IDEAS home Printed from https://ideas.repec.org/p/boc/usug06/01.html
   My bibliography  Save this paper

On the central role of Somers' D

Author

Listed:
  • Roger Newson

    (National Heart and Lung Institute, Imperial College London)

Abstract

Somers' D and Kendall's tau-a are parameters behind rank or nonparametric statistics, interpreted as differences between proportions. Given two bivariate data pairs (X1, Y1) and (X2, Y2), Kendall’s tau-a parameter tau-XY is the difference between the probability that the two X–Y pairs are concordant and the probability that the two X–Y pairs are discordant, and Somers' D parameter DYX is the difference between the corresponding conditional probabilities, given that the X-values are ordered. The somersd package computes confidence intervals for both parameters. The Stata 9 version of somersd uses Mata to increase computing speed and greatly extends the definition of Somers' D, allowing the X and/or Y variables to be left- or right-censored and allowing multiple versions of Somers' D for multiple sampling schemes for the X–Y pairs. In particular, we may define stratified versions of Somers' D, in which we compare only X–Y pairs from the same stratum. The strata may be defined by grouping a Rubin–Rosenbaum propensity score, based on the values of multiple confounders for an association between exposure variable X and an outcome variable Y . Therefore, rank statistics can have not only confidence intervals but also confounder-adjusted confidence intervals. Usually, we either estimate DYX as a measure of the effect of X on Y , or we estimate DXY as a measure of the performance of X as a predictor of Y, compared with other predictors. Alternative rank-based measures of the effect of X on Y include the Hodges–Lehmann median difference and the Theil–Sen median slope, both of which are defined in terms of Somers' D.

Suggested Citation

  • Roger Newson, 2006. "On the central role of Somers' D," United Kingdom Stata Users' Group Meetings 2006 01, Stata Users Group.
  • Handle: RePEc:boc:usug06:01
    as

    Download full text from publisher

    File URL: http://repec.org/usug2006/newson_ohp1.pdf
    File Function: presentation slides
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roger Newson, 2006. "Confidence intervals for rank statistics: Somers' D and extensions," Stata Journal, StataCorp LP, vol. 6(3), pages 309-334, September.
    2. Roger Newson, 2002. "Parameters behind "nonparametric" statistics: Kendall's tau,Somers' D and median differences," Stata Journal, StataCorp LP, vol. 2(1), pages 45-64, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jeannette Brosig‐Koch & Heike Hennig‐Schmidt & Nadja Kairies‐Schwarz & Daniel Wiesen, 2017. "The Effects of Introducing Mixed Payment Systems for Physicians: Experimental Evidence," Health Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 243-262, February.
    2. 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 - Leibniz Centre for European Economic Research.
    3. Dirk Tasche, 2009. "Estimating discriminatory power and PD curves when the number of defaults is small," Papers 0905.3928, arXiv.org, revised Mar 2010.
    4. 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).
    5. 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.
    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. John, Katrin & Thomsen, Stephan L., 2015. "School-track environment or endowment: What determines different other-regarding behavior across peer groups?," Games and Economic Behavior, Elsevier, vol. 94(C), pages 122-141.
    8. Gala, Kaushik & Schwab, Andreas & Mueller, Brandon A., 2024. "Star entrepreneurs on digital platforms: Heavy-tailed performance distributions and their generative mechanisms," Journal of Business Venturing, Elsevier, vol. 39(1).
    9. Ichiro Kunitsugu & Masayuki Okuda & Shinichi Sugiyama & Norikazu Yoshitake & Yukio Tanizawa & Satoshi Sasaki & Tatsuya Hobara, 2012. "Meat intake frequency and anemia in Japanese children and adolescents," Nursing & Health Sciences, John Wiley & Sons, vol. 14(2), pages 197-203, June.
    10. Roger B. Newson, 2010. "Comparing the predictive powers of survival models using Harrell’s C or Somers’ D," Stata Journal, StataCorp LP, vol. 10(3), pages 339-358, September.
    11. Chakrabarty, Manisha & Hildenbrand, Werner, 2011. "Engel's Law Reconsidered," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 289-299.
    12. Guerra, Alice & Zhuravleva, Tatyana, 2021. "Do bystanders react to bribery?," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 442-462.
    13. Roger Newson, 2016. "The role of Somers's D in propensity modeling," United Kingdom Stata Users' Group Meetings 2016 01, Stata Users Group.
    14. Philipp Chapkovski & Luca Corazzini & Valeria Maggian, 2021. "Does Whistleblowing on Tax Evaders Reduce Ingroup Cooperation?," Working Papers 2021:20, Department of Economics, University of Venice "Ca' Foscari".
    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. Cingl, Lubomír & Lichard, Tomáš & Miklánek, Tomáš, 2023. "Tax designation effects on compliance: An online experiment with taxpayers," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 615-633.
    17. Lukasz Prorokowski, 2016. "Rank-order statistics for validating discriminative power of credit risk models," Bank i Kredyt, Narodowy Bank Polski, vol. 47(3), pages 227-250.
    18. Marszalec, Daniel, 2018. "Fear not the simplicity - An experimental analysis of auctions for complements," Journal of Economic Behavior & Organization, Elsevier, vol. 152(C), pages 81-97.
    19. Newson, Roger, 2005. "Efficient Calculation of Jackknife Confidence Intervals for Rank Statistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 15(i01).
    20. Navarro, Noemí & Veszteg, Róbert F., 2020. "On the empirical validity of axioms in unstructured bargaining," Games and Economic Behavior, Elsevier, vol. 121(C), pages 117-145.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:usug06:01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F Baum (email available below). General contact details of provider: https://edirc.repec.org/data/stataea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.