method_optimal: Optimal Pair Matching

method_optimalR Documentation

Optimal Pair Matching


In matchit(), setting method = "optimal" performs optimal pair matching. The matching is optimal in the sense that that sum of the absolute pairwise distances in the matched sample is as small as possible. The method functionally relies on \pkgfunoptmatchfullmatch.

Advantages of optimal pair matching include that the matching order is not required to be specified and it is less likely that extreme within-pair distances will be large, unlike with nearest neighbor matching. Generally, however, as a subset selection method, optimal pair matching tends to perform similarly to nearest neighbor matching in that similar subsets of units will be selected to be matched.

This page details the allowable arguments with method = "optmatch". 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 optimal pair matching:

        data = NULL,
        method = "optimal",
        distance = "glm",
        link = "logit",
        distance.options = list(),
        estimand = "ATT",
        exact = NULL,
        mahvars = NULL,
        antiexact = NULL,
        discard = "none",
        reestimate = FALSE,
        s.weights = NULL,
        ratio = 1,
        min.controls = NULL,
        max.controls = NULL,
        verbose = FALSE,



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.


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


set here to "optimal".


the distance measure to be used. See distance for allowable options. Can be supplied as a distance matrix.


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.


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


a string containing the desired estimand. Allowable options include "ATT" and "ATC". See Details.


for which variables exact matching should take place.


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


for which variables ant-exact matching should take place. Anti-exact matching is processed using \pkgfunoptmatchantiExactMatch.


a string containing a method for discarding units outside a region of common support. Only allowed when distance is not "mahalanobis" and not a matrix.


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


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


how many control units should be matched to each treated unit for k:1 matching. For variable ratio matching, see section "Variable Ratio Matching" in Details below.

min.controls, max.controls

for variable ratio matching, the minimum and maximum number of controls units to be matched to each treated unit. See section "Variable Ratio Matching" in Details below.


logical; whether information about the matching process should be printed to the console. What is printed depends on the matching method. Default is FALSE for no printing other than warnings.


additional arguments passed to \pkgfunoptmatchfullmatch. Allowed arguments include tol and solver. See the \pkgfunoptmatchfullmatch documentation for details. In general, tol should be set to a low number (e.g., 1e-7) to get a more precise solution.

The arguments replace, caliper, and m.order are ignored with a warning.


Mahalanobis Distance Matching

Mahalanobis distance matching can be done one of two ways:

  1. If no propensity score needs to be estimated, distance should be set to "mahalanobis", and Mahalanobis distance matching will occur using all the variables in formula. Arguments to discard and mahvars will be ignored. For example, to perform simple Mahalanobis distance matching, the following could be run:

    matchit(treat ~ X1 + X2, method = "nearest",
            distance = "mahalanobis") 

    With this code, the Mahalanobis distance is computed using X1 and X2, and matching occurs on this distance. The distance component of the matchit() output will be empty.

  2. If a propensity score needs to be estimated for common support with discard, distance should be whatever method is used to estimate the propensity score or a vector of distance measures, i.e., it should not be "mahalanobis". Use mahvars to specify the variables used to create the Mahalanobis distance. For example, to perform Mahalanobis after discarding units outside the common support of the propensity score in both groups, the following could be run:

    matchit(treat ~ X1 + X2 + X3, method = "nearest",
            distance = "glm", discard = "both",
            mahvars = ~ X1 + X2) 

    With this code, X1, X2, and X3 are used to estimate the propensity score (using the "glm" method, which by default is logistic regression), which is used to identify the common support. The actual matching occurs on the Mahalanobis distance computed only using X1 and X2, which are supplied to mahvars. The estimated propensity scores will be included in the distance component of the matchit() output.


The estimand argument controls whether control units are selected to be matched with treated units (estimand = "ATT") or treated units are selected to be matched with control units (estimand = "ATC"). The "focal" group (e.g., the treated units for the ATT) is typically made to be the smaller treatment group, and a warning will be thrown if it is not set that way unless replace = TRUE. Setting estimand = "ATC" is equivalent to swapping all treated and control labels for the treatment variable. When estimand = "ATC", the match.matrix component of the output will have the names of the control units as the rownames and be filled with the names of the matched treated units (opposite to when estimand = "ATT"). Note that the argument supplied to estimand doesn't necessarily correspond to the estimand actually targeted; it is merely a switch to trigger which treatment group is considered "focal".

Variable Ratio Matching

matchit() can perform variable ratio matching, which involves matching a different number of control units to each treated unit. When ratio > 1, rather than requiring all treated units to receive ratio matches, the arguments to max.controls and min.controls can be specified to control the maximum and minimum number of matches each treated unit can have. ratio controls how many total control units will be matched: n1 * ratio control units will be matched, where n1 is the number of treated units, yielding the same total number of matched controls as fixed ratio matching does.

Variable ratio matching can be used with any distance specification. ratio does not have to be an integer but must be greater than 1 and less than n0/n1, where n0 and n1 are the number of control and treated units, respectively. Setting ratio = n0/n1 performs a restricted form of full matching where all control units are matched. If min.controls is not specified, it is set to 1 by default. min.controls must be less than ratio, and max.controls must be greater than ratio. See the Examples section of method_nearest() for an example of their use, which is the same as it is with optimal matching.


All outputs described in matchit() are returned with method = "optimal". When include.obj = TRUE in the call to matchit(), the output of the call to optmatch::fullmatch() 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.


Optimal pair matching is a restricted form of optimal full matching where the number of treated units in each subclass is equal to 1, whereas in unrestricted full matching, multiple treated units can be assigned to the same subclass. \pkgfunoptmatchpairmatch is simply a wrapper for \pkgfunoptmatchfullmatch, which performs optimal full matching and is the workhorse for method_full. In the same way, matchit() uses optmatch::fullmatch() under the hood, imposing the restrictions that make optimal full matching function like optimal pair matching (which is simply to set min.controls >= 1 and to pass ratio to the mean.controls argument). This distinction is not important for regular use but may be of interest to those examining the source code.

The option "optmatch_max_problem_size" is automatically set to Inf during the matching process, different from its default in optmatch. This enables matching problems of any size to be run, but may also let huge, infeasible problems get through and potentially take a long time or crash R. See \pkgfunoptmatchsetMaxProblemSize for more details.


In a manuscript, be sure to cite the following paper if using matchit() with method = "optimal":

Hansen, B. B., & Klopfer, S. O. (2006). Optimal Full Matching and Related Designs via Network Flows. Journal of Computational and Graphical Statistics, 15(3), 609–627. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/106186006X137047")}

For example, a sentence might read:

Optimal pair matching was performed using the MatchIt package (Ho, Imai, King, & Stuart, 2011) in R, which calls functions from the optmatch package (Hansen & Klopfer, 2006).

See Also

matchit() for a detailed explanation of the inputs and outputs of a call to matchit().


optmatchfullmatch, which is the workhorse.

method_full for optimal full matching, of which optimal pair matching is a special case, and which relies on similar machinery.



#1:1 optimal PS matching with exact matching on race
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "optimal", exact = ~race)

#2:1 optimal matching on the scaled Euclidean distance
m.out2 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "optimal", ratio = 2,
                  distance = "scaled_euclidean")
summary(m.out2, un = FALSE)

MatchIt documentation built on Oct. 13, 2023, 9:08 a.m.