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Matching Without Groups

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Design of Observational Studies

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

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Abstract

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.

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Notes

  1. 1.

    Fortran code by Derigs [11] has been made available inside R by Bo Lu et al. [24] through a function nonbimatch( n,d) , where d is the vector form of an n×n symmetric matrix of nonnegative integer distances.

    >dm

        1   2   3   4   5   6

    1   0 106 119 231 110 101

    2 106   0 207 126 192  68

    3 119 207   0 156 247  25

    4 231 126 156   0  34  67

    5 110 192 247  34   0 212

    6 101  68  25  67 212   0

    >nonbimatch( 6,as.vector( dm) )

    [1] 2 1 6 5 4 3

    This says that unit 1 is paired with unit 2, unit 2 is paired with unit 1, unit 3 is paired with unit 6, unit 4 is paired with unit 5, unit 5 is paired with unit 4, and unit 6 is paired with unit 3.

  2. 2.

    Card and Krueger’s [4, 5] data are at Princeton University’s Industrial Relations Section webpage http://www.irs.princeton.edu . Restaurants were interviewed twice, once in February 1992, before New Jersey increased its minimum wage, and once in November 1992, after New Jersey increased its minimum wage. Card and Krueger define full-time-equivalent employment as the number of managers plus the number of full-time employees plus half the number of part-time employees, which is NMGRS+EMPFT+EMPPT/2 in their first interview and NMGRS2+EMPFT2+EMPPT2/2 in the second, and the change in employment is the difference between these two quantities, November−minus−February. The price of a full meal refers to the sum of the price of a soda, fries, and an entree, or PSODA+PFRY+PENTREE in the first interview and PSODA2+PFRY2+PENTREE2 in the second, and the change in price is the difference of these two quantities. The starting wage before the increase in the minimum wage is WAGE_ST from the first interview. Other variables used are the restaurant chain (CHAIN), whether the restaurant was company owned (CO_OWNED), and hours open (HRSOPEN). There are 410 restaurants, but the analysis here uses the 351 restaurants with complete data on employment and starting wage. The variable SHEET is Card and Krueger’s identification number for a restaurant.

  3. 3.

    As it turned out, the discarded restaurant was a company owned Pennsylvania KFC open 10 h per day and paying a starting wage before the increase of $5.25. It was Sheet #481.

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  1. Statistics Department, Wharton School, University of Pennsylvania, Philadelphia, PA, USA

    Paul R. Rosenbaum

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R. Rosenbaum, P. (2020). Matching Without Groups. In: Design of Observational Studies. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-46405-9_12

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