Skip to main content

Preference Modeling

  • Chapter
  • First Online:
Modern Psychometrics with R

Part of the book series: Use R! ((USE R))

  • 5751 Accesses

Abstract

This chapter focuses on modeling particular types of input data: ratings, rankings, and paired comparisons. It begins with elaborations on the classical Bradley-Terry model for paired comparisons of objects. Each object gets a parameter on an underlying continuum. Subsequently, the Bradley-Terry model is extended in terms of incorporating predictors. Two modern approaches are considered: recursive partitioning trees and lasso. The second part of the chapter deals with log-linear model formulations for preference data. So called pattern models are introduced, and versions for ratings, rankings, and paired comparisons are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Note that there is a strong connection between the BT model and the Rasch model from Sect. 4.2.1. In fact, it can be shown that the Rasch model in its multiplicative form is a special case of the BT model.

  2. 2.

    An easy-to-read introduction to CV can be found in James et al. (2013).

References

  • Aizaki, H., Nakatami, T., & Sato, K. (2015). Stated preference methods using R. Boca Raton: CRC Press.

    Google Scholar 

  • Bak, A., & Bartlomowicz, T. (2012). Conjoint analysis method and its implementation in conjoint R package. In: J. Pociecha & R. Decker (Eds.), Data analysis methods and its applications (pp. 239–248). Warsaw: Beck.

    Google Scholar 

  • Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs I: The method of paired comparisons. Biometrika, 39, 324–345.

    MathSciNet  MATH  Google Scholar 

  • Dabic, M., & Hatzinger, R. (2009). Zielgruppenadäquate Abläufe in Konfigurationssystemen: Eine empirische Studie im Automobilmarkt – Partial Rankings [Targeted processes in configuration systems: An empirical study on the car market – Partial rankings]. In R. Hatzinger, R. Dittrich, & T. Salzberger (Eds.), Präferenzanalyse mit R : Anwendungen aus Marketing, Behavioural Finance und Human Resource Management [Analysis of preferences with R : Applications in marketing, behavioral finance and human resource management] (pp. 119–150). Vienna: Facultas.

    Google Scholar 

  • Dittrich, R., Hatzinger, R., & Katzenbeisser, W. (1998). Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47, 511–525.

    Article  Google Scholar 

  • Dittrich, R., Hatzinger, R., & Katzenbeisser, W. (2002). Modelling dependencies in paired comparison experiments. Computational Statistics & Data Analysis, 40, 39–57.

    Article  MathSciNet  Google Scholar 

  • Grand, A., & Dittrich, R. (2015). Modelling assumed metric paired comparison data – Application to learning related emotions. Austrian Journal of Statistics, 44, 3–15.

    Article  Google Scholar 

  • Hatzinger, R., & Dittrich, R. (2012). prefmod: An R package for modeling preferences based on paired comparisons, rankings, or ratings. Journal of Statistical Software, 48(10), 1–31. https://www.jstatsoft.org/v048/i10

    Article  Google Scholar 

  • James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning with applications in R. New York: Springer.

    Book  Google Scholar 

  • Krantz, D. H., & Tversky, A. (1971). Conjoint measurement analysis of composition rules in psychology. Psychological Review, 78, 151–169.

    Article  Google Scholar 

  • Louviere, J. J., Flynn, T. N., & Carson, R. T. (2010). Discrete choice experiments are not conjoint analysis. Journal of Choice Modelling, 3, 57–72.

    Article  Google Scholar 

  • Luce, R. D., & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new scale type of fundamental measurement. Journal of Mathematical Psychology, 1, 1–27.

    Article  Google Scholar 

  • Sarrias, M. (2016). Discrete choice models with random parameters in R: The Rchoice package. Journal of Statistical Software, 74(10), 1–31. https://www.jstatsoft.org/v074/i10

    Article  Google Scholar 

  • Schauberger, G. (2017). BTLLasso: Modelling heterogeneity in paired comparison data. R package version 0.1-7. https://CRAN.R-project.org/package=BTLLasso

  • Schauberger, G., & Tutz, G. (2017). Subject-specific modelling of paired comparison data: A lasso-type penalty approach. Statistical Modelling, 17, 223–243.

    Article  MathSciNet  Google Scholar 

  • Strobl, C., Wickelmaier, F., & Zeileis, A. (2011). Accounting for individual differences in Bradley-Terry models by means of recursive partitioning. Journal of Educational and Behavioral Statistics, 36, 135–153.

    Article  Google Scholar 

  • Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.

    Article  Google Scholar 

  • Turner, H., & Firth, D. (2012). Bradley-terry models in R: The BradleyTerry2 package. Journal of Statistical Software, 48(9), 1–21. http://www.jstatsoft.org/v48/i09/

    Article  Google Scholar 

  • Zeileis, A., Hothorn, T., & Hornik, K. (2008). Model-based recursive partitioning. Journal of Computational and Graphical Statistics, 17, 492–514.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mair, P. (2018). Preference Modeling. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_5

Download citation

Publish with us

Policies and ethics