29.6 Coarsened Exact Matching

Steps from Gray King’s slides International Methods Colloquium talk 2015

  • Temporarily coarsen \(X\)

  • Apply exact matching to the coarsened \(X, C(X)\)

    • sort observation into strata, each with unique values of \(C(X)\)

    • prune stratum with 0 treated or 0 control units

  • Pass on original (uncoarsened) units except those pruned

Properties:

  • Monotonic imbalance bounding (MIB) matching method

    • maximum imbalance between the treated and control chosen ex ante

  • meets congruence principle

  • robust to measurement error

  • can be implemented with multiple imputation

  • works well for multi-category treatments

Assumptions:

  • Ignorability (i.e., no omitted variable bias)

More detail in (Iacus, King, and Porro 2012)

Example by package’s authors

library(cem)
data(LeLonde)

Le <- data.frame(na.omit(LeLonde)) # remove missing data
# treated and control groups
tr <- which(Le$treated==1)
ct <- which(Le$treated==0)
ntr <- length(tr)
nct <- length(ct)

# unadjusted, biased difference in means
mean(Le$re78[tr]) - mean(Le$re78[ct])
#> [1] 759.0479

# pre-treatment covariates
vars <-
    c(
        "age",
        "education",
        "black",
        "married",
        "nodegree",
        "re74",
        "re75",
        "hispanic",
        "u74",
        "u75",
        "q1"
    )

# overall imbalance statistics
imbalance(group=Le$treated, data=Le[vars]) # L1 = 0.902
#> 
#> Multivariate Imbalance Measure: L1=0.902
#> Percentage of local common support: LCS=5.8%
#> 
#> Univariate Imbalance Measures:
#> 
#>               statistic   type           L1 min 25%      50%       75%
#> age        -0.252373042 (diff) 5.102041e-03   0   0   0.0000   -1.0000
#> education   0.153634710 (diff) 8.463851e-02   1   0   1.0000    1.0000
#> black      -0.010322734 (diff) 1.032273e-02   0   0   0.0000    0.0000
#> married    -0.009551495 (diff) 9.551495e-03   0   0   0.0000    0.0000
#> nodegree   -0.081217371 (diff) 8.121737e-02   0  -1   0.0000    0.0000
#> re74      -18.160446880 (diff) 5.551115e-17   0   0 284.0715  806.3452
#> re75      101.501761679 (diff) 5.551115e-17   0   0 485.6310 1238.4114
#> hispanic   -0.010144756 (diff) 1.014476e-02   0   0   0.0000    0.0000
#> u74        -0.045582186 (diff) 4.558219e-02   0   0   0.0000    0.0000
#> u75        -0.065555292 (diff) 6.555529e-02   0   0   0.0000    0.0000
#> q1          7.494021189 (Chi2) 1.067078e-01  NA  NA       NA        NA
#>                  max
#> age          -6.0000
#> education     1.0000
#> black         0.0000
#> married       0.0000
#> nodegree      0.0000
#> re74      -2139.0195
#> re75        490.3945
#> hispanic      0.0000
#> u74           0.0000
#> u75           0.0000
#> q1                NA

# drop other variables that are not pre - treatmentt matching variables
todrop <- c("treated", "re78")
imbalance(group=Le$treated, data=Le, drop=todrop)
#> 
#> Multivariate Imbalance Measure: L1=0.902
#> Percentage of local common support: LCS=5.8%
#> 
#> Univariate Imbalance Measures:
#> 
#>               statistic   type           L1 min 25%      50%       75%
#> age        -0.252373042 (diff) 5.102041e-03   0   0   0.0000   -1.0000
#> education   0.153634710 (diff) 8.463851e-02   1   0   1.0000    1.0000
#> black      -0.010322734 (diff) 1.032273e-02   0   0   0.0000    0.0000
#> married    -0.009551495 (diff) 9.551495e-03   0   0   0.0000    0.0000
#> nodegree   -0.081217371 (diff) 8.121737e-02   0  -1   0.0000    0.0000
#> re74      -18.160446880 (diff) 5.551115e-17   0   0 284.0715  806.3452
#> re75      101.501761679 (diff) 5.551115e-17   0   0 485.6310 1238.4114
#> hispanic   -0.010144756 (diff) 1.014476e-02   0   0   0.0000    0.0000
#> u74        -0.045582186 (diff) 4.558219e-02   0   0   0.0000    0.0000
#> u75        -0.065555292 (diff) 6.555529e-02   0   0   0.0000    0.0000
#> q1          7.494021189 (Chi2) 1.067078e-01  NA  NA       NA        NA
#>                  max
#> age          -6.0000
#> education     1.0000
#> black         0.0000
#> married       0.0000
#> nodegree      0.0000
#> re74      -2139.0195
#> re75        490.3945
#> hispanic      0.0000
#> u74           0.0000
#> u75           0.0000
#> q1                NA

automated coarsening

mat <-
    cem(
        treatment = "treated",
        data = Le,
        drop = "re78",
        keep.all = TRUE
    )
#> 
#> Using 'treated'='1' as baseline group
mat
#>            G0  G1
#> All       392 258
#> Matched    95  84
#> Unmatched 297 174

# mat$w

coarsening by explicit user choice

# categorial variables
levels(Le$q1) # grouping option
#> [1] "agree"             "disagree"          "neutral"          
#> [4] "no opinion"        "strongly agree"    "strongly disagree"
q1.grp <-
    list(
        c("strongly agree", "agree"),
        c("neutral", "no opinion"),
        c("strongly disagree", "disagree")
    ) # if you want ordered categories

# continuous variables
table(Le$education)
#> 
#>   3   4   5   6   7   8   9  10  11  12  13  14  15 
#>   1   5   4   6  12  55 106 146 173 113  19   9   1
educut <- c(0, 6.5, 8.5, 12.5, 17)  # use cutpoints

mat1 <-
    cem(
        treatment = "treated",
        data = Le,
        drop = "re78",
        cutpoints = list(education = educut),
        grouping = list(q1 = q1.grp)
    )
#> 
#> Using 'treated'='1' as baseline group
mat1
#>            G0  G1
#> All       392 258
#> Matched   158 115
#> Unmatched 234 143

  • Can also use progressive coarsening method to control the number of matches.

  • cem can also handle some missingness.

References

Iacus, Stefano M, Gary King, and Giuseppe Porro. 2012. “Causal Inference Without Balance Checking: Coarsened Exact Matching.” Political Analysis 20 (1): 1–24.