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The Bradley–Terry Regression Trunk approach for Modeling Preference Data with Small Trees

Author

Listed:
  • Alessio Baldassarre

    (University of Cagliari)

  • Elise Dusseldorp

    (Leiden University)

  • Antonio D’Ambrosio

    (University of Naples Federico II)

  • Mark de Rooij

    (Leiden University)

  • Claudio Conversano

    (University of Cagliari)

Abstract

This paper introduces the Bradley–Terry regression trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the preferences expressed by individuals depend on their characteristics. Within the framework of tree-based partitioning, we specify a tree-based model estimating the joint effects of subject-specific covariates over and above their main effects. We, therefore, combine a tree-based model and the log-linear Bradley-Terry model using the outcome of the comparisons as response variable. The proposed model provides a solution to discover interaction effects when no a-priori hypotheses are available. It produces a small tree, called trunk, that represents a fair compromise between a simple interpretation of the interaction effects and an easy to read partition of judges based on their characteristics and the preferences they have expressed. We present an application on a real dataset following two different approaches, and a simulation study to test the model’s performance. Simulations showed that the quality of the model performance increases when the number of rankings and objects increases. In addition, the performance is considerably amplified when the judges’ characteristics have a high impact on their choices.

Suggested Citation

  • Alessio Baldassarre & Elise Dusseldorp & Antonio D’Ambrosio & Mark de Rooij & Claudio Conversano, 2023. "The Bradley–Terry Regression Trunk approach for Modeling Preference Data with Small Trees," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1443-1465, December.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:4:d:10.1007_s11336-022-09882-6
    DOI: 10.1007/s11336-022-09882-6
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    References listed on IDEAS

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    1. Lee, Paul H. & Yu, Philip L.H., 2010. "Distance-based tree models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1672-1682, June.
    2. Antonio D’Ambrosio & Willem J. Heiser, 2016. "A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 774-794, September.
    3. Claudio Conversano & Elise Dusseldorp, 2017. "Modeling Threshold Interaction Effects Through the Logistic Classification Trunk," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 399-426, October.
    4. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    5. Hatzinger, Reinhold & Dittrich, Regina, 2012. "prefmod: An R Package for Modeling Preferences Based on Paired Comparisons, Rankings, or Ratings," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i10).
    6. Anders Skrondal & Sophia Rabe-Hesketh, 2003. "Multilevel logistic regression for polytomous data and rankings," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 267-287, June.
    7. Brian Francis & Regina Dittrich & Reinhold Hatzinger & Roger Penn, 2002. "Analysing partial ranks by using smoothed paired comparison methods: an investigation of value orientation in Europe," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 319-336, July.
    8. Elise Dusseldorp & Jacqueline Meulman, 2004. "The regression trunk approach to discover treatment covariate interaction," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 355-374, September.
    9. Turner, Heather & Firth, David, 2012. "Bradley-Terry Models in R: The BradleyTerry2 Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i09).
    10. Frank Busing & Patrick Groenen & Willem Heiser, 2005. "Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 71-98, March.
    11. Vicente Rodríguez Montequín & Joaquín Manuel Villanueva Balsera & Marina Díaz Piloñeta & César Álvarez Pérez, 2020. "A Bradley-Terry Model-Based Approach to Prioritize the Balance Scorecard Driving Factors: The Case Study of a Financial Software Factory," Mathematics, MDPI, vol. 8(2), pages 1-15, February.
    12. Amodio, S. & D’Ambrosio, A. & Siciliano, R., 2016. "Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 667-676.
    13. Carolin Strobl & Florian Wickelmaier & Achim Zeileis, 2011. "Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 135-153, April.
    14. Dittrich, Regina & Francis, Brian & Hatzinger, Reinhold & Katzenbeisser, Walter, 2006. "Modelling dependency in multivariate paired comparisons: A log-linear approach," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 197-209, September.
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