Genetic Matching


This function finds optimal balance using multivariate matching where a genetic search algorithm determines the weight each covariate is given. Balance is determined by examining cumulative probability distribution functions of a variety of standardized statistics. By default, these statistics include t-tests and Kolmogorov-Smirnov tests. A variety of descriptive statistics based on empirical-QQ (eQQ) plots can also be used or any user provided measure of balance. The statistics are not used to conduct formal hypothesis tests, because no measure of balance is a monotonic function of bias and because balance should be maximized without limit. The object returned by GenMatch can be supplied to the Match function (via the Weight.matrix option) to obtain causal estimates. GenMatch uses genoud to perform the genetic search. Using the cluster option, one may use multiple computers, CPUs or cores to perform parallel computations.


GenMatch(Tr, X, BalanceMatrix=X, estimand="ATT", M=1, weights=NULL,
         pop.size = 100, max.generations=100,
         wait.generations=4, hard.generation.limit=FALSE,
         exact=NULL, caliper=NULL, replace=TRUE, ties=TRUE,
         CommonSupport=FALSE, nboots=0, ks=TRUE, verbose=FALSE,
         min.weight=0, max.weight=1000,
         Domains=NULL, print.level=2,
         paired=TRUE, loss=1,
         cluster=FALSE, balance=TRUE, ...)



A vector indicating the observations which are in the treatment regime and those which are not. This can either be a logical vector or a real vector where 0 denotes control and 1 denotes treatment.


A matrix containing the variables we wish to match on. This matrix may contain the actual observed covariates or the propensity score or a combination of both.


A matrix containing the variables we wish to achieve balance on. This is by default equal to X, but it can in principle be a matrix which contains more or less variables than X or variables which are transformed in various ways. See the examples.


A character string for the estimand. The default estimand is "ATT", the sample average treatment effect for the treated. "ATE" is the sample average treatment effect, and "ATC" is the sample average treatment effect for the controls.


A scalar for the number of matches which should be found. The default is one-to-one matching. Also see the ties option.


A vector the same length as Y which provides observation specific weights.


Population Size. This is the number of individuals genoud uses to solve the optimization problem. The theorems proving that genetic algorithms find good solutions are asymptotic in population size. Therefore, it is important that this value not be small. See genoud for more details.


Maximum Generations. This is the maximum number of generations that genoud will run when optimizing. This is a soft limit. The maximum generation limit will be binding only if hard.generation.limit has been set equal to TRUE. Otherwise, wait.generations controls when optimization stops. See genoud for more details.


If there is no improvement in the objective function in this number of generations, optimization will stop. The other options controlling termination are max.generations and hard.generation.limit.


This logical variable determines if the max.generations variable is a binding constraint. If hard.generation.limit is FALSE, then the algorithm may exceed the max.generations count if the objective function has improved within a given number of generations (determined by wait.generations).


This vector's length is equal to the number of variables in X. This vector contains the starting weights each of the variables is given. The starting.values vector is a way for the user to insert one individual into the starting population. genoud will randomly create the other individuals. These values correspond to the diagonal of the Weight.matrix as described in detail in the Match function.


The balance metric GenMatch should optimize. The user may choose from the following or provide a function:
pvals: maximize the p.values from (paired) t-tests and Kolmogorov-Smirnov tests conducted for each column in BalanceMatrix. Lexical optimization is conducted—see the loss option for details.
qqmean.mean: calculate the mean standardized difference in the eQQ plot for each variable. Minimize the mean of these differences across variables.
qqmean.max: calculate the mean standardized difference in the eQQ plot for each variable. Minimize the maximum of these differences across variables. Lexical optimization is conducted.
qqmedian.mean: calculate the median standardized difference in the eQQ plot for each variable. Minimize the median of these differences across variables.
qqmedian.max: calculate the median standardized difference in the eQQ plot for each variable. Minimize the maximum of these differences across variables. Lexical optimization is conducted.
qqmax.mean: calculate the maximum standardized difference in the eQQ plot for each variable. Minimize the mean of these differences across variables.
qqmax.max: calculate the maximum standardized difference in the eQQ plot for each variable. Minimize the maximum of these differences across variables. Lexical optimization is conducted.
Users may provide their own fit.func. The name of the user provided function should not be backquoted or quoted. This function needs to return a fit value that will be minimized, by lexical optimization if more than one fit value is returned. The function should expect two arguments. The first being the matches object returned by GenMatch—see below. And the second being a matrix which contains the variables to be balanced—i.e., the BalanceMatrix the user provided to GenMatch. For an example see


This variable controls if genoud sets up a memory matrix. Such a matrix ensures that genoud will request the fitness evaluation of a given set of parameters only once. The variable may be TRUE or FALSE. If it is FALSE, genoud will be aggressive in conserving memory. The most significant negative implication of this variable being set to FALSE is that genoud will no longer maintain a memory matrix of all evaluated individuals. Therefore, genoud may request evaluations which it has previously requested. When the number variables in X is large, the memory matrix consumes a large amount of RAM.

genoud's memory matrix will require significantly less memory if the user sets hard.generation.limit equal to TRUE. Doing this is a good way of conserving memory while still making use of the memory matrix structure.


A logical scalar or vector for whether exact matching should be done. If a logical scalar is provided, that logical value is applied to all covariates in X. If a logical vector is provided, a logical value should be provided for each covariate in X. Using a logical vector allows the user to specify exact matching for some but not other variables. When exact matches are not found, observations are dropped. distance.tolerance determines what is considered to be an exact match. The exact option takes precedence over the caliper option. Obviously, if exact matching is done using all of the covariates, one should not be using GenMatch unless the distance.tolerance has been set unusually high.


A scalar or vector denoting the caliper(s) which should be used when matching. A caliper is the distance which is acceptable for any match. Observations which are outside of the caliper are dropped. If a scalar caliper is provided, this caliper is used for all covariates in X. If a vector of calipers is provided, a caliper value should be provided for each covariate in X. The caliper is interpreted to be in standardized units. For example, caliper=.25 means that all matches not equal to or within .25 standard deviations of each covariate in X are dropped. The ecaliper object which is returned by GenMatch shows the enforced caliper on the scale of the X variables. Note that dropping observations generally changes the quantity being estimated.


A logical flag for whether matching should be done with replacement. Note that if FALSE, the order of matches generally matters. Matches will be found in the same order as the data are sorted. Thus, the match(es) for the first observation will be found first, the match(es) for the second observation will be found second, etc. Matching without replacement will generally increase bias. Ties are randomly broken when replace==FALSE—see the ties option for details.


A logical flag for whether ties should be handled deterministically. By default ties==TRUE. If, for example, one treated observation matches more than one control observation, the matched dataset will include the multiple matched control observations and the matched data will be weighted to reflect the multiple matches. The sum of the weighted observations will still equal the original number of observations. If ties==FALSE, ties will be randomly broken. If the dataset is large and there are many ties, setting ties=FALSE often results in a large speedup. Whether two potential matches are close enough to be considered tied, is controlled by the distance.tolerance option.


This logical flag implements the usual procedure by which observations outside of the common support of a variable (usually the propensity score) across treatment and control groups are discarded. The caliper option is to be preferred to this option because CommonSupport, consistent with the literature, only drops outliers and leaves inliers while the caliper option drops both. If CommonSupport==TRUE, common support will be enforced on the first variable in the X matrix. Note that dropping observations generally changes the quantity being estimated. Use of this option renders it impossible to use the returned object matches to reconstruct the matched dataset. Seriously, don't use this option; use the caliper option instead.


The number of bootstrap samples to be run for the ks test. By default this option is set to zero so no bootstraps are done. See ks.boot for additional details.


A logical flag for if the univariate bootstrap Kolmogorov-Smirnov (KS) test should be calculated. If the ks option is set to true, the univariate KS test is calculated for all non-dichotomous variables. The bootstrap KS test is consistent even for non-continuous variables. By default, the bootstrap KS test is not used. To change this see the nboots option. If a given variable is dichotomous, a t-test is used even if the KS test is requested. See ks.boot for additional details.


A logical flag for whether details of each fitness evaluation should be printed. Verbose is set to FALSE if the cluster option is used.


This is a scalar which is used to determine if distances between two observations are different from zero. Values less than distance.tolerance are deemed to be equal to zero. This option can be used to perform a type of optimal matching.


This is a scalar which is used to determine numerical tolerances. This option is used by numerical routines such as those used to determine if a matrix is singular.


This is the minimum weight any variable may be given.


This is the maximum weight any variable may be given.


This is a ncol(X) *2 matrix. The first column is the lower bound, and the second column is the upper bound for each variable over which genoud will search for weights. If the user does not provide this matrix, the bounds for each variable will be determined by the min.weight and max.weight options.


This option controls the level of printing. There are four possible levels: 0 (minimal printing), 1 (normal), 2 (detailed), and 3 (debug). If level 2 is selected, GenMatch will print details about the population at each generation, including the best individual found so far. If debug level printing is requested, details of the genoud population are printed in the "" file which is located in the temporary R directory returned by the tempdir function. See the project.path option for more details. Because GenMatch runs may take a long time, it is important for the user to receive feedback. Hence, print level 2 has been set as the default.


This is the path of the genoud project file. By default no file is produced unless print.level=3. In that case, genoud places its output in a file called "" located in the temporary directory provided by tempdir. If a file path is provided to the project.path option, a file will be created regardless of the print.level. The behavior of the project file, however, will depend on the print.level chosen. If the print.level variable is set to 1, then the project file is rewritten after each generation. Therefore, only the currently fully completed generation is included in the file. If the print.level variable is set to 2 or higher, then each new generation is simply appended to the project file. No project file is generated for print.level=0.


A flag for whether the paired t.test should be used when determining balance.


The loss function to be optimized. The default value, 1, implies "lexical" optimization: all of the balance statistics will be sorted from the most discrepant to the least and weights will be picked which minimize the maximum discrepancy. If multiple sets of weights result in the same maximum discrepancy, then the second largest discrepancy is examined to choose the best weights. The processes continues iteratively until ties are broken.

If the value of 2 is used, then only the maximum discrepancy is examined. This was the default behavior prior to version 1.0. The user may also pass in any function she desires. Note that the option 1 corresponds to the sort function and option 2 to the min function. Any user specified function should expect a vector of balance statistics ("p-values") and it should return either a vector of values (in which case "lexical" optimization will be done) or a scalar value (which will be maximized). Some possible alternative functions are mean or median.


By default, floating-point weights are considered. If this option is set to TRUE, search will be done over integer weights. Note that before version 4.1, the default was to use integer weights.


A matrix which restricts the possible matches. This matrix has one row for each restriction and three columns. The first two columns contain the two observation numbers which are to be restricted (for example 4 and 20), and the third column is the restriction imposed on the observation-pair. Negative numbers in the third column imply that the two observations cannot be matched under any circumstances, and positive numbers are passed on as the distance between the two observations for the matching algorithm. The most commonly used positive restriction is 0 which implies that the two observations will always be matched.

Exclusion restriction are even more common. For example, if we want to exclude the observation pair 4 and 20 and the pair 6 and 55 from being matched, the restrict matrix would be: restrict=rbind(c(4,20,-1),c(6,55,-1))


This can either be an object of the 'cluster' class returned by one of the makeCluster commands in the parallel package or a vector of machine names so that GenMatch can setup the cluster automatically. If it is the latter, the vector should look like:
This vector would create a cluster with four nodes: one on the localhost another on "deckard" and two on the machine named "musil". Two nodes on a given machine make sense if the machine has two or more chips/cores. GenMatch will setup a SOCK cluster by a call to makePSOCKcluster. This will require the user to type in her password for each node as the cluster is by default created via ssh. One can add on usernames to the machine name if it differs from the current shell: "username@musil". Other cluster types, such as PVM and MPI, which do not require passwords, can be created by directly calling makeCluster, and then passing the returned cluster object to GenMatch. For an example of how to manually setup up a cluster with a direct call to makeCluster see For an example of how to get around a firewall by ssh tunneling see:


This logical flag controls if load balancing is done across the cluster. Load balancing can result in better cluster utilization; however, increased communication can reduce performance. This option is best used if each individual call to Match takes at least several minutes to calculate or if the nodes in the cluster vary significantly in their performance. If cluster==FALSE, this option has no effect.


Other options which are passed on to genoud.



The fit values at the solution. By default, this is a vector of p-values sorted from the smallest to the largest. There will generally be twice as many p-values as there are variables in BalanceMatrix, unless there are dichotomous variables in this matrix. There is one p-value for each covariate in BalanceMatrix which is the result of a paired t-test and another p-value for each non-dichotomous variable in BalanceMatrix which is the result of a Kolmogorov-Smirnov test. Recall that these p-values cannot be interpreted as hypothesis tests. They are simply measures of balance.


A vector of the weights given to each variable in X.


A matrix whose diagonal corresponds to the weight given to each variable in X. This object corresponds to the Weight.matrix in the Match function.


A matrix where the first column contains the row numbers of the treated observations in the matched dataset. The second column contains the row numbers of the control observations. And the third column contains the weight that each matched pair is given. These objects may not correspond respectively to the index.treated, index.control and weights objects which are returned by Match because they may be ordered in a different way. Therefore, end users should use the objects returned by Match because those are ordered in the way that users expect.


The size of the enforced caliper on the scale of the X variables. This object has the same length as the number of covariates in X.


Jasjeet S. Sekhon, UC Berkeley,,


Sekhon, Jasjeet S. 2011. "Multivariate and Propensity Score Matching Software with Automated Balance Optimization.” Journal of Statistical Software 42(7): 1-52.

Diamond, Alexis and Jasjeet S. Sekhon. 2013. "Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies.” Review of Economics and Statistics. 95 (3): 932–945.

Sekhon, Jasjeet Singh and Walter R. Mebane, Jr. 1998. "Genetic Optimization Using Derivatives: Theory and Application to Nonlinear Models.” Political Analysis, 7: 187-210.

See Also

Also see Match, summary.Match, MatchBalance, genoud, balanceUV, qqstats, ks.boot, GerberGreenImai, lalonde



#The covariates we want to match on
X = cbind(age, educ, black, hisp, married, nodegr, u74, u75, re75, re74)

#The covariates we want to obtain balance on
BalanceMat <- cbind(age, educ, black, hisp, married, nodegr, u74, u75, re75, re74,

#Let's call GenMatch() to find the optimal weight to give each
#covariate in 'X' so as we have achieved balance on the covariates in
#'BalanceMat'. This is only an example so we want GenMatch to be quick
#so the population size has been set to be only 16 via the 'pop.size'
#option. This is *WAY* too small for actual problems.
#For details see
genout <- GenMatch(Tr=treat, X=X, BalanceMatrix=BalanceMat, estimand="ATE", M=1,
                   pop.size=16, max.generations=10, wait.generations=1)

#The outcome variable

# Now that GenMatch() has found the optimal weights, let's estimate
# our causal effect of interest using those weights
mout <- Match(Y=Y, Tr=treat, X=X, estimand="ATE", Weight.matrix=genout)

#Let's determine if balance has actually been obtained on the variables of interest
mb <- MatchBalance(treat~age +educ+black+ hisp+ married+ nodegr+ u74+ u75+
                   re75+ re74+ I(re74*re75),
                   match.out=mout, nboots=500)

# For more examples see:
comments powered by Disqus