximities," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 195-224, September.
    7. Ó González-Benito & M P Martínez-Ruiz & A Molla-Descals, 2009. "Spatial mapping of price competition using logit-type market share models and store-level scanner-data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 52-62, January.
    8. 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.

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