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Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses

Author

Listed:
  • Michel Denuit

    (Université Catholique de Louvain (UCL))

  • Mhamed Mesfioui

    (Université du Québec à Trois-Rivières)

  • Julien Trufin

    (Université Libre de Bruxelles (ULB))

Abstract

Association measures based on concordance, such as Kendall’s tau, Somers’ delta or Goodman and Kruskal’s gamma are often used to measure explained variations in regression models for binary outcomes. As responses only assume values in {0, 1}, these association measures are constrained, which makes their interpretation more difficult as a relatively small value may in fact strongly support the fitted model. In this paper, we derive the set of attainable values for concordance-based association measures in this setting so that the closeness to the best-possible fit can be properly assessed.

Suggested Citation

  • Michel Denuit & Mhamed Mesfioui & Julien Trufin, 2019. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 491-509, June.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:2:d:10.1007_s11009-017-9613-0
    DOI: 10.1007/s11009-017-9613-0
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    References listed on IDEAS

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    1. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    2. Neslehová, Johanna, 2007. "On rank correlation measures for non-continuous random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 544-567, March.
    3. Mesfioui, Mhamed & Quessy, Jean-François, 2010. "Concordance measures for multivariate non-continuous random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2398-2410, November.
    4. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    5. Tuhao Chen & Fred M. Hoppe & Satish Iyengar & David Brent, 2003. "A Hybrid Logistic Model for Case-Control Studies," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 419-426, December.
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