Fast Generalized Full Matching

In matchit(), setting method = "quick" performs generalized full matching, which is a form of subclassification wherein all units, both treatment and control (i.e., the "full" sample), are assigned to a subclass and receive at least one match. It uses an algorithm that is extremely fast compared to optimal full matching, which is why it is labeled as "quick", at the expense of true optimality. The method is described in Sävje, Higgins, & Sekhon (2021). The method relies on and is a wrapper for quickmatchquickmatch.

Advantages of generalized full matching include that the matching order is not required to be specified, units do not need to be discarded, and it is less likely that extreme within-subclass distances will be large, unlike with standard subclassification. The primary output of generalized full matching is a set of matching weights that can be applied to the matched sample; in this way, generalized full matching can be seen as a robust alternative to propensity score weighting, robust in the sense that the propensity score model does not need to be correct to estimate the treatment effect without bias.

This page details the allowable arguments with method = "quick". See matchit() for an explanation of what each argument means in a general context and how it can be specified.

Below is how matchit() is used for generalized full matching:


matchit(formula,
        data = NULL,
        method = "quick",
        distance = "glm",
        link = "logit",
        distance.options = list(),
        estimand = "ATT",
        exact = NULL,
        mahvars = NULL,
        discard = "none",
        reestimate = FALSE,
        s.weights = NULL,
        caliper = NULL,
        std.caliper = TRUE,
        verbose = FALSE,
        ...)

Arguments

formula

a two-sided formula object containing the treatment and covariates to be used in creating the distance measure used in the matching. This formula will be supplied to the functions that estimate the distance measure.

data

a data frame containing the variables named in formula. If not found in data, the variables will be sought in the environment.

method

set here to "quick".

distance

the distance measure to be used. See distance for allowable options. Cannot be supplied as a matrix.

link

when distance is specified as a method of estimating propensity scores, an additional argument controlling the link function used in estimating the distance measure. See distance for allowable options with each option.

distance.options

a named list containing additional arguments supplied to the function that estimates the distance measure as determined by the argument to distance.

estimand

a string containing the desired estimand. Allowable options include "ATT", "ATC", and "ATE". The estimand controls how the weights are computed; see the Computing Weights section at matchit() for details.

exact

for which variables exact matching should take place.

mahvars

for which variables Mahalanobis distance matching should take place when distance corresponds to a propensity score (e.g., to discard units for common support). If specified, the distance measure will not be used in matching.

discard

a string containing a method for discarding units outside a region of common support. Only allowed when distance corresponds to a propensity score.

reestimate

if discard is not "none", whether to re-estimate the propensity score in the remaining sample prior to matching.

s.weights

the variable containing sampling weights to be incorporated into propensity score models and balance statistics.

caliper

the width of the caliper used for caliper matching. A caliper can only be placed on the propensity score.

std.caliper

logical; when a caliper is specified, whether it is in standard deviation units (TRUE) or raw units (FALSE).

verbose

logical; whether information about the matching process should be printed to the console.

...

additional arguments passed to quickmatchquickmatch. Allowed arguments include treatment_constraints, size_constraint, target, and other arguments passed to scclust::sc_clustering() (see quickmatchquickmatch for details). In particular, changing seed_method from its default can improve performance. No arguments will be passed to distances::distances().

The arguments replace, ratio, min.controls, max.controls, m.order, and antiexact are ignored with a warning.

Details

Generalized full matching is similar to optimal full matching, but has some additional flexibility that can be controlled by some of the extra arguments available. By default, method = "quick" performs a standard full match in which all units are matched (unless restricted by the caliper) and assigned to a subclass. Each subclass could contain multiple units from each treatment group. The subclasses are chosen to minimize the largest within-subclass distance between units (including between units of the same treatment group). Notably, generalized full matching requires less memory and can run much faster than optimal full matching and optimal pair matching and, in some cases, even than nearest neighbor matching, and it can be used with huge datasets (e.g., in the millions) while running in under a minute.

Outputs

All outputs described in matchit() are returned with method = "quick" except for match.matrix. This is because matching strata are not indexed by treated units as they are in some other forms of matching. When include.obj = TRUE in the call to matchit(), the output of the call to quickmatchquickmatch will be included in the output. When exact is specified, this will be a list of such objects, one for each stratum of the exact variables.

References

In a manuscript, be sure to cite the quickmatch package if using matchit() with method = "quick":

Sävje, F., Sekhon, J., & Higgins, M. (2018). quickmatch: Quick generalized full matching. https://CRAN.R-project.org/package=quickmatch

For example, a sentence might read:

Generalized full matching was performed using the MatchIt package (Ho, Imai, King, & Stuart, 2011) in R, which calls functions from the quickmatch package (Savje, Sekhon, & Higgins, 2018).

You should also cite the following paper, which develops and describes the method:

Sävje, F., Higgins, M. J., & Sekhon, J. S. (2021). Generalized Full Matching. Political Analysis, 29(4), 423–447. doi:10.1017/pan.2020.32

Examples

data("lalonde")

# Generalize full PS matching
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "quick")
m.out1
#> A `matchit` object
#>  - method: Generalized full matching
#>  - distance: Propensity score             - estimated with logistic regression
#>  - number of obs.: 614 (original), 614 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ, race, nodegree, married, re74, re75
summary(m.out1)
#> 
#> Call:
#> matchit(formula = treat ~ age + educ + race + nodegree + married + 
#>     re74 + re75, data = lalonde, method = "quick")
#> 
#> Summary of Balance for All Data:
#>            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance          0.5774        0.1822          1.7941     0.9211    0.3774
#> age              25.8162       28.0303         -0.3094     0.4400    0.0813
#> educ             10.3459       10.2354          0.0550     0.4959    0.0347
#> raceblack         0.8432        0.2028          1.7615          .    0.6404
#> racehispan        0.0595        0.1422         -0.3498          .    0.0827
#> racewhite         0.0973        0.6550         -1.8819          .    0.5577
#> nodegree          0.7081        0.5967          0.2450          .    0.1114
#> married           0.1892        0.5128         -0.8263          .    0.3236
#> re74           2095.5737     5619.2365         -0.7211     0.5181    0.2248
#> re75           1532.0553     2466.4844         -0.2903     0.9563    0.1342
#>            eCDF Max
#> distance     0.6444
#> age          0.1577
#> educ         0.1114
#> raceblack    0.6404
#> racehispan   0.0827
#> racewhite    0.5577
#> nodegree     0.1114
#> married      0.3236
#> re74         0.4470
#> re75         0.2876
#> 
#> Summary of Balance for Matched Data:
#>            Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance          0.5774        0.5764          0.0047     0.9895    0.0044
#> age              25.8162       25.4476          0.0515     0.5099    0.0728
#> educ             10.3459       10.6781         -0.1652     0.5742    0.0251
#> raceblack         0.8432        0.8376          0.0155          .    0.0056
#> racehispan        0.0595        0.0607         -0.0052          .    0.0012
#> racewhite         0.0973        0.1017         -0.0148          .    0.0044
#> nodegree          0.7081        0.6602          0.1054          .    0.0479
#> married           0.1892        0.1355          0.1371          .    0.0537
#> re74           2095.5737     2873.4651         -0.1592     0.8886    0.0709
#> re75           1532.0553     1634.2731         -0.0318     1.8751    0.0736
#>            eCDF Max Std. Pair Dist.
#> distance     0.0541          0.0202
#> age          0.2659          1.2519
#> educ         0.0855          1.2506
#> raceblack    0.0056          0.0265
#> racehispan   0.0012          0.4970
#> racewhite    0.0044          0.3641
#> nodegree     0.0479          0.9324
#> married      0.0537          0.4870
#> re74         0.3004          0.8699
#> re75         0.2760          0.8428
#> 
#> Sample Sizes:
#>               Control Treated
#> All            429.       185
#> Matched (ESS)   50.74     185
#> Matched        429.       185
#> Unmatched        0.         0
#> Discarded        0.         0
#>

Arguments

Details

Outputs

References

See also

Examples