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Confidence intervals for rank statistics: Somers' D and extensions

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  • Roger Newson

    () (Imperial College London)

Abstract

Somers' D is an asymmetric measure of association between two variables, which plays a central role as a parameter behind rank or nonparametric statistical methods. Given predictor variable X and outcome variable Y, we may estimate D(YX) as a measure of the effect of X on Y, or we may estimate D(XY) as a performance indicator of X as a predictor of Y. The somersd package allows the estimation of Somers’ D and Kendall’s tau-a with confidence limits as well as p-values. The Stata 9 version of somersd can estimate extended versions of Somers' D not previously available, including the Gini index, the parameter tested by the sign test, and extensions to left- or right-censored data. It can also estimate stratified versions of Somers' D, restricted to pairs in the same stratum. Therefore, it is possible to define strata by grouping values of a confounder, or of a propensity score based on multiple confounders, and to estimate versions of Somers' D that measure the association between the outcome and the predictor, adjusted for the confounders. The Stata 9 version of somersd uses the Mata language for improved computational efficiency with large datasets. Copyright 2006 by StataCorp LP.

Suggested Citation

  • Roger Newson, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 309-334, September.
  • Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:309-334
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    References listed on IDEAS

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    1. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    2. Roger Newson, 2001. "somersd-Confidence intervals for nonparametric statistics and their differences," Stata Technical Bulletin, StataCorp LP, vol. 10(55).
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    Cited by:

    1. Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928, arXiv.org, revised Mar 2010.
    2. Martin Rezac & Frantisek Rezac, 2011. "How to Measure the Quality of Credit Scoring Models," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 61(5), pages 486-507, November.
    3. Roger Newson, 2006. "Confidence intervals for rank statistics: Percentile slopes, differences, and ratios," Stata Journal, StataCorp LP, vol. 6(4), pages 497-520, December.
    4. Orth, Walter, 2010. "The predictive accuracy of credit ratings: Measurement and statistical inference," MPRA Paper 30148, University Library of Munich, Germany, revised 16 Feb 2011.
    5. Diego Rios-Zertuche & Jose Cuchilla & Paola Zúñiga-Brenes & Bernardo Hernández & Patricia Jara & Ali H. Mokdad & Emma Iriarte, 2017. "Alcohol abuse and other factors associated with risky sexual behaviors among adolescent students from the poorest areas in Costa Rica," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 62(2), pages 271-282, March.
    6. Cogneau, Philippe & Hübner, Georges, 2015. "The prediction of fund failure through performance diagnostics," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 224-241.
    7. Roger Newson, 2016. "The role of Somers's D in propensity modeling," United Kingdom Stata Users' Group Meetings 2016 01, Stata Users Group.
    8. Daniel Marszalec, 2016. "Auctions For Complements –An Experimental Analysis," CIRJE F-Series CIRJE-F-1018, CIRJE, Faculty of Economics, University of Tokyo.
    9. Graevenitz, Georg von & Weber, Richard, 2011. "How to Educate Entrepreneurs?," Discussion Papers in Business Administration 12280, University of Munich, Munich School of Management.
    10. Ahdesmäki Miika & Lancashire Lee & Proutski Vitali & Wilson Claire & Davison Timothy S. & Harkin D. Paul & Kennedy Richard D., 2013. "Model selection for prognostic time-to-event gene signature discovery with applications in early breast cancer data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(5), pages 619-635, October.
    11. Löschel, Andreas & Sturm, Bodo & Uehleke, Reinhard, 2013. "Revealed preferences for climate protection when the purely individual perspective is relaxed: Evidence from a framed field experiment," ZEW Discussion Papers 13-006, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    12. Alena MINÃ ROVÃ, 2012. "Evaluation Of Dependence Of Occurrence Of Risk Events In Logistics On Risk Factors By Means Of Somers' D Coefficient," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 7(1(19)/ Sp), pages 73-86.
    13. Roger Newson, 2009. "Homoskedastic adjustment inflation factors in model selection," United Kingdom Stata Users' Group Meetings 2009 15, Stata Users Group.
    14. Peter, Eckley, 2015. "Measuring economic uncertainty using news-media textual data," MPRA Paper 64874, University Library of Munich, Germany, revised 01 May 2015.
    15. Orth, Walter, 2012. "The predictive accuracy of credit ratings: Measurement and statistical inference," International Journal of Forecasting, Elsevier, vol. 28(1), pages 288-296.
    16. Löschel, Andreas & Sturm, Bodo & Uehleke, Reinhard, 2017. "Revealed preferences for voluntary climate change mitigation when the purely individual perspective is relaxed – evidence from a framed field experiment," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 67(C), pages 149-160.
    17. Roger Newson, 2006. "On the central role of Somers' D," United Kingdom Stata Users' Group Meetings 2006 01, Stata Users Group.
    18. Roger Newson, 2014. "Easy-to-use packages for estimating rank and spline parameters," United Kingdom Stata Users' Group Meetings 2014 01, Stata Users Group.
    19. Roger Newson, 2015. "Somers' D: A common currency for associations," United Kingdom Stata Users' Group Meetings 2015 01, Stata Users Group.

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