Hierarchical models for permutations: Analysis of auto racing results

Journal of the American Statistical Association

Volumn 98, Issue 462, 2003, Pages 282-291

  Graves, Todd ^a   Reese, C Shane ^b   Fitzgerald, Mark ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b BRIGHAM YOUNG UNIVERSITY   (United States)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

Bayesian hierarchical models; Bradley Terry model; Markov chain Monte Carlo

Indexed keywords

EID: 0042744739     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214503000053     Document Type: Article

References (24)

1. Berry, S. M., Reese. C. S., and Larkey, P. L. (1999), "Bridging Different Eras in Sports" (with discussion), Journal of the American Statistical Association, 94, 661-686.
2. Bradley, R. A., and Terry, M. E. (1952), "Rank Analysis of Incomplete Block Designs, I: The Method of Paired Comparisons," Biometrika, 39, 324-345.
3. Bradlow, E. T., and Fader, P. S. (2001), "A Bayesian Lifetime Model for the 'Hot 100' Billboard Songs," Journal of the American Statistical Association, 96, 368-381.
4. Breslow, N. E. (1984), "Extra-Poisson Variation in Log-Linear Models," Applied Statistics, 33, 38-44.
5. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
6. Clayton, D. G. (1994), "Bayesian Analysis of Frailty Models," Technical Report, Cambridge Medical Research Council, p. 22.
7. Draper, D., Gaver, D. P., Goel, P. K., Greenhouse, J. B., Hedges, L. V., Morris, C. N., Tucker, J. R., and Watemaux, C. M. (1992), "Combining Information: Statistical Issues and Opportunities for Research," in Contemporary Statistics, Vol. 1. eds. D. Cochran and J. Farrally, Washington, DC: National Academy Press, pp. 109-180.
8. Fleischman, B. and Pearce, A. (1999), The Unauthorized NASCAR Fan Guide, Detroit: Visible Ink Press.
9. Graves, T. L. (2001), "Yadas: An Object-Oriented Framework for Data Analysis Using Markov Chain Monte Carlo," Technical Report LA-UR-01-4804, Los Alamos National Laboratory.
10. Hastings, W. K. (1970), "Monte Carlo Sampling Methods Using Markov Chains and Their Applications," Biometrika, 57, 97-109.
11. Johnson, V. E., Deaner, R. O., and van Schaik, C. P. (2002), "Bayesian Analysis of Multi-Study Rank Data With Application to Primate Intelligence Ratings," Journal of the American Statistical Association.
12. Kass, R. E. and Raftery, A. E. (1995), "Bayes Factors," Journal of the American Statistical Association, 90, 773-795.
13. Luce, R. D. (1959), Individual Choice Behavior, New York: John Wiley.
14. Marden, J. I. (1995), Analyzing and Modeling Rank Data, London: Chapman & Hall.
15. Martin, M. (2000), NASCAR for Dummies, Foster City, CA: IDG Books Worldwide.
16. Meng, X. L., and Wong, W. H. (1996), "Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration." Statistica Sinica, 6, 831-860.
17. Mockus, A., Hibino, S. L., and Graves, T. L. (2000), "A Web-Based Approach to Interactive Visualization in Context," in Advanced Visual Interfaces 2000 Conference Proceedings, Palermo, Italy: ACM Press, pp. 181-188.
18. Plackett, R. L. (1975), "The Analysis of Permutations," Applied Statistics, 24, 193-202.
19. Raftery, A. E. and Lewis, S. M. (1996), "Implementing MCMC," in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, London: Chapman & Hall, pp. 115-130.
20. Spiegelhalter, D., Thomas, A., Best, N., and Gilks, W. (1999), BUGS Examples, available at http://www.mrc-bsu.cam.ac.uk/bugs/documentation/exampVoll/bugs.html.
21. Stem, H. (1990), "Models for Distributions on Permutations," Journal of the American Statistical Association, 85, 558-564.
22. Sullivan, T. S. (2000), "Not Just Around in Circles: A Statistical Analysis of NASCAR Winston Cup Racing," Working Paper 00-0904, Southern Illinois University Edwardsville, Dept. of Economics.
23. Tenebein, A. (1971), "The Racing Car Problem," The American Statistician, 25, 38-40.
24. Yu, P. L. H., and Lam, K. (1996), "Analysis of Duplicate Bridge Tournament Data," Scandinavian Journal of Statistics. 23, 621-633.