Matching Without Groups

Part of the Springer Series in Statistics book series (SSS)


Optimal matching without groups, or optimal nonbipartite matching, offers many additional options for matched designs in both observational studies and experiments. One starts with a square, symmetric distance matrix with one row and one column for each subject recording the distance between any two subjects. Then the subjects are divided into pairs to minimize the total distance within pairs. The method may be used to match with doses of treatment, or with multiple control groups, or as an aid to risk-set matching. An extended discussion of Card and Krueger’s study of the minimum wage is used to illustrate.


Propensity Score Minimum Wage Distance Matrix Statist Assoc Wage Increase 
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  1. Cahuc, P., Zylberberg, A.: Labor Economics. Cambridge, MA: MIT Press (2004)Google Scholar
  2. Card, D., Krueger, A.B.: Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. Am Econ Rev 84, 772–793 (1994)Google Scholar
  3. Card, D., Krueger, A.B.: Myth and Measurement: The New Economics of the Minimum Wage. Princeton, NJ: Princeton University Press (1995) Data:
  4. Cochran, W.G., Cox, G.M.: Experimental Designs. New York: Wiley (1957)MATHGoogle Scholar
  5. Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. New York: Wiley (1998)MATHGoogle Scholar
  6. Cook, W., Rohe, A. : Computing minimum-weight perfect matchings. INFORMS J Comput 11, 138–148 (1999) Software:
  7. Cox, D.R., Reid, N.: The Theory of the Design of Experiments. New York: Chapman and Hall/CRC (2000)MATHGoogle Scholar
  8. Daniel, S., Armstrong, K., Silber, J.H., Rosenbaum, P.R.: An algorithm for optimal tapered matching, with application to disparities in survival. J Comput Graph Statist 17, 914–924 (2008)CrossRefGoogle Scholar
  9. Derigs, U. : Solving nonbipartite matching problems by shortest path techniques. Ann Operat Res 13, 225–261 (1988)CrossRefMathSciNetGoogle Scholar
  10. Edmonds, J. : Matching and a polyhedron with 0–1 vertices. J Res Nat Bur Stand 65B, 125–130 (1965)MathSciNetGoogle Scholar
  11. Greevy, R., Lu, B., Silber, J.H., Rosenbaum, P.R.: Optimal matching before randomization. Biostatistics 5, 263–275 (2004)MATHCrossRefGoogle Scholar
  12. Hornik, R., Jacobsohn, L., Orwin, R., Piesse, A., Kalton, G.: Effects of the national youth anti-drug media campaign on youths. Am J Public Health 98, 2229–2236 (2008)CrossRefGoogle Scholar
  13. Imai, K., van Dyk, D.A. : Causal inference with general treatment regimes: generalizing the propensity score. J Am Statist Assoc 99, 854–866 (2004)MATHCrossRefGoogle Scholar
  14. Imbens, G.W. : The role of the propensity score in estimating dose-response functions. Biometrika 87, 706–710 (2000)MATHCrossRefMathSciNetGoogle Scholar
  15. Joffe, M.M., Rosenbaum, P.R.: Propensity scores. Am J Epidemiol 150, 327–333 (1999)Google Scholar
  16. Li, Y.F.P., Propert, K.J., Rosenbaum, P.R.: Balanced risk set matching. J Am Statist Assoc 96, 870–882 (2001)MATHCrossRefMathSciNetGoogle Scholar
  17. Lu, B., Zanutto, E., Hornik, R., Rosenbaum, P.R.: Matching with doses in an observational study of a media campaign against drug abuse. J Am Statist Assoc 96, 1245–1253 (2001)MATHCrossRefMathSciNetGoogle Scholar
  18. Lu, B., Rosenbaum, P.R.: Optimal matching with two control groups. J Comput Graph Statist 13, 422–434 (2004)CrossRefMathSciNetGoogle Scholar
  19. Lu, B.: Propensity score matching with time-dependent covariates. Biometrics 61, 721–728 (2005) Google Scholar
  20. Lu, B., Greevy, R., Xu, X., Beck, C.: Optimal nonbipartite matching and its statistical applications. Manuscript. (2009)Google Scholar
  21. Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice Hall (1982)MATHGoogle Scholar
  22. R Development Core Team.: R: A Language and Environment for Statistical Computing. Vienna: R Foundation, (2007)
  23. Rosenbaum, P.R.: An exact, distribution free test comparing two multivariate distributions based on adjacency. J Royal Statist Soc B 67, 515–530 (2005)MATHCrossRefMathSciNetGoogle Scholar
  24. Rosenbaum, P.R., Silber, J.H.: Sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units. J Am Statist Assoc 104, 501–511 (2009)CrossRefGoogle Scholar
  25. Silber, J.H., Lorch, S.L., Rosenbaum, P.R., Medoff-Cooper, B., Bakewell-Sachs, S., Millman, A., Mi, L., Even-Shoshan, O., Escobar, G.E. : Additional maturity at discharge and subsequent health care costs. Health Serv Res 44, 444–463 (2009)CrossRefGoogle Scholar
  26. Stigler, G.J. : The economics of minimum wage legislation. Am Econ Rev 36, 358–365 (1946)Google Scholar

Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Statistics Department Wharton SchoolUniversity of PennsylvaniaPhiladelphiaUSA

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