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

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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.

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References

  • Akaike, H. (1977): On Entropy Maximization Principle. In: P. R. Krishnaiah (ed.): Applications of Statistics. North Holland, Amsterdam, 27–41.

    Google Scholar 

  • Baier, D. (1994): Konzipierung und Realisierung einer Unterstützung des kombinierten Einsatzes von Methoden bei der Positionierungsanalyse. Lang, Frankfurt.

    Google Scholar 

  • 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 

  • Bock, H.-H. (1995): Probabilistic Models in Cluster Analysis. Computational Statistics and Data Analysis (accepted).

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Bozdogan, H. (1987): Model Selection and Akaike’s Information Criterion: The General Theory and Its Analytical Extensions. Psychometrika, 52, 345–370.

    Article  Google Scholar 

  • 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 

  • Bryant, P.G., and Williamson, J.A. (1978): The Asymptotic Behavior of Classification Maximum Likelihood Estimates. Biometrika, 65, 273–281.

    Article  Google Scholar 

  • 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 

  • Carroll, J.D., and Arabie, P. (1980): Multidimensional Scaling. Annual Review of Psychology, 31, 607–649.

    Article  Google Scholar 

  • Cooper, L. G., and Nakanishi, N. (1983): Two Logit Models for External Analysis of Preferences. Psychometrika, 48, 607–620.

    Article  Google Scholar 

  • David, H.A. (1988): The Method of Paired Comparisons. Griffin, London.

    Google Scholar 

  • Desarbo, W.S., Wedel, M., Vriens, M., and Ramaswamy, V. (1992): Latent Class Metric Conjoint Analysis. Marketing Letters, 3, 273–288.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gaul, W. (1978): Zur Methode der paarweisen Vergleiche und ihrer Anwendung im Marketingbereich. Methods of Operations Research, 35, 123–139.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Gaul, W., and Baier, D. (1994): Marktforschung und Marketing Management, 2nd edition. Oldenbourg, München.

    Google Scholar 

  • Gaul, W., and Schader, M. (1988): Clusterwise Aggregation of Relations. Applied Stochastic Models and Data Analysis, 4, 273–282.

    Article  Google Scholar 

  • 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 

  • De Soete, G., and Carroll, J.D. (1983): A Maximum Likelihood Method for Fitting the Wandering Vector Model. Psychometrika, 48, 553–566.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Windham, M. P. (1987): Parameter Modification for Clustering Criteria. Journal of Classification, 4, 191–214.

    Article  Google Scholar 

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© 1996 Springer-Verlag Berlin · Heidelberg

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Baier, D., Gaul, W. (1996). Analyzing Paired Comparisons Data Using Probabilistic Ideal Point Models and Probabilistic Vector Models. In: Bock, HH., Polasek, W. (eds) Data Analysis and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80098-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-80098-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60774-8

  • Online ISBN: 978-3-642-80098-6

  • eBook Packages: Springer Book Archive

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