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Tscale: A new multidimensional scaling procedure based on tversky's contrast model

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Abstract

Tversky's contrast model of proximity was initially formulated to account for the observed violations of the metric axioms often found in empirical proximity data. This set-theoretic approach models the similarity/dissimilarity between any two stimuli as a linear (or ratio) combination of measures of the common and distinctive features of the two stimuli. This paper proposes a new spatial multidimensional scaling (MDS) procedure called TSCALE based on Tversky's linear contrast model for the analysis of generally asymmetric three-way, two-mode proximity data. We first review the basic structure of Tversky's conceptual contrast model. A brief discussion of alternative MDS procedures to accommodate asymmetric proximity data is also provided. The technical details of the TSCALE procedure are given, as well as the program options that allow for the estimation of a number of different model specifications. The nonlinear estimation framework is discussed, as are the results of a modest Monte Carlo analysis. Two consumer psychology applications are provided: one involving perceptions of fast-food restaurants and the other regarding perceptions of various competitive brands of cola soft-drinks. Finally, other applications and directions for future research are mentioned.

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Authors and Affiliations

  1. Marketing Department School of Business Administration, University of Michigan, USA

    Michael D. Johnson

  2. Department of Business Administration College of Business and Economics, University of Delaware, USA

    Ajay K. Manrai & Lalita A. Manrai

  3. Marketing and Statistics Depts., School of Business Administration, The University of Michigan, 48109-1234, Ann Arbor, MI

    Wayne S. DeSarbo & Elizabeth A. Edwards

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  1. Wayne S. DeSarbo
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  2. Michael D. Johnson
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  3. Ajay K. Manrai
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  4. Lalita A. Manrai
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  5. Elizabeth A. Edwards
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The authors wish to acknowledge the reviews of prior versions of this manuscript by three anonymous reviewers and the editor.

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DeSarbo, W.S., Johnson, M.D., Manrai, A.K. et al. Tscale: A new multidimensional scaling procedure based on tversky's contrast model. Psychometrika 57, 43–69 (1992). https://doi.org/10.1007/BF02294658

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