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 `optmatch::fullmatch()`

.

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 in`data`

, the variables will be sought in the environment.- method
set here to

`"full"`

.- distance
the distance measure to be used. See

`distance`

for allowable options. Can be supplied as a distance 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., 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 ant-exact matching should take place. Anti-exact matching is processed using

`optmatch::antiExactMatch()`

.- 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(s) of the caliper(s) used for caliper matching. Calipers are processed by

`optmatch::caliper()`

. 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

`optmatch::fullmatch()`

. Allowed arguments include`min.controls`

,`max.controls`

,`omit.fraction`

,`mean.controls`

,`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`

,`m.order`

, and`ratio`

are 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,

`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, 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 using`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 any reason, e.g., for common support with

`discard`

or for creating a caliper,`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 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`

, and`X3`

are 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 using`X1`

and`X2`

, which are supplied to`mahvars`

. 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 the`distance`

component of the`matchit()`

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 `optmatch::setMaxProblemSize()`

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 `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.

## 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()`

.

`optmatch::fullmatch()`

, 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
#>
```