In matchit(), setting method = "nearest" performs greedy nearest
neighbor matching. A distance is computed between each treated unit and each
control unit, and, one by one, each treated unit is assigned a control unit
as a match. The matching is "greedy" in the sense that there is no action
taken to optimize an overall criterion; each match is selected without
considering the other matches that may occur subsequently.
This page details the allowable arguments with method = "nearest".
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 nearest neighbor matching:
matchit(formula,
data = NULL,
method = "nearest",
distance = "glm",
link = "logit",
distance.options = list(),
estimand = "ATT",
exact = NULL,
mahvars = NULL,
antiexact = NULL,
discard = "none",
reestimate = FALSE,
s.weights = NULL,
replace = TRUE,
m.order = NULL,
caliper = NULL,
ratio = 1,
min.controls = NULL,
max.controls = NULL,
verbose = FALSE,
...) Arguments
- formula
a two-sided formula object containing the treatment and covariates to be used in creating the distance measure used in the matching.
- 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
"nearest".- 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"and"ATC". See Details.- exact
for which variables exact matching should take place; two units with different values of an exact matching variable will not be paired.
- 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; two units with the same value of an anti-exact matching variable will not be paired.
- 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.
- replace
whether matching should be done with replacement (i.e., whether control units can be used as matches multiple times). See also the
reuse.maxargument below. Default isFALSEfor matching without replacement.- m.order
the order that the matching takes place. Allowable options include
"largest", where matching takes place in descending order of distance measures;"smallest", where matching takes place in ascending order of distance measures;"closest", where matching takes place in ascending order of the smallest distance between units;"farthest", where matching takes place in descending order of the smallest distance between units;"random", where matching takes place in a random order; and"data"where matching takes place based on the order of units in the data. Whenm.order = "random", results may differ across different runs of the same code unless a seed is set and specified withset.seed(). The default ofNULLcorresponds to"largest"when a propensity score is estimated or supplied as a vector and"data"otherwise. See Details for more information.- caliper
the width(s) of the caliper(s) used for caliper matching. Two units with a difference on a caliper variable larger than the caliper will not be paired. See Details and Examples.
- std.caliper
logical; when calipers are specified, whether they are in standard deviation units (TRUE) or raw units (FALSE).- ratio
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. When
ratiois greater than 1, all treated units will be attempted to be matched with a control unit before any treated unit is matched with a second control unit, etc. This reduces the possibility that control units will be used up before some treated units receive any matches.- 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.
- verbose
logical; whether information about the matching process should be printed to the console. WhenTRUE, a progress bar implemented using RcppProgress will be displayed along with an estimate of the time remaining.- ...
additional arguments that control the matching specification:
reuse.maxnumeric; the maximum number of times each control can be used as a match. Settingreuse.max = 1corresponds to matching without replacement (i.e.,replace = FALSE), and settingreuse.max = Infcorresponds to traditional matching with replacement (i.e.,replace = TRUE) with no limit on the number of times each control unit can be matched. Other values restrict the number of times each control can be matched when matching with replacement.replaceis ignored whenreuse.maxis specified.unit.idone or more variables containing a unit ID for each observation, i.e., in case multiple observations correspond to the same unit. Once a control observation has been matched, no other observation with the same unit ID can be used as matches. This ensures each control unit is used only once even if it has multiple observations associated with it. Omitting this argument is the same as giving each observation a unique ID.
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. 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.
Estimand
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 default m.order is
"smallest", and 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 "extremal" matching as described by Ming and Rosenbaum (2000; doi:10.1111/j.0006-341X.2000.00118.x
). This
method tends to result in better balance than fixed ratio matching at the
expense of some precision. When ratio > 1, rather than requiring all
treated units to receive ratio matches, each treated unit is assigned
a value that corresponds to the number of control units they will be matched
to. These values are controlled by the arguments min.controls and
max.controls, which correspond to \(\alpha\) and \(\beta\),
respectively, in Ming and Rosenbaum (2000), and trigger variable ratio
matching to occur. Some treated units will receive min.controls
matches and others will receive max.controls matches (and one unit
may have an intermediate number of matches); how many units are assigned
each number of matches is determined by the algorithm described in Ming and
Rosenbaum (2000, p119). 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 cannot be used with Mahalanobis distance matching or
when distance is supplied as a matrix. The calculations of the
numbers of control units each treated unit will be matched to occurs without
consideration of caliper or discard. 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 crude 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
Examples below for an example of their use.
Using m.order = "closest" or "farthest"
m.order can be set to "closest" or "farthest", which work regardless of how the distance measure is specified. This matches in order of the distance between units. First, all the closest match is found for all treated units and the pairwise distances computed; when m.order = "closest" the pair with the smallest of the distances is matched first, and when m.order = "farthest", the pair with the largest of the distances is matched first. Then, the pair with the second smallest (or largest) is matched second. If the matched control is ineligible (i.e., because it has already been used in a prior match), a new match is found for the treated unit, the new pair's distance is re-computed, and the pairs are re-ordered by distance.
Using m.order = "closest" ensures that the best possible matches are given priority, and in that sense should perform similarly to m.order = "smallest". It can be used to ensure the best matches, especially when matching with a caliper. Using m.order = "farthest" ensures that the hardest units to match are given their best chance to find a close match, and in that sense should perform similarly to m.order = "largest". It can be used to reduce the possibility of extreme imbalance when there are hard-to-match units competing for controls. Note that m.order = "farthest" does not implement "far matching" (i.e., finding the farthest control unit from each treated unit); it defines the order in which the closest matches are selected.
Reproducibility
Nearest neighbor matching involves a random component only when m.order = "random" (or when the propensity is estimated using a method with randomness; see distance for details), so a seed must be set in that case using set.seed() to ensure reproducibility. Otherwise, it is purely deterministic, and any ties are broken based on the order in which the data appear.
Outputs
All outputs described in matchit() are returned with
method = "nearest". When replace = TRUE, the subclass
component is omitted. include.obj is ignored.
References
In a manuscript, you don't need to cite another package when
using method = "nearest" because the matching is performed completely
within MatchIt. For example, a sentence might read:
Nearest neighbor matching was performed using the MatchIt package (Ho, Imai, King, & Stuart, 2011) in R.
See also
matchit() for a detailed explanation of the inputs and outputs of
a call to matchit().
method_optimal() for optimal pair matching, which is similar to
nearest neighbor matching without replacement except that an overall distance criterion is
minimized (i.e., as an alternative to specifying m.order).
Examples
data("lalonde")
# 1:1 greedy NN matching on the PS
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75,
data = lalonde,
method = "nearest")
m.out1
#> A `matchit` object
#> - method: 1:1 nearest neighbor matching without replacement
#> - distance: Propensity score
#> - estimated with logistic regression
#> - number of obs.: 614 (original), 370 (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 = "nearest")
#>
#> 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 0.3629 0.9739 0.7566 0.1321
#> age 25.8162 25.3027 0.0718 0.4568 0.0847
#> educ 10.3459 10.6054 -0.1290 0.5721 0.0239
#> raceblack 0.8432 0.4703 1.0259 . 0.3730
#> racehispan 0.0595 0.2162 -0.6629 . 0.1568
#> racewhite 0.0973 0.3135 -0.7296 . 0.2162
#> nodegree 0.7081 0.6378 0.1546 . 0.0703
#> married 0.1892 0.2108 -0.0552 . 0.0216
#> re74 2095.5737 2342.1076 -0.0505 1.3289 0.0469
#> re75 1532.0553 1614.7451 -0.0257 1.4956 0.0452
#> eCDF Max Std. Pair Dist.
#> distance 0.4216 0.9740
#> age 0.2541 1.3938
#> educ 0.0757 1.2474
#> raceblack 0.3730 1.0259
#> racehispan 0.1568 1.0743
#> racewhite 0.2162 0.8390
#> nodegree 0.0703 1.0106
#> married 0.0216 0.8281
#> re74 0.2757 0.7965
#> re75 0.2054 0.7381
#>
#> Sample Sizes:
#> Control Treated
#> All 429 185
#> Matched 185 185
#> Unmatched 244 0
#> Discarded 0 0
#>
# 3:1 NN Mahalanobis distance matching with
# replacement within a PS caliper
m.out2 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75,
data = lalonde,
method = "nearest",
replace = TRUE,
mahvars = ~ age + educ + re74 + re75,
ratio = 3,
caliper = .02)
m.out2
#> A `matchit` object
#> - method: 3:1 nearest neighbor matching with replacement
#> - distance: Mahalanobis [matching]
#> Propensity score [caliper]
#>
#> - estimated with logistic regression
#> - caliper: <distance> (0.006)
#> - number of obs.: 614 (original), 300 (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 = "nearest", mahvars = ~age +
#> educ + re74 + re75, replace = TRUE, caliper = 0.02, ratio = 3)
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance 0.5660 0.5660 0.0003 0.9880 0.0037
#> age 25.5000 24.0010 0.2095 0.5178 0.0835
#> educ 10.3086 10.3930 -0.0420 0.7356 0.0115
#> raceblack 0.8210 0.8169 0.0113 . 0.0041
#> racehispan 0.0679 0.0576 0.0435 . 0.0103
#> racewhite 0.1111 0.1255 -0.0486 . 0.0144
#> nodegree 0.7037 0.6852 0.0407 . 0.0185
#> married 0.1914 0.1132 0.1996 . 0.0782
#> re74 1831.9348 2119.9268 -0.0589 1.2783 0.0528
#> re75 1400.4354 1386.7669 0.0042 2.2735 0.0623
#> eCDF Max Std. Pair Dist.
#> distance 0.0432 0.0128
#> age 0.3508 0.9787
#> educ 0.0381 0.7836
#> raceblack 0.0041 0.0358
#> racehispan 0.0103 0.2643
#> racewhite 0.0144 0.1845
#> nodegree 0.0185 0.5556
#> married 0.0782 0.4588
#> re74 0.2984 0.4634
#> re75 0.2428 0.5274
#>
#> Sample Sizes:
#> Control Treated
#> All 429. 185
#> Matched (ESS) 64.23 162
#> Matched 138. 162
#> Unmatched 291. 23
#> Discarded 0. 0
#>
# 1:1 NN Mahalanobis distance matching within calipers
# on re74 and re75 and exact matching on married and race
m.out3 <- matchit(treat ~ age + educ + re74 + re75,
data = lalonde,
method = "nearest",
distance = "mahalanobis",
exact = ~ married + race,
caliper = c(re74 = .2, re75 = .15))
#> Warning: Fewer control units than treated units in some `exact` strata; not all
#> treated units will get a match.
m.out3
#> A `matchit` object
#> - method: 1:1 nearest neighbor matching without replacement
#> - distance: Mahalanobis - caliper: re74 (1295.593), re75 (494.352)
#> - number of obs.: 614 (original), 166 (matched)
#> - target estimand: ATT
#> - covariates: age, educ, re74, re75, married, race
summary(m.out3, un = FALSE)
#>
#> Call:
#> matchit(formula = treat ~ age + educ + re74 + re75, data = lalonde,
#> method = "nearest", distance = "mahalanobis", exact = ~married +
#> race, caliper = c(re74 = 0.2, re75 = 0.15))
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> age 24.7711 24.6024 0.0236 0.4804 0.0753
#> educ 10.3976 10.0482 0.1738 0.4610 0.0361
#> re74 705.7326 864.0131 -0.0324 0.9038 0.0270
#> re75 592.6384 640.9355 -0.0150 1.0194 0.0150
#> married 0.1687 0.1687 0.0000 . 0.0000
#> raceblack 0.7349 0.7349 0.0000 . 0.0000
#> racehispan 0.0723 0.0723 0.0000 . 0.0000
#> racewhite 0.1928 0.1928 0.0000 . 0.0000
#> eCDF Max Std. Pair Dist.
#> age 0.2410 0.7544
#> educ 0.0964 0.7131
#> re74 0.2410 0.0537
#> re75 0.1084 0.0358
#> married 0.0000 0.0000
#> raceblack 0.0000 0.0000
#> racehispan 0.0000 0.0000
#> racewhite 0.0000 0.0000
#>
#> Sample Sizes:
#> Control Treated
#> All 429 185
#> Matched 83 83
#> Unmatched 346 102
#> Discarded 0 0
#>
# 2:1 variable ratio NN matching on the PS
m.out4 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75,
data = lalonde,
method = "nearest",
ratio = 2,
min.controls = 1,
max.controls = 12)
m.out4
#> A `matchit` object
#> - method: Variable ratio 2:1 nearest neighbor matching without replacement
#> - distance: Propensity score
#> - estimated with logistic regression
#> - number of obs.: 614 (original), 555 (matched)
#> - target estimand: ATT
#> - covariates: age, educ, race, nodegree, married, re74, re75
summary(m.out4, un = FALSE)
#>
#> Call:
#> matchit(formula = treat ~ age + educ + race + nodegree + married +
#> re74 + re75, data = lalonde, method = "nearest", ratio = 2,
#> min.controls = 1, max.controls = 12)
#>
#> Summary of Balance for Matched Data:
#> Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance 0.5774 0.3608 0.9835 0.7425 0.1414
#> age 25.8162 25.4459 0.0518 0.4560 0.0830
#> educ 10.3459 10.4887 -0.0710 0.5654 0.0236
#> raceblack 0.8432 0.4703 1.0259 . 0.3730
#> racehispan 0.0595 0.2110 -0.6408 . 0.1515
#> racewhite 0.0973 0.3187 -0.7472 . 0.2214
#> nodegree 0.7081 0.6517 0.1240 . 0.0564
#> married 0.1892 0.2218 -0.0833 . 0.0326
#> re74 2095.5737 2614.8070 -0.1063 1.1615 0.0611
#> re75 1532.0553 1714.9169 -0.0568 1.3486 0.0498
#> eCDF Max Std. Pair Dist.
#> distance 0.4216 0.5600
#> age 0.2457 1.4044
#> educ 0.0659 1.3187
#> raceblack 0.3730 0.5129
#> racehispan 0.1515 1.0629
#> racewhite 0.2214 0.8390
#> nodegree 0.0564 1.0760
#> married 0.0326 1.0420
#> re74 0.2912 0.9210
#> re75 0.2020 0.8587
#>
#> Sample Sizes:
#> Control Treated
#> All 429 185
#> Matched (ESS) 202 185
#> Matched 370 185
#> Unmatched 59 0
#> Discarded 0 0
#>
# Some units received 1 match and some received 12
table(table(m.out4$subclass[m.out4$treat == 0]))
#>
#> 1 10 12
#> 168 1 16