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Dynamic paired comparison models with stochastic variances

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  • Mark Glickman

Abstract

In paired comparison experiments, the worth or merit of a unit is measured through comparisons against other units. When paired comparison outcomes are collected over time and the merits of the units may be changing, it is often convenient to assume the data follow a non-linear state-space model. Typical paired comparison state-space models that assume a fixed (unknown) autoregressive variance do not account for the possibility of sudden changes in the merits. This is a particular concern, for example, in modeling cognitive ability in human development; cognitive ability not only changes over time, but also can change abruptly. We explore a particular extension of conventional state-space models for paired comparison data that allows the state variance to vary stochastically. Models of this type have recently been developed and applied to modeling financial data, but can be seen to have applicability in modeling paired comparison data. A filtering algorithm is also derived that can be used in place of likelihood-based computations when the number of objects being compared is large. Applications to National Football League game outcomes and chess game outcomes are presented.

Suggested Citation

  • Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:6:p:673-689
    DOI: 10.1080/02664760120059219
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    Cited by:

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    3. Alexandra Grand & Regina Dittrich & Brian Francis, 2015. "Markov models of dependence in longitudinal paired comparisons: an application to course design," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 237-257, April.
    4. Araki, Kenji & Hirose, Yoshihiro & Komaki, Fumiyasu, 2019. "Paired comparison models with age effects modeled as piecewise quadratic splines," International Journal of Forecasting, Elsevier, vol. 35(2), pages 733-740.
    5. Blaž Krese & Erik Štrumbelj, 2021. "A Bayesian approach to time-varying latent strengths in pairwise comparisons," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-17, May.
    6. Beaudoin, David & Swartz, Tim, 2018. "A computationally intensive ranking system for paired comparison data," Operations Research Perspectives, Elsevier, vol. 5(C), pages 105-112.
    7. Newton Paul K & Aslam Kamran, 2009. "Monte Carlo Tennis: A Stochastic Markov Chain Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-44, July.
    8. Maria Bolsinova & Gunter Maris & Abe D. Hofman & Han L. J. van der Maas & Matthieu J. S. Brinkhuis, 2022. "Urnings: A new method for tracking dynamically changing parameters in paired comparison systems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 91-118, January.
    9. Mitchell J. Lovett & Ron Shachar, 2011. "The Seeds of Negativity: Knowledge and Money," Marketing Science, INFORMS, vol. 30(3), pages 430-446, 05-06.
    10. Koopmeiners Joseph S., 2012. "A Comparison of the Autocorrelation and Variance of NFL Team Strengths Over Time using a Bayesian State-Space Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(3), pages 1-19, October.
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    12. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.

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