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Bayesian linear models for cardinal paired comparison data

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  • Osei, Prince P.
  • Davidov, Ori

Abstract

This paper develops a methodology for Bayesian updating in normal linear models in situations where the parameter of interest is restricted to a linear subspace. The methodology is motivated by and applied to the calculation of posterior distributions for the merit parameters and ranks arising in paired comparison data. The Bayesian paradigm is found to be ideal for assessing and quantifying the uncertainty in ranking procedures. The methodology is illustrated using simulated data and applied to two data sets: a network meta–analysis example and to the ranking of teams in the National Basketball Association (NBA).

Suggested Citation

  • Osei, Prince P. & Davidov, Ori, 2022. "Bayesian linear models for cardinal paired comparison data," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:csdana:v:172:y:2022:i:c:s0167947322000615
    DOI: 10.1016/j.csda.2022.107481
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    References listed on IDEAS

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    1. 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.
    2. Ori Davidov & Casey M. Jelsema & Shyamal Peddada, 2018. "Testing for Inequality Constraints in Singular Models by Trimming or Winsorizing the Variance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 906-918, April.
    3. Bhimasankaram, P. & Sengupta, D., 1991. "Testing for the mean vector of a multivariate normal distribution with a possibly singular dispersion matrix and related results," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 473-478, June.
    4. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
    5. Julio González-Díaz & Ruud Hendrickx & Edwin Lohmann, 2014. "Paired comparisons analysis: an axiomatic approach to ranking methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 139-169, January.
    6. 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.
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