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 optmatch::fullmatch().
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:
matchit(formula,
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 optmatch::antiExactMatch().
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.
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 optmatch::fullmatch().
Allowed arguments include tol and solver. See the
optmatch::fullmatch() 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.
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.
Mahalanobis distance matching can be done one of two ways:
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") X1 and
X2, and matching occurs on this distance. The distance
component of the matchit() output will be empty.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) 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".
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.
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. 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).
matchit() for a detailed explanation of the inputs and outputs of
a call to matchit().
optmatch::fullmatch(), 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.
if (FALSE) { # requireNamespace("optmatch", quietly = TRUE)
data("lalonde")
#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)
m.out1
summary(m.out1)
#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")
m.out2
summary(m.out2, un = FALSE)
}
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