The optmatch package implements the optimal full matching algorithm for bipartite matching problems. Given a matrix describing the distances between two groups (where one group is represented by row entries, and the other by column entries), the algorithm finds a matching between units that minimizes the average within grouped distances. This algorithm is a popular choice for covariate balancing applications (e.g. propensity score matching), but it also can be useful for design stage applications such as blocking. For more on the application and its implementation, see:
optmatch is available on CRAN:
There are two different packages implementing the actual solver which can be used.
- The default, starting in 0.10.0, is the LEMON graph library’s Min Cost Flow solver, implemented in the rlemon package.
- In previous versions, the default was the RELAX-IV solver, which is now implemented in the rrelaxiv package.
Users wishing to utilize the RELAX-IV solver must install rrelaxiv separately, see that page for details. Once installed, RELAX-IV becomes the default solver.
The LEMON solver has four separate algorithms implemented, Cycle Cancelling (the default), Network Simplex, Cost Scaling, and Capacity Scaling. Each has its own trade-offs and performance quirks. See
help(fullmatch) for details of how to choose which is being used.
In addition to the optimal full matching algorithm, the package contains useful functions for generating distance specifications, combining and editing distance specifications, and summarizing and displaying matches. This walk through shows how to use these tools in your matching workflow.
Before we start, let’s generate some simulated data. We will have two groups, the “treated” and “control” groups. Without our knowledge, nature assigned units from a pool into one of these two groups. The probability of being a treated unit depends on some covariates. In the vector
Z, let a 1 denote treated units and 0 denote control units
set.seed(20120111) # set this to get the exact same answers as I do n <- 26 # chosen so we can divide the alphabet in half W <- data.frame(w1 = rbeta(n, 4, 2), w2 = rbinom(n, 1, p = .33)) # nature assigns to treatment tmp <- numeric(n) tmp[sample(1:n, prob = W$w1^(1 + W$w2), size = n/2)] <- 1 W$z <- tmp # for convenience, let's give the treated units capital letter names tmp <- character(n) tmp[W$z == 1] <- LETTERS[1:(n/2)] tmp[W$z == 0] <- letters[(26 - n/2 + 1):26] rownames(W) <- tmp
As we can see with a simple table and plot, these groups are not balanced on the covariates, as they would be (in expectation) with a randomly assigned treatment.
The next steps use the covariates to pair up similar treated and control units. For more on assessing the amount and severity of imbalance between groups on observed covariates, see the RItools
These two groups are different, but how different are individual treated units from individual control units? In answering this question, we will produce several distance specifications: matrices of treated units (rows) by control units (columns) with entries denoting distances. optmatch provides several ways of generating these matrices so that you don’t have to do it by hand.
Let’s begin with a simple Euclidean distance on the space defined by
method argument tells the
match_on function how to compute the distances over the space defined by the formula. The default method extends the simple Euclidean distance by rescaling the distances by the covariance of the variables, the Mahalanobis distance:
You can write additional distance computation functions. See the documentation for
match_on for more details on how to create these functions.
To create distances, we could also try regressing the treatment indicator on the covariates and computing the difference distance for each treated and control pair. To make this process easier,
match_on has methods for
glm objects (and for big data problems,
glm method is a wrapper around the
numeric method for
numeric method takes a vector of scores (for example, the linear prediction for each unit from the model) and a vector indicating treatment status (
z) for each unit. This method returns the absolute difference between each treated and control pair on their scores (additionally, the
glm method rescales the data before invoking the
numeric method). If you wish to fit a “caliper” to your distance matrix, a hard limit on allowed distances between treated and control units, you can pass a
caliper argument, a scalar numeric value. Any treated and control pair that is larger than the caliper value will be replaced by
Inf, an unmatchable value. The
caliper argument also applies to
glm method. Calipers are covered in more detail in the next section.
The final convenience method of
match_on is using an arbitrary function. This function is probably most useful for advanced users of optmatch. See the documentation of the
match_on function for more details on how to write your own arbitrary computation functions.
We have created several representations of the matching problem, using Euclidean distance, Mahalanobis distance, the estimated propensity score, and an arbitrary function. We can combine these distances into single metric using standard arithmetic functions:
You may find it convenient to work in smaller pieces at first and then stitch the results together into a bigger distance. The
cbind functions let us add additional treated and control entries to a distance specification for each of the existing control and treated units, respectively. For example, we might want to combine a Mahalanobis score for units
s with a propensity score for units
exactMatch function creates “stratified” matching problems, in which there are subgroups that are completely separate. Such matching problems are often much easier to solve than problems where a treated unit could be connected to any control unit.
There is another method for creating reduced matching problems. The
caliper function compares each entry in an existing distance specification and disallows any that are larger than a specified value. For example, we can trim our previous combined distance to anything smaller than the median value:
exactMatch function, the results of
caliper used the sparse matrix representation mentioned above, so can be very efficient for large, sparse problems. As noted previously, if using the
numeric methods of
match_on, passing the caliper’s width in the
caliper argument can be more efficient.
In addition to the space advantages of only storing the finite entries in a sparse matrix, the results of
caliper can be used to speed up computation of new distances. The
match_on function that we saw earlier has an argument called
within that helps filter the resulting computation to only the finite entries in the
within matrix. Since
caliper use finite entries denote valid pairs, they make excellent sources of the
Instead of creating the entire Euclidean distance matrix and then filtering out cross-strata matches, we use the results of
exactMatch to compute only the interesting cases:
Users of previous versions of optmatch may notice that the
within argument is similar to the old
structure.formula argument. Like
structure.formula focused distance on within strata pairs. Unlike
within argument allows using any distance specification as an argument, including those created with
caliper. For example, here is the Mahalanobis distance computed only for units that differ by less than one on the propensity score.
Now that we have generated several distances specifications, let’s put them to use. Here is the simplest way to evaluate all distances specifications:
The result of the matching process is a named factor, where the names correspond to the units (both treated and control) and the levels of the factors are the matched groups. Including the
data argument is highly recommended. This argument will make sure that the result of
fullmatch will be in the same order as the original
data.frame that was used to build the distance specification. This will make appending the results of
fullmatch on to the original
data.frame much more convenient.
fullmatch function as several arguments for fine tuning the allowed ratio of treatment to control units in a match, and how much of the pool to throw away as unmatchable. One common pattern for these arguments are pairs: one treated to one control unit. Not every distance specification is amendable to this pattern (e.g. when there are more treated units than control units in
exactMatch created stratum). However, it can be done with the Mahalanobis distance matrix we created earlier:
pairmatch also allows fine tuning the ratio of matches to allow larger groupings. It is can be helpful as it computes what percentage of the group to throw away, giving better odds of successfully finding a matching solution.
Once one has generated a match, you may wish to view the results. The results of calls to
pairmatch produce optmatch objects (specialized factors). This object has a special option to the
If you wish to join the match factor back to the original
Make sure to include the
data argument to
pairmatch, otherwise results are not guaranteed to be in the same order as your original
This section will help you get the latest development version of optmatch and start using the latest features. Before starting, you should know which branch you wish to install. Currently, the “master” branch is the main code base. Additional features are added in their own branches. A list of branches is available at (the optmatch project page)[https://github.com/markmfredrickson/optmatch].
We recommend using
dev_mode from the
devtools package to install in-development version of the package so that you can keep the current CRAN version as the primary package. Activating
dev_mode creates a secondary library of packages which can only be accessed while in
dev_mode. Packages normally installed can still be used, but if different versions are installed normally and in
dev_mode version takes precedent if in
Install and load the
Note that the prompt changes from
d> to let you know you’re in
dev_mode. Now choose the development branch you want to use. To install
Either way, the package is then loaded in the usual fashion, provided you’re still in
Once you’ve done this you can disable
dev_mode as follows
The development version of the package remains loaded.
Note that if you load the package – ie, enter
library(optmatch) (when the package hasn’t already been loaded otherwise) – while not in
dev_mode, then you’ll get whatever version of the package may be installed in your library tree, not this development version.
If you want to switch between versions of optmatch, we suggest re-starting R.
You may use RStudio to develop for optmatch, by opening the
optmatch.Rproj file. We suggest you ensure all required dependencies are installed by running
devtools::install_deps(dependencies = TRUE)
We prefer changes that include unit tests demonstrating the problem or showing how the new feature should be added. The test suite uses the testthat package to write and run tests. (Please ensure you have the latest version of testthat (or at least v0.11.0), as older versions stored the tests in a different directory, and may not test properly.) See the
tests/testthat directory for examples. You can run the test suite via Build -> Test Package.
New features should include inline Roxygen documentation. You can generate all
.Rd documents from the
Roxygen code using Build -> Document.
Finally, you can use Build -> Build and Reload or Build -> Clean and Rebuild to load an updated version of optmatch in your current RStudio session. Alternatively, to install the developed version permanently, use Build -> Build Binary Version, followed by
You can revert back to the current CRAN version by
Note: If you are building for release on CRAN, you need to ensure vignettes are compacted. This should be enabled automatically in the .Rproj file, but if not see this stackoverflow answer for some concerns about dealing with this with RStudio.
If you prefer not to use RStudio, you can develop using Make.
make test: Run the full test suite.
make document: Update all documentation from Roxygen inline comments.
make interactive: Start up an interactive session with optmatch loaded. (
make interactive-emacswill start the session inside emacs.)
make check: Run
R CMD checkon the package
make build: Build a binary package.
make vignette: Builds any vignettes in
make clean: Removes files built by
make check. Should not be generally necessary, but can be useful for debugging.
make release: Starts an interactive R session to submit a release to CRAN.
When your change is ready, make a pull request on github.