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A Model for the Analysis of Asymmetric Data in Marketing Research

Author

Listed:
  • Richard A. Harshman

    (University of Western Ontario, London, Ontario N6A 5B9, Canada)

  • Paul E. Green

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Yoram Wind

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Margaret E. Lundy

    (University of Western Ontario, London, Ontario N6A 5B9, Canada)

Abstract

Over the last decade, numerous methods for the multidimensional scaling (MDS) of perceptions and preferences have been applied by researchers in marketing. However, one notable gap in MDS methodology has been the lack of suitable models for analyzing inherently asymmetric data relationships. Recently, Harshman (Harshman, R. A. 1978. Models for analysis of asymmetrical relationships among objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology. McMaster University, Hamilton, Ontario, August; Harshman, R. A. 1982a. DEDICOM: A family of models generalizing factor analysis and multidimensional scaling for decomposition of asymmetric relationships. Unpublished manuscript, University of Western Ontario.) has proposed a new family of models—called DEDICOM (DEcomposition into Directional COMponents)—for analyzing data matrices that are intrinsically asymmetric. In this article, the single-domain DEDICOM model is described and applied to two illustrative cases in marketing research. The examples demonstrate that DEDICOM solutions will sometimes make more substantive sense and provide significantly better fits to asymmetric data than solutions obtained by factor analysis or MDS. DEDICOM also provides a novel type of information—a description of asymmetric relations among dimensions or clusters. Such information will often have useful marketing implications.

Suggested Citation

  • Richard A. Harshman & Paul E. Green & Yoram Wind & Margaret E. Lundy, 1982. "A Model for the Analysis of Asymmetric Data in Marketing Research," Marketing Science, INFORMS, vol. 1(2), pages 205-242.
    • Handle: RePEc:inm:ormksc:v:1:y:1982:i:2:p:205-242
    DOI: 10.1287/mksc.1.2.205
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    Citations

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    Cited by:

    1. Richard Harshman & Margaret Lundy, 1996. "Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/candecomp," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 133-154, March.
    2. Jay Verkuilen, 2006. "Data analysis of asymmetric structures," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 781-783, December.
    3. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
    4. Sato-Ilic, Mika & Sato, Yoshiharu, 2000. "Asymmetric aggregation operator and its application to fuzzy clustering model," Computational Statistics & Data Analysis, Elsevier, vol. 32(3-4), pages 379-394, January.
    5. 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.
    6. Kishen Iyengar & Venugopal Balijepally, 2015. "Ranking journals using the dominance hierarchy procedure: an illustration with IS journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 5-23, January.
    7. Berrie Zielman & Willem Heiser, 1993. "Analysis of asymmetry by a slide-vector," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 101-114, March.
    8. Giuseppe Bove & Akinori Okada, 2018. "Methods for the analysis of asymmetric pairwise relationships," 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. 12(1), pages 5-31, March.
    9. Henk Kiers, 1989. "An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 515-521, September.
    10. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
    11. Henk Kiers & Jos Berge & Yoshio Takane & Jan Leeuw, 1990. "A generalization of Takane's algorithm for dedicom," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 151-158, March.
    12. Oded Netzer & Ronen Feldman & Jacob Goldenberg & Moshe Fresko, 2012. "Mine Your Own Business: Market-Structure Surveillance Through Text Mining," Marketing Science, INFORMS, vol. 31(3), pages 521-543, May.
    13. Davies, Antony & Cline, Thomas W., 2005. "A consumer behavior approach to modeling monopolistic competition," Journal of Economic Psychology, Elsevier, vol. 26(6), pages 797-826, December.
    14. Yoshio Takane & Henk Kiers, 1997. "Latent class DEDICOM," Journal of Classification, Springer;The Classification Society, vol. 14(2), pages 225-247, September.
    15. Saburi, S. & Chino, N., 2008. "A maximum likelihood method for an asymmetric MDS model," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4673-4684, June.
    16. ten Berge, Jos M. F., 1997. "Reduction of asymmetry by rank-one matrices," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 357-366, May.
    17. Henk Kiers & Yoshio Takane, 1993. "Constrained DEDICOM," Psychometrika, Springer;The Psychometric Society, vol. 58(2), pages 339-355, June.
    18. Marti Sagarra & Frank M. T. A. Busing & Cecilio Mar-Molinero & Josep Rialp, 2018. "Assessing the asymmetric effects on branch rivalry of Spanish financial sector restructuring," 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. 12(1), pages 131-153, March.

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    Keywords

    multidimensional scaling; factor analyses;

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