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Confidence intervals for rank statistics: Somers' D and extensions


  • Newson, Roger


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 DYX as a measure of the effect of X on Y , or we may estimate DXY as a performance indicator of X as a predictor of Y. The somersd package allows the estimation of Somers’ D and Kendall’s τα 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.

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  • Newson, Roger, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 1-26.
  • Handle: RePEc:ags:stataj:117583

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    References listed on IDEAS

    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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    1. 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.
    2. Orth, Walter, 2012. "The predictive accuracy of credit ratings: Measurement and statistical inference," International Journal of Forecasting, Elsevier, vol. 28(1), pages 288-296.
    3. Roger Newson, 2009. "Homoskedastic adjustment inflation factors in model selection," United Kingdom Stata Users' Group Meetings 2009 15, Stata Users Group.
    4. 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.
    5. Roger Newson, 2016. "The role of Somers's D in propensity modeling," United Kingdom Stata Users' Group Meetings 2016 01, Stata Users Group.
    6. Peter, Eckley, 2015. "Measuring economic uncertainty using news-media textual data," MPRA Paper 64874, University Library of Munich, Germany, revised 01 May 2015.
    7. 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.
    8. Roger Newson, 2006. "On the central role of Somers' D," United Kingdom Stata Users' Group Meetings 2006 01, Stata Users Group.
    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. Newson, Roger B., 2013. "Attributable and unattributable risks and fractions and other scenario comparisons," Stata Journal, StataCorp LP, vol. 0(Number 4), pages 1-29.
    12. Daniel Marszalec, 2016. "Auctions For Complements –An Experimental Analysis," CIRJE F-Series CIRJE-F-1018, CIRJE, Faculty of Economics, University of Tokyo.
    13. 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.
    14. Hanna Karolina Szymborska, 2018. "Household wealth structures and position in the income distribution – econometric analysis for the USA, 1989-2013," Working Papers PKWP1806, Post Keynesian Economics Society (PKES).
    15. Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928,, revised Mar 2010.
    16. Newson, Roger, 2006. "Confidence intervals for rank statistics: Percentile slopes, differences, and ratios," Stata Journal, StataCorp LP, vol. 0(Number 4), pages 1-24.
    17. 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.
    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. 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.
    20. Roger Newson, 2015. "Somers' D: A common currency for associations," United Kingdom Stata Users' Group Meetings 2015 01, Stata Users Group.
    21. Cogneau, Philippe & Hübner, Georges, 2015. "The prediction of fund failure through performance diagnostics," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 224-241.

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