In matchit(), setting method = "full" performs optimal 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. The matching is optimal in the sense that
that sum of the absolute distances between the treated and control units in
each subclass is as small as possible. The method relies on and is a wrapper
for optmatchfullmatch.
Advantages of optimal 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 full matching is a set of
matching weights that can be applied to the matched sample; in this way,
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. Note: with large samples, the optimization may fail or run very slowly; one can try using method = "quick" instead, which also performs full matching but can be much faster.
This page details the allowable arguments with method = "full".
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 full matching:
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 indata, the variables will be sought in the environment.- method
set here to
"full".- distance
the distance measure to be used. See
distancefor allowable options. Can be supplied as a distance matrix.- link
when
distanceis specified as a method of estimating propensity scores, an additional argument controlling the link function used in estimating the distance measure. Seedistancefor 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 atmatchit()for details.- exact
for which variables exact matching should take place.
- mahvars
for which variables Mahalanobis distance matching should take place when
distancecorresponds 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.- antiexact
for which variables anti-exact matching should take place. Anti-exact matching is processed using optmatchantiExactMatch.
- discard
a string containing a method for discarding units outside a region of common support. Only allowed when
distancecorresponds to a propensity score.- reestimate
if
discardis 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(s) of the caliper(s) used for caliper matching. Calipers are processed by optmatchcaliper. See Notes and Examples.
- std.caliper
logical; when calipers are specified, whether they are 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 optmatchfullmatch. Allowed arguments include
min.controls,max.controls,omit.fraction,mean.controls,tol, andsolver. See the optmatchfullmatch documentation for details. In general,tolshould be set to a low number (e.g.,1e-7) to get a more precise solution.The arguments
replace,m.order, andratioare ignored with a warning.
Details
Mahalanobis Distance Matching
Mahalanobis distance matching can be done one of two ways:
If no propensity score needs to be estimated,
distanceshould be set to"mahalanobis", and Mahalanobis distance matching will occur using all the variables informula. Arguments todiscardandmahvarswill be ignored, and a caliper can only be placed on named variables. For example, to perform simple Mahalanobis distance matching, the following could be run:With this code, the Mahalanobis distance is computed usingmatchit(treat ~ X1 + X2, method = "nearest", distance = "mahalanobis")X1andX2, and matching occurs on this distance. Thedistancecomponent of thematchit()output will be empty.If a propensity score needs to be estimated for any reason, e.g., for common support with
discardor for creating a caliper,distanceshould be whatever method is used to estimate the propensity score or a vector of distance measures, i.e., it should not be"mahalanobis". Usemahvarsto specify the variables used to create the Mahalanobis distance. For example, to perform Mahalanobis within a propensity score caliper, the following could be run:With this code,matchit(treat ~ X1 + X2 + X3, method = "nearest", distance = "glm", caliper = .25, mahvars = ~ X1 + X2)X1,X2, andX3are used to estimate the propensity score (using the"glm"method, which by default is logistic regression), which is used to create a matching caliper. The actual matching occurs on the Mahalanobis distance computed only usingX1andX2, which are supplied tomahvars. Units whose propensity score difference is larger than the caliper will not be paired, and some treated units may therefore not receive a match. The estimated propensity scores will be included in thedistancecomponent of thematchit()output. See Examples.
Note
Calipers can only be used when min.controls is left at its
default.
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 optmatchsetMaxProblemSize for more details.
Outputs
All outputs described in matchit() are returned with
method = "full" 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 optmatchfullmatch 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 following paper if using
matchit() with method = "full":
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. doi:10.1198/106186006X137047
For example, a sentence might read:
Optimal full matching was performed using the MatchIt package (Ho, Imai, King, & Stuart, 2011) in R, which calls functions from the optmatch package (Hansen & Klopfer, 2006).
Theory is also developed in the following article:
Hansen, B. B. (2004). Full Matching in an Observational Study of Coaching for the SAT. Journal of the American Statistical Association, 99(467), 609–618. doi:10.1198/016214504000000647
See also
matchit() for a detailed explanation of the inputs and outputs of
a call to matchit().
optmatchfullmatch, which is the workhorse.
method_optimal for optimal pair matching, which is a special
case of optimal full matching, and which relies on similar machinery.
Results from method = "optimal" can be replicated with method = "full" by setting min.controls, max.controls, and
mean.controls to the desired ratio.
method_quick for fast generalized quick matching, which is very similar to optimal full matching but can be dramatically faster at the expense of optimality and is less customizable.
Examples
data("lalonde")
# Optimal full PS matching
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
method = "full")
m.out1
#> A `matchit` object
#> - method: Optimal 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 = "full")
#>
#> 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 0.5762 0.0054 0.9930 0.0041
#> age 25.8162 24.8095 0.1407 0.4976 0.0795
#> educ 10.3459 10.3452 0.0004 0.5830 0.0206
#> raceblack 0.8432 0.8347 0.0236 . 0.0086
#> racehispan 0.0595 0.0657 -0.0266 . 0.0063
#> racewhite 0.0973 0.0996 -0.0078 . 0.0023
#> nodegree 0.7081 0.7056 0.0056 . 0.0025
#> married 0.1892 0.1368 0.1338 . 0.0524
#> re74 2095.5737 2363.4473 -0.0548 1.1080 0.0424
#> re75 1532.0553 1632.4020 -0.0312 1.8588 0.0704
#> eCDF Max Std. Pair Dist.
#> distance 0.0486 0.0192
#> age 0.3131 1.3111
#> educ 0.0548 1.2390
#> raceblack 0.0086 0.0324
#> racehispan 0.0063 0.5400
#> racewhite 0.0023 0.3911
#> nodegree 0.0025 0.9593
#> married 0.0524 0.4715
#> re74 0.2492 0.8654
#> re75 0.2366 0.8099
#>
#> Sample Sizes:
#> Control Treated
#> All 429. 185
#> Matched (ESS) 52.11 185
#> Matched 429. 185
#> Unmatched 0. 0
#> Discarded 0. 0
#>
# Optimal full Mahalanobis distance matching within a PS caliper
m.out2 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
method = "full", caliper = .01,
mahvars = ~ age + educ + re74 + re75)
m.out2
#> A `matchit` object
#> - method: Optimal full matching
#> - distance: Mahalanobis [matching]
#> Propensity score [caliper]
#> - estimated with logistic regression
#> - caliper: <distance> (0.003)
#> - number of obs.: 614 (original), 349 (matched)
#> - target estimand: ATT
#> - covariates: age, educ, race, nodegree, married, re74, re75
summary(m.out2, un = FALSE)
#>
#> Call:
#> matchit(formula = treat ~ age + educ + race + nodegree + married +
#> re74 + re75, data = lalonde, method = "full", mahvars = ~age +
#> educ + re74 + re75, caliper = 0.01)
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance 0.5564 0.5566 -0.0012 0.9885 0.0028
#> age 25.1940 24.4645 0.1020 0.5323 0.0681
#> educ 10.3060 10.5529 -0.1228 0.6813 0.0193
#> raceblack 0.7985 0.8022 -0.0103 . 0.0037
#> racehispan 0.0672 0.0596 0.0321 . 0.0076
#> racewhite 0.1343 0.1382 -0.0131 . 0.0039
#> nodegree 0.6716 0.6742 -0.0057 . 0.0026
#> married 0.1642 0.1189 0.1157 . 0.0453
#> re74 1504.8003 2669.4440 -0.2383 0.4985 0.0889
#> re75 1242.9898 1479.5812 -0.0735 1.8382 0.0762
#> eCDF Max Std. Pair Dist.
#> distance 0.0373 0.0063
#> age 0.2709 1.1149
#> educ 0.0812 1.1082
#> raceblack 0.0037 0.0105
#> racehispan 0.0076 0.5788
#> racewhite 0.0039 0.4490
#> nodegree 0.0026 0.8782
#> married 0.0453 0.4951
#> re74 0.3362 0.6849
#> re75 0.2368 0.6460
#>
#> Sample Sizes:
#> Control Treated
#> All 429. 185
#> Matched (ESS) 61.97 134
#> Matched 215. 134
#> Unmatched 214. 51
#> Discarded 0. 0
#>
# Optimal full Mahalanobis distance matching within calipers
# of 500 on re74 and re75
m.out3 <- matchit(treat ~ age + educ + re74 + re75,
data = lalonde, distance = "mahalanobis",
method = "full",
caliper = c(re74 = 500, re75 = 500),
std.caliper = FALSE)
m.out3
#> A `matchit` object
#> - method: Optimal full matching
#> - distance: Mahalanobis - caliper: re74 (500), re75 (500)
#> - number of obs.: 614 (original), 391 (matched)
#> - target estimand: ATT
#> - covariates: age, educ, re74, re75
summary(m.out3, addlvariables = ~race + nodegree + married,
data = lalonde, un = FALSE)
#>
#> Call:
#> matchit(formula = treat ~ age + educ + re74 + re75, data = lalonde,
#> method = "full", distance = "mahalanobis", caliper = c(re74 = 500,
#> re75 = 500), std.caliper = FALSE)
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> age 25.8438 26.6668 -0.1150 0.6314 0.0391
#> educ 10.2562 10.2998 -0.0217 0.5406 0.0266
#> re74 902.3844 927.5659 -0.0052 0.9952 0.0089
#> re75 661.1024 674.8033 -0.0043 1.0111 0.0090
#> raceblack 0.8500 0.3065 1.4948 . 0.5435
#> racehispan 0.0437 0.1258 -0.3469 . 0.0820
#> racewhite 0.1062 0.5677 -1.5570 . 0.4614
#> nodegree 0.7312 0.6768 0.1197 . 0.0544
#> married 0.1625 0.4717 -0.7895 . 0.3092
#> eCDF Max Std. Pair Dist.
#> age 0.0868 0.5037
#> educ 0.0623 0.5850
#> re74 0.1957 0.0249
#> re75 0.0871 0.0421
#> raceblack 0.5435 1.7611
#> racehispan 0.0820 0.7605
#> racewhite 0.4614 1.8935
#> nodegree 0.0544 0.3086
#> married 0.3092 1.1113
#>
#> Sample Sizes:
#> Control Treated
#> All 429. 185
#> Matched (ESS) 54.18 160
#> Matched 231. 160
#> Unmatched 198. 25
#> Discarded 0. 0
#>