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Confidence intervals for rank statistics: Somers' D and extensions

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Author Info

  • 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.

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Bibliographic Info

Article provided by StataCorp LP in its journal Stata Journal.

Volume (Year): 6 (2006)
Issue (Month): 3 (September)
Pages: 309-334

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Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:309-334

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Related research

Keywords: somersd; Somers' D; Kendall’s tau-a ; Harrell’s c; ROC area; Gini index; population-attributable risk; rank correlation; rank-sum test; Wilcoxon test; sign test; confidence intervals; nonparametric methods; propensity score;

References

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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. 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.
  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. Graevenitz, Georg von & Weber, Richard, 2011. "How to Educate Entrepreneurs?," Discussion Papers in Business Administration 12440, University of Munich, Munich School of Management.
  4. 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.
  5. Roger Newson, 2009. "Homoskedastic adjustment inflation factors in model selection," United Kingdom Stata Users' Group Meetings 2009 15, Stata Users Group.

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