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Empirical Bayes Ranking Methods

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  • Nan M. Laird
  • Thomas A. Louis

Abstract

Ranking problems arise in setting priorities for investigations, in providing a simple summary of performance, in comparing objects in a manner robust to measurement scale, and in a wide variety of other applications. Commonly, rankings are computed from measurements that depend on the true attribute. Using the Gaussian model, we propose and compare methods for using these measurements to estimate the ranks of the underlying attributes and show that those based on an empirical Bayes model produce estimates that differ from ranking observed data. These differences result both from the effect of shrinking posterior means towards a common value by an amount that depends on the precision of individual measurements and from the Bayes processing of the posterior distribution to produce estimates that account for the uncertainty in the distribution of the ranks. We illustrate different ranking methods using data on school achievement reported by Aitkin and Longford (1986) . Mathematical and empirical results highlight the importance of using appropriate ranking methods and identify issues requiring further research.

Suggested Citation

  • Nan M. Laird & Thomas A. Louis, 1989. "Empirical Bayes Ranking Methods," Journal of Educational and Behavioral Statistics, , vol. 14(1), pages 29-46, March.
  • Handle: RePEc:sae:jedbes:v:14:y:1989:i:1:p:29-46
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    Cited by:

    1. Daniel Bonnéry & Yang Cheng & Neung Soo Ha & Partha Lahiri, 2015. "Triple-goal estimation of unemployment rates for U.S. states using the U.S. Current Population Survey data," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 511-522, December.
    2. Nicholas T. Longford, 2004. "Missing data and small area estimation in the UK Labour Force Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(2), pages 341-373, May.
    3. Huilin Li & Barry I. Graubard & Mitchell H. Gail, 2010. "Covariate Adjustment and Ranking Methods to Identify Regions with High and Low Mortality Rates," Biometrics, The International Biometric Society, vol. 66(2), pages 613-620, June.
    4. Rubiana Chamarbagwala & Rusty Tchernis, 2006. "The Role of Social Norms in Child Labor and Schooling in India," CAEPR Working Papers 2006-016, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    5. Mahlet G. Tadesse & Joseph G. Ibrahim & Robert Gentleman & Sabina Chiaretti & Jerome Ritz & Robin Foa, 2005. "Bayesian Error-in-Variable Survival Model for the Analysis of GeneChip Arrays," Biometrics, The International Biometric Society, vol. 61(2), pages 488-497, June.
    6. Nicholas C. Henderson & Michael A. Newton, 2016. "Making the cut: improved ranking and selection for large-scale inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 781-804, September.

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    Keywords

    ranking and selection; empirical Bayes;

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