In `matchit()`

, setting `method = "cem"`

performs coarsened exact
matching. With coarsened exact matching, covariates are coarsened into bins,
and a complete cross of the coarsened covariates is used to form subclasses
defined by each combination of the coarsened covariate levels. Any subclass
that doesn't contain both treated and control units is discarded, leaving
only subclasses containing treatment and control units that are exactly
equal on the coarsened covariates. The coarsening process can be controlled
by an algorithm or by manually specifying cutpoints and groupings. The
benefits of coarsened exact matching are that the tradeoff between exact
matching and approximate balancing can be managed to prevent discarding too
many units, which can otherwise occur with exact matching.

This page details the allowable arguments with `method = "cem"`

. 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 coarsened exact matching:

```
matchit(formula,
data = NULL,
method = "cem",
estimand = "ATT",
s.weights = NULL,
verbose = FALSE,
...)
```

## Arguments

- formula
a two-sided formula object containing the treatment and covariates to be used in creating the subclasses defined by a full cross of the coarsened covariate levels.

- 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

`"cem"`

.- 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. When`k2k = TRUE`

(see below),`estimand`

also controls how the matching is done.- s.weights
the variable containing sampling weights to be incorporated into balance statistics or the scaling factors when

`k2k = TRUE`

and certain methods are used.- verbose
`logical`

; whether information about the matching process should be printed to the console.- ...
additional arguments to control the matching process.

`grouping`

a named list with an (optional) entry for each categorical variable to be matched on. Each element should itself be a list, and each entry of the sublist should be a vector containing levels of the variable that should be combined to form a single level. Any categorical variables not included in

`grouping`

will remain as they are in the data, which means exact matching, with no coarsening, will take place on these variables. See Details.`cutpoints`

a named list with an (optional) entry for each numeric variable to be matched on. Each element describes a way of coarsening the corresponding variable. They can be a vector of cutpoints that demarcate bins, a single number giving the number of bins, or a string corresponding to a method of computing the number of bins. Allowable strings include

`"sturges"`

,`"scott"`

, and`"fd"`

, which use the functions`grDevices::nclass.Sturges()`

,`grDevices::nclass.scott()`

, and`grDevices::nclass.FD()`

, respectively. The default is`"sturges"`

for variables that are not listed or if no argument is supplied. Can also be a single value to be applied to all numeric variables. See Details.`k2k`

`logical`

; whether 1:1 matching should occur within the matched strata. If`TRUE`

nearest neighbor matching without replacement will take place within each stratum, and any unmatched units will be dropped (e.g., if there are more treated than control units in the stratum, the treated units without a match will be dropped). The`k2k.method`

argument controls how the distance between units is calculated.`k2k.method`

`character`

; how the distance between units should be calculated if`k2k = TRUE`

. Allowable arguments include`NULL`

(for random matching), any argument to`distance()`

for computing a distance matrix from covariates (e.g.,`"mahalanobis"`

), or any allowable argument to`method`

in`dist()`

. Matching will take place on the original (non-coarsened) variables. The default is`"mahalanobis"`

.`mpower`

if

`k2k.method = "minkowski"`

, the power used in creating the distance. This is passed to the`p`

argument of`dist()`

.

The arguments

`distance`

(and related arguments),`exact`

,`mahvars`

,`discard`

(and related arguments),`replace`

,`m.order`

,`caliper`

(and related arguments), and`ratio`

are ignored with a warning.

## Details

If the coarsening is such that there are no exact matches with the coarsened
variables, the `grouping`

and `cutpoints`

arguments can be used to
modify the matching specification. Reducing the number of cutpoints or
grouping some variable values together can make it easier to find matches.
See Examples below. Removing variables can also help (but they will likely
not be balanced unless highly correlated with the included variables). To
take advantage of coarsened exact matching without failing to find any
matches, the covariates can be manually coarsened outside of
`matchit()`

and then supplied to the `exact`

argument in a call to
`matchit()`

with another matching method.

Setting `k2k = TRUE`

is equivalent to first doing coarsened exact
matching with `k2k = FALSE`

and then supplying stratum membership as an
exact matching variable (i.e., in `exact`

) to another call to
`matchit()`

with `method = "nearest"`

, `distance = "mahalanobis"`

and an argument to `discard`

denoting unmatched units.
It is also equivalent to performing nearest neighbor matching supplying
coarsened versions of the variables to `exact`

, except that
`method = "cem"`

automatically coarsens the continuous variables. The
`estimand`

argument supplied with `method = "cem"`

functions the
same way it would in these alternate matching calls, i.e., by determining
the "focal" group that controls the order of the matching.

### Grouping and Cutpoints

The `grouping`

and `cutpoints`

arguments allow one to fine-tune the coarsening of the covariates.
`grouping`

is used for combining categories of categorical covariates
and `cutpoints`

is used for binning numeric covariates. The values
supplied to these arguments should be iteratively changed until a matching
solution that balances covariate balance and remaining sample size is
obtained. The arguments are described below.

`grouping`

The argument to `grouping`

must be a list, where each component has the
name of a categorical variable, the levels of which are to be combined. Each
component must itself be a list; this list contains one or more vectors of
levels, where each vector corresponds to the levels that should be combined
into a single category. For example, if a variable `amount`

had levels
`"none"`

, `"some"`

, and `"a lot"`

, one could enter
`grouping = list(amount = list(c("none"), c("some", "a lot")))`

, which
would group `"some"`

and `"a lot"`

into a single category and
leave `"none"`

in its own category. Any levels left out of the list for
each variable will be left alone (so `c("none")`

could have been
omitted from the previous code). Note that if a categorical variable does
not appear in `grouping`

, it will not be coarsened, so exact matching
will take place on it. `grouping`

should not be used for numeric
variables with more than a few values; use `cutpoints`

, described below, instead.

`cutpoints`

The argument to `cutpoints`

must also be a list, where each component
has the name of a numeric variables that is to be binned. (As a shortcut, it
can also be a single value that will be applied to all numeric variables).
Each component can take one of three forms: a vector of cutpoints that
separate the bins, a single number giving the number of bins, or a string
corresponding to an algorithm used to compute the number of bins. Any values
at a boundary will be placed into the higher bin; e.g., if the cutpoints
were `c(0, 5, 10)`

, values of 5 would be placed into the same bin as
values of 6, 7, 8, or 9, and values of 10 would be placed into a different
bin. Internally, values of `-Inf`

and `Inf`

are appended to the
beginning and end of the range. When given as a single number defining the
number of bins, the bin boundaries are the maximum and minimum values of the
variable with bin boundaries evenly spaced between them, i.e., not
quantiles. A value of 0 will not perform any binning (equivalent to exact
matching on the variable), and a value of 1 will remove the variable from
the exact matching variables but it will be still used for pair matching
when `k2k = TRUE`

. The allowable strings include `"sturges"`

,
`"scott"`

, and `"fd"`

, which use the corresponding binning method,
and `"q#"`

where `#`

is a number, which splits the variable into
`#`

equally-sized bins (i.e., quantiles).

An example of a way to supply an argument to `cutpoints`

would be the
following:

This would split `X1`

into 4 bins, `X2`

into bins based on the provided boundaries, `X3`

into a number of bins
determined by `grDevices::nclass.scott()`

, and `X4`

into
quintiles. All other numeric variables would be split into a number of bins
determined by `grDevices::nclass.Sturges()`

, the default.

## Note

This method does not rely on the *cem* package, instead using
code written for *MatchIt*, but its design is based on the original
*cem* functions. Versions of *MatchIt* prior to 4.1.0 did rely on
*cem*, so results may differ between versions. There are a few
differences between the ways *MatchIt* and *cem* (and older
versions of *MatchIt*) differ in executing coarsened exact matching,
described below.

In

*MatchIt*, when a single number is supplied to`cutpoints`

, it describes the number of bins; in*cem*, it describes the number of cutpoints separating bins. The*MatchIt*method is closer to how`hist()`

processes breaks points to create bins.In

*MatchIt*, values on the cutpoint boundaries will be placed into the higher bin; in*cem*, they are placed into the lower bin. To avoid consequences of this choice, ensure the bin boundaries do not coincide with observed values of the variables.When

`cutpoints`

are used,`"ss"`

(for Shimazaki-Shinomoto's rule) can be used in*cem*but not in*MatchIt*.When

`k2k = TRUE`

,*MatchIt*matches on the original variables (scaled), whereas*cem*matches on the coarsened variables. Because the variables are already exactly matched on the coarsened variables, matching in*cem*is equivalent to random matching within strata.When

`k2k = TRUE`

, in*MatchIt*matched units are identified by pair membership, and the original stratum membership prior to 1:1 matching is discarded. In*cem*, pairs are not identified beyond the stratum the members are part of.When

`k2k = TRUE`

,`k2k.method = "mahalanobis"`

can be requested in*MatchIt*but not in*cem*.

## Outputs

All outputs described in `matchit()`

are returned with
`method = "cem"`

except for `match.matrix`

. When `k2k = TRUE`

, a `match.matrix`

component with the matched pairs is also
included. `include.obj`

is ignored.

## References

In a manuscript, you don't need to cite another package when
using `method = "cem"`

because the matching is performed completely
within *MatchIt*. For example, a sentence might read:

*Coarsened exact matching was performed using the MatchIt package (Ho,
Imai, King, & Stuart, 2011) in R.*

It would be a good idea to cite the following article, which develops the theory behind coarsened exact matching:

Iacus, S. M., King, G., & Porro, G. (2012). Causal Inference without Balance
Checking: Coarsened Exact Matching. *Political Analysis*, 20(1), 1–24. doi:10.1093/pan/mpr013

## See also

`matchit()`

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

.

The *cem* package, upon which this method is based and which provided
the workhorse in previous versions of *MatchIt*.

`method_exact`

for exact matching, which performs exact matching
on the covariates without coarsening.

## Examples

```
data("lalonde")
# Coarsened exact matching on age, race, married, and educ with educ
# coarsened into 5 bins and race coarsened into 2 categories,
# grouping "white" and "hispan" together
m.out1 <- matchit(treat ~ age + race + married + educ, data = lalonde,
method = "cem", cutpoints = list(educ = 5),
grouping = list(race = list(c("white", "hispan"),
c("black"))))
m.out1
#> A matchit object
#> - method: Coarsened exact matching
#> - number of obs.: 614 (original), 393 (matched)
#> - target estimand: ATT
#> - covariates: age, race, married, educ
summary(m.out1)
#>
#> Call:
#> matchit(formula = treat ~ age + race + married + educ, data = lalonde,
#> method = "cem", cutpoints = list(educ = 5), grouping = list(race = list(c("white",
#> "hispan"), c("black"))))
#>
#> Summary of Balance for All Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> age 25.8162 28.0303 -0.3094 0.4400 0.0813
#> 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
#> married 0.1892 0.5128 -0.8263 . 0.3236
#> educ 10.3459 10.2354 0.0550 0.4959 0.0347
#> eCDF Max
#> age 0.1577
#> raceblack 0.6404
#> racehispan 0.0827
#> racewhite 0.5577
#> married 0.3236
#> educ 0.1114
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> age 24.1007 23.7091 0.0547 0.8882 0.0140
#> raceblack 0.8188 0.8188 0.0000 . 0.0000
#> racehispan 0.0671 0.0360 0.1317 . 0.0312
#> racewhite 0.1141 0.1452 -0.1051 . 0.0312
#> married 0.1745 0.1745 -0.0000 . 0.0000
#> educ 10.5369 10.8649 -0.1631 0.7974 0.0177
#> eCDF Max Std. Pair Dist.
#> age 0.0897 0.1555
#> raceblack 0.0000 0.0000
#> racehispan 0.0312 0.4829
#> racewhite 0.0312 0.3853
#> married 0.0000 0.0000
#> educ 0.1865 0.3962
#>
#> Sample Sizes:
#> Control Treated
#> All 429. 185
#> Matched (ESS) 52.84 149
#> Matched 244. 149
#> Unmatched 185. 36
#> Discarded 0. 0
#>
# The same but requesting 1:1 Mahalanobis distance matching with
# the k2k and k2k.method argument. Note the remaining number of units
# is smaller than when retaining the full matched sample.
m.out2 <- matchit(treat ~ age + race + married + educ, data = lalonde,
method = "cem", cutpoints = list(educ = 5),
grouping = list(race = list(c("white", "hispan"),
"black")),
k2k = TRUE, k2k.method = "mahalanobis")
m.out2
#> A matchit object
#> - method: Coarsened exact matching
#> - number of obs.: 614 (original), 170 (matched)
#> - target estimand: ATT
#> - covariates: age, race, married, educ
summary(m.out2, un = FALSE)
#>
#> Call:
#> matchit(formula = treat ~ age + race + married + educ, data = lalonde,
#> method = "cem", cutpoints = list(educ = 5), grouping = list(race = list(c("white",
#> "hispan"), "black")), k2k = TRUE, k2k.method = "mahalanobis")
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> age 23.6353 23.4118 0.0312 0.9022 0.0126
#> raceblack 0.6824 0.6824 0.0000 . 0.0000
#> racehispan 0.1176 0.0706 0.1990 . 0.0471
#> racewhite 0.2000 0.2471 -0.1588 . 0.0471
#> married 0.2118 0.2118 0.0000 . 0.0000
#> educ 10.2588 10.5176 -0.1287 0.8036 0.0149
#> eCDF Max Std. Pair Dist.
#> age 0.0824 0.1003
#> raceblack 0.0000 0.0000
#> racehispan 0.0471 0.1990
#> racewhite 0.0471 0.1588
#> married 0.0000 0.0000
#> educ 0.1294 0.2106
#>
#> Sample Sizes:
#> Control Treated
#> All 429 185
#> Matched 85 85
#> Unmatched 344 100
#> Discarded 0 0
#>
```