method_full {MatchIt}

Optimal Full Matching

Description

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:

matchit(formula,
        data = NULL,
        method = "full",
        distance = "glm",
        link = "logit",
        distance.options = list(),
        estimand = "ATT",
        exact = NULL,
        mahvars = NULL,
        anitexact = NULL,
        discard = "none",
        reestimate = FALSE,
        s.weights = NULL,
        caliper = NULL,
        std.caliper = TRUE,
        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. 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:

1. 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:

   matchit(treat ~ X1 + X2, method = "nearest",
           distance = "mahalanobis") 

   With this code, the Mahalanobis distance is computed using X1 and X2, and matching occurs on this distance. The distance component of the matchit() output will be empty.

2. 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:

   matchit(treat ~ X1 + X2 + X3, method = "nearest",
           distance =  "glm", caliper = .25,
           mahvars = ~ X1 + X2) 

   With this code, 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.

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.

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.

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
summary(m.out1)

# 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
summary(m.out2, un = FALSE)

# 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
summary(m.out3, addlvariables = ~race + nodegree + married,
        data = lalonde, un = FALSE)