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Analysis of Ordinal Paired Comparison Data

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  • Alan Agresti

Abstract

Two types of model are discussed for paired comparisons of several treatments using ordinal scales such as (A B, A » B, A ⋙ B), where A ≪ B denotes strong preference for treatment B over treatment A, A ≪ B denotes moderate preference for B, A B), special cases of the models using logit transforms simplify to the Bradley‐Terry model. When the same raters compare each pair of treatments, one can allow within‐rater dependence by fitting the models with constrained maximum likelihood.

Suggested Citation

  • Alan Agresti, 1992. "Analysis of Ordinal Paired Comparison Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 287-297, June.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:2:p:287-297
    DOI: 10.2307/2347562
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    Cited by:

    1. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "A generalization of the Thurstone method for multiple choice and incomplete paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 133-159, March.
    2. Basak, Indrani, 2001. "The categorical data analysis approach for ratio model of pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 128(3), pages 532-544, February.
    3. Dittrich, R. & Hatzinger, R. & Katzenbeisser, W., 2002. "Modelling dependencies in paired comparison data: A log-linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 39-57, July.
    4. 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.
    5. Szczecinski Leszek, 2022. "G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 18(1), pages 1-14, March.
    6. Ulf Böckenholt & William Dillon, 1997. "Modeling within-subject dependencies in ordinal paired comparison data," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 411-434, September.
    7. Gunther Schauberger & Andreas Groll & Gerhard Tutz, 2018. "Analysis of the importance of on-field covariates in the German Bundesliga," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(9), pages 1561-1578, July.
    8. Martin Junge & Rainer Reisenzein, 2015. "Maximum Likelihood Difference Scaling versus Ordinal Difference Scaling of emotion intensity: a comparison," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 2169-2185, September.
    9. Maydeu-Olivares, Albert, 2002. "Limited information estimation and testing of Thurstonian models for preference data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 467-483, July.
    10. Alain De Beuckelaer & Jarl Kampen & J. Van Trijp, 2013. "An empirical assessment of the cross-national measurement validity of graded paired comparisons," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 1063-1076, February.
    11. 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.
    12. Gerhard Tutz & Gunther Schauberger, 2015. "Extended ordered paired comparison models with application to football data from German Bundesliga," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 209-227, April.
    13. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "Incomplete paired comparisons in case of multiple choice and general log-concave probability density functions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 515-532, June.

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