Analyzing Paired Comparisons Data Using Probabilistic Ideal Point Models and Probabilistic Vector Models

  • Daniel Baier
  • Wolfgang Gaul
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Summary

Various probabilistic ideal point and vector models have been proposed for the analysis of paired comparisons data. In order to show whether older sequential approaches (where an a priori clustering of respondents is used) are outperformed by newer simultaneous approaches (where clustering and choice model parameters are estimated simultaneously), a framework for empirical comparisons is developed. A formulation is presented, which includes sequential and simultaneous approaches as special cases. An application to the analysis of preference judgments related to print ads for beer brands shows advantages of the simultaneous approaches.

Keywords

Entropy Marketing 

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References

  1. Akaike, H. (1977): On Entropy Maximization Principle. In: P. R. Krishnaiah (ed.): Applications of Statistics. North Holland, Amsterdam, 27–41.Google Scholar
  2. Baier, D. (1994): Konzipierung und Realisierung einer Unterstützung des kombinierten Einsatzes von Methoden bei der Positionierungsanalyse. Lang, Frankfurt.Google Scholar
  3. Bock, H.-H. (1986): Loglinear Models and Entropy Clustering Methods. In: W. Gaul and M. Schader (eds.): Classification as a Tool of Research. North-Holland, Amsterdam, 19–26.Google Scholar
  4. Bock, H.-H. (1995): Probabilistic Models in Cluster Analysis. Computational Statistics and Data Analysis (accepted).Google Scholar
  5. Böckenholt, I., and Gaul, W. (1986): Analysis of Choice Behavior via Probabilistic Ideal Point and Vector Models. Applied Stochastic Models and Data Analysis, 2, 202–226.CrossRefGoogle Scholar
  6. Böckenholt, I., and Gaul, W. (1988): Probabilistic Multidimensional Scaling of Paired Comparisons Data. In: H.-H. Bock (ed.): Classification and Related Methods of Data Analysis. North-Holland, Amsterdam, 405–412.Google Scholar
  7. Bozdogan, H. (1987): Model Selection and Akaike’s Information Criterion: The General Theory and Its Analytical Extensions. Psychometrika, 52, 345–370.CrossRefGoogle Scholar
  8. Bozdogan, H. (1993): Choosing the Number of Component Clusters in the Mixture-Model Using a New Informational Complexity Criterion of the Inverse- Fisher Information Matrix. In: O. Opitz, B. Lausen and R. Klar (eds.): Information and Classification. Springer, Berlin, 40–54.Google Scholar
  9. Bryant, P.G., and Williamson, J.A. (1978): The Asymptotic Behavior of Classification Maximum Likelihood Estimates. Biometrika, 65, 273–281.CrossRefGoogle Scholar
  10. Bryant, P.G., and Williamson, J.A. (1986): Maximum Likelihood and Classification: A Comparison of Three Approaches. In: W. Gaul and M. Schader (eds.): Classification as a Tool of Research. North-Holland, Amsterdam, 35–45.Google Scholar
  11. Carroll, J.D., and Arabie, P. (1980): Multidimensional Scaling. Annual Review of Psychology, 31, 607–649.CrossRefGoogle Scholar
  12. Cooper, L. G., and Nakanishi, N. (1983): Two Logit Models for External Analysis of Preferences. Psychometrika, 48, 607–620.CrossRefGoogle Scholar
  13. David, H.A. (1988): The Method of Paired Comparisons. Griffin, London.Google Scholar
  14. Desarbo, W.S., Wedel, M., Vriens, M., and Ramaswamy, V. (1992): Latent Class Metric Conjoint Analysis. Marketing Letters, 3, 273–288.CrossRefGoogle Scholar
  15. Dillon, W.R., Kumar, A., and Smith De Borrero, M. (1993): Capturing Individual Differences in Paired Comparisons: An Extended BTL Model Incorporating Descriptor Variables. Journal of Marketing Research, 30, 42–51.CrossRefGoogle Scholar
  16. Gaul, W. (1978): Zur Methode der paarweisen Vergleiche und ihrer Anwendung im Marketingbereich. Methods of Operations Research, 35, 123–139.Google Scholar
  17. Gaul, W. (1989): Probabilistic Choice Behavior Models and Their Combination With Additional Tools Needed for Applications to Marketing. In: G. De Soete, H. Feger and K. C. Klauer (eds.): New Developments in Psychological Choice Modeling. North-Holland, Amsterdam, 317–337.CrossRefGoogle Scholar
  18. Gaul, W., and Baier, D. (1994): Marktforschung und Marketing Management, 2nd edition. Oldenbourg, München.Google Scholar
  19. Gaul, W., and Schader, M. (1988): Clusterwise Aggregation of Relations. Applied Stochastic Models and Data Analysis, 4, 273–282.CrossRefGoogle Scholar
  20. De Soete, G. (1990): A Latent Class Approach to Modeling Pairwise Preferential Choice Data. In: M. Schader and W. Gaul (eds.): Knowledge, Data and Computer-Assisted Decisions. Springer, Berlin, 103–113.Google Scholar
  21. De Soete, G., and Carroll, J.D. (1983): A Maximum Likelihood Method for Fitting the Wandering Vector Model. Psychometrika, 48, 553–566.CrossRefGoogle Scholar
  22. De Soete, G., Carroll, J.D., and Desarbo, W.S. (1986): The Wandering Ideal Point Model: A Probabilistic Multidimensional Unfolding Model for Paired Comparisons Data. Journal of Mathematical Psychology, 30, 28–41.CrossRefGoogle Scholar
  23. Wedel, M., and Desarbo, W.S. (1993): A Latent Class Binomial Log it Methodology for the Analysis of Paired Comparison Choice Data. Decision Sciences, 24, 1157–1170.CrossRefGoogle Scholar
  24. Windham, M. P. (1987): Parameter Modification for Clustering Criteria. Journal of Classification, 4, 191–214.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • Daniel Baier
    • 1
  • Wolfgang Gaul
    • 1
  1. 1.Institut für Entscheidungstheorie und UnternehmensforschungUniversität Karlsruhe (TH)KarlsruheGermany

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