IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v28y2001i6p673-689.html
   My bibliography  Save this article

Dynamic paired comparison models with stochastic variances

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760120059219
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664760120059219?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Douglas Critchlow & Michael Fligner, 1991. "Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation on GLIM," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 517-533, September.
    3. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
    4. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
    5. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    6. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: II. The effect of an aberrant standard deviation when equal standard deviations and equal correlations are assumed," Psychometrika, Springer;The Psychometric Society, vol. 16(2), pages 203-206, June.
    7. Harry Joe, 1990. "Extended Use of Paired Comparison Models, with Application to Chess Rankings," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(1), pages 85-93, March.
    8. Stern, Hal, 1992. "Are all linear paired comparison models empirically equivalent?," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 103-117, February.
    9. Frederick Mosteller, 1951. "Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations," Psychometrika, Springer;The Psychometric Society, vol. 16(1), pages 3-9, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.
    2. Baker, Rose D. & McHale, Ian G., 2017. "An empirical Bayes model for time-varying paired comparisons ratings: Who is the greatest women’s tennis player?," European Journal of Operational Research, Elsevier, vol. 258(1), pages 328-333.
    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.
    11. Devlin Stephen & Treloar Thomas & Creagar Molly & Cassels Samuel, 2021. "An iterative Markov rating method," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 117-127, June.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    2. 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.
    3. 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.
    4. Vincent Buskens & Jeroen Weesie, 2000. "An Experiment On The Effects Of Embeddedness In Trust Situations," Rationality and Society, , vol. 12(2), pages 227-253, May.
    5. Strickland, Chris M. & Martin, Gael M. & Forbes, Catherine S., 2008. "Parameterisation and efficient MCMC estimation of non-Gaussian state space models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2911-2930, February.
    6. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    7. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    8. Antonello Loddo & Shawn Ni & Dongchu Sun, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 342-355, July.
    9. Garland Durham, 2004. "Likelihood-based estimation and specification analysis of one- and two-factor SV models with leverage effects," Econometric Society 2004 North American Summer Meetings 294, Econometric Society.
    10. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    11. Pitt, M.K. & Walker, S.G., 2001. "Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models," The Warwick Economics Research Paper Series (TWERPS) 595, University of Warwick, Department of Economics.
    12. Minchul Shin & Molin Zhong, 2020. "A New Approach to Identifying the Real Effects of Uncertainty Shocks," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 367-379, April.
    13. Lendie Follett & Heath Henderson, 2022. "A hybrid approach to targeting social assistance," Papers 2201.01356, arXiv.org.
    14. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    15. Centola, Damon & van de Rijt, Arnout, 2015. "Choosing your network: Social preferences in an online health community," Social Science & Medicine, Elsevier, vol. 125(C), pages 19-31.
    16. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    17. Liesenfeld, Roman & Richard, Jean-François, 2008. "Improving MCMC, using efficient importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 272-288, December.
    18. Csató, László, 2013. "Rangsorolás páros összehasonlításokkal. Kiegészítések a felvételizői preferencia-sorrendek módszertanához [Paired comparisons ranking. A supplement to the methodology of application-based preferenc," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1333-1353.
    19. Junji Shimada & Yoshihiko Tsukuda, 2004. "Estimation of Stochastic Volatility Models : An Approximation to the Nonlinear State Space," Econometric Society 2004 Far Eastern Meetings 611, Econometric Society.
    20. Osei, Prince P. & Davidov, Ori, 2022. "Bayesian linear models for cardinal paired comparison data," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:28:y:2001:i:6:p:673-689. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.