Version: 4.10-15

Date: 2024年10月14日

Title: Multivariate and Propensity Score Matching with Balance Optimization

Maintainer: Jasjeet Singh Sekhon <jas.sekhon@yale.edu>

Description: Provides functions for multivariate and propensity score matching and for finding optimal balance based on a genetic search algorithm. A variety of univariate and multivariate metrics to determine if balance has been obtained are also provided. For details, see the paper by Jasjeet Sekhon (2007, <doi:10.18637/jss.v042.i07>).

Depends: R (≥ 2.6.0), MASS (≥ 7.2-1), graphics, grDevices, stats

Suggests: parallel, rgenoud (≥ 2.12), testthat

License: GPL-3

URL: https://github.com/JasjeetSekhon/Matching

NeedsCompilation: yes

RoxygenNote: 7.2.1

Packaged: 2024年10月14日 13:11:12 UTC; theosaa

Author: Jasjeet Singh Sekhon [aut, cre], Theo Saarinen [aut]

Repository: CRAN

Date/Publication: 2024年10月14日 14:20:02 UTC

GenMatch(Tr, X, BalanceMatrix=X, estimand="ATT", M=1, weights=NULL,
 pop.size = 100, max.generations=100,
 wait.generations=4, hard.generation.limit=FALSE,
 starting.values=rep(1,ncol(X)),
 fit.func="pvals",
 MemoryMatrix=TRUE,
 exact=NULL, caliper=NULL, replace=TRUE, ties=TRUE,
 CommonSupport=FALSE, nboots=0, ks=TRUE, verbose=FALSE,
 distance.tolerance=1e-05,
 tolerance=sqrt(.Machine$double.eps),
 min.weight=0, max.weight=1000,
 Domains=NULL, print.level=2,
 project.path=NULL,
 paired=TRUE, loss=1,
 data.type.integer=FALSE,
 restrict=NULL,
 cluster=FALSE, balance=TRUE, ...)

Tr

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.

X

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.

BalanceMatrix

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.

estimand

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.

M

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

weights

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

pop.size

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.

max.generations

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.

wait.generations

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.

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).

starting.values

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.

fit.func

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 https://www.jsekhon.com.

MemoryMatrix

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.

exact

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.

caliper

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.

replace

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.

ties

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.

CommonSupport

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.

nboots

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.

ks

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.

verbose

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

distance.tolerance

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.

tolerance

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.

min.weight

This is the minimum weight any variable may be given.

max.weight

This is the maximum weight any variable may be given.

Domains

This is a ncol(X) \times 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.

print.level

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 "genoud.pro" 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.

project.path

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 "genoud.pro" 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.

paired

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

loss

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 .

data.type.integer

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.

restrict

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))

cluster

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:
c("localhost","musil","musil","deckard").
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 https://www.jsekhon.com. For an example of how to get around a firewall by ssh tunneling see: https://www.jsekhon.com.

balance

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 .

value

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.

par

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

Weight.matrix

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.

matches

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.

ecaliper

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.

data(lalonde)
attach(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,
 I(re74*re75))
#
#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 https://www.jsekhon.com.
#
genout <- GenMatch(Tr=treat, X=X, BalanceMatrix=BalanceMat, estimand="ATE", M=1,
 pop.size=16, max.generations=10, wait.generations=1)
#The outcome variable
Y=re78/1000
#
# 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)
summary(mout)
# 
#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: https://www.jsekhon.com.

data(GerberGreenImai)

Match(Y=NULL, Tr, X, Z = X, V = rep(1, length(Y)), estimand = "ATT", M = 1,
 BiasAdjust = FALSE, exact = NULL, caliper = NULL, replace=TRUE, ties=TRUE,
 CommonSupport=FALSE,Weight = 1, Weight.matrix = NULL, weights = NULL,
 Var.calc = 0, sample = FALSE, restrict=NULL, match.out = NULL,
 distance.tolerance = 1e-05, tolerance=sqrt(.Machine$double.eps),
 version="standard")

Y

A vector containing the outcome of interest. Missing values are not allowed. An outcome vector is not required because the matches generated will be the same regardless of the outcomes. Of course, without any outcomes no causal effect estimates will be produced, only a matched dataset.

Tr

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.

X

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. All columns of this matrix must have positive variance or Match will return an error.

Z

A matrix containing the covariates for which we wish to make bias adjustments.

V

A matrix containing the covariates for which the variance of the causal effect may vary. Also see the Var.calc option, which takes precedence.

estimand

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.

M

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

BiasAdjust

A logical scalar for whether regression adjustment should be used. See the Z matrix.

exact

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.

caliper

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. Note that dropping observations generally changes the quantity being estimated.

replace

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.

ties

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.

CommonSupport

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 objects index.treated and index.control to reconstruct the matched dataset. The returned object mdata will, however, still contain the matched dataset. Seriously, don't use this option; use the caliper option instead.

Weight

A scalar for the type of weighting scheme the matching algorithm should use when weighting each of the covariates in X. The default value of 1 denotes that weights are equal to the inverse of the variances. 2 denotes the Mahalanobis distance metric, and 3 denotes that the user will supply a weight matrix (Weight.matrix). Note that if the user supplies a Weight.matrix, Weight will be automatically set to be equal to 3.

Weight.matrix

This matrix denotes the weights the matching algorithm uses when weighting each of the covariates in X—see the Weight option. This square matrix should have as many columns as the number of columns of the X matrix. This matrix is usually provided by a call to the GenMatch function which finds the optimal weight each variable should be given so as to achieve balance on the covariates.

For most uses, this matrix has zeros in the off-diagonal cells. This matrix can be used to weight some variables more than others. For example, if X contains three variables and we want to match as best as we can on the first, the following would work well:
> Weight.matrix <- diag(3)
> Weight.matrix[1,1] <- 1000/var(X[,1])
> Weight.matrix[2,2] <- 1/var(X[,2])
> Weight.matrix[3,3] <- 1/var(X[,3])
This code changes the weights implied by the inverse of the variances by multiplying the first variable by a 1000 so that it is highly weighted. In order to enforce exact matching see the exact and caliper options.

weights

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

Var.calc

A scalar for the variance estimate that should be used. By default Var.calc=0 which means that homoscedasticity is assumed. For values of Var.calc > 0, robust variances are calculated using Var.calc matches.

sample

A logical flag for whether the population or sample variance is returned.

distance.tolerance

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

tolerance

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.

restrict

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 restrictions 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))

match.out

The return object from a previous call to Match. If this object is provided, then Match will use the matches found by the previous invocation of the function. Hence, Match will run faster. This is useful when the treatment does not vary across calls to Match and one wants to use the same set of matches as found before. This often occurs when one is trying to estimate the causal effect of the same treatment (Tr) on different outcomes (Y). When using this option, be careful to use the same arguments as used for the previous invocation of Match unless you know exactly what you are doing.

version

The version of the code to be used. The "fast" C/C++ version of the code does not calculate Abadie-Imbens standard errors. Additional speed can be obtained by setting ties=FALSE or replace=FALSE if the dataset is large and/or has many ties. The "legacy" version of the code does not make a call to an optimized C/C++ library and is included only for historical compatibility. The "fast" version of the code is significantly faster than the "standard" version for large datasets, and the "legacy" version is much slower than either of the other two.

est

The estimated average causal effect.

se

The Abadie-Imbens standard error. This standard error has correct coverage if X consists of either covariates or a known propensity score because it takes into account the uncertainty of the matching procedure. If an estimated propensity score is used, the uncertainty involved in its estimation is not accounted for although the uncertainty of the matching procedure itself still is.

est.noadj

The estimated average causal effect without any BiasAdjust. If BiasAdjust is not requested, this is the same as est.

se.standard

The usual standard error. This is the standard error calculated on the matched data using the usual method of calculating the difference of means (between treated and control) weighted by the observation weights provided by weights. Note that the standard error provided by se takes into account the uncertainty of the matching procedure while se.standard does not. Neither se nor se.standard take into account the uncertainty of estimating a propensity score. se.standard does not take into account any BiasAdjust. Summary of both types of standard error results can be requested by setting the full=TRUE flag when using the summary.Match function on the object returned by Match.

se.cond

The conditional standard error. The practitioner should not generally use this.

mdata

A list which contains the matched datasets produced by Match. Three datasets are included in this list: Y, Tr and X.

index.treated

A vector containing the observation numbers from the original dataset for the treated observations in the matched dataset. This index in conjunction with index.control can be used to recover the matched dataset produced by Match. For example, the X matrix used by Match can be recovered by rbind(X[index.treated,],X[index.control,]). The user should generally just examine the output of mdata.

index.control

A vector containing the observation numbers from the original data for the control observations in the matched data. This index in conjunction with index.treated can be used to recover the matched dataset produced by Match. For example, the X matrix used by Match can be recovered by rbind(X[index.treated,],X[index.control,]). The user should generally just examine the output of mdata.

index.dropped

A vector containing the observation numbers from the original data which were dropped (if any) in the matched dataset because of various options such as caliper and exact. If no observations were dropped, this index will be NULL.

weights

A vector of weights. There is one weight for each matched-pair in the matched dataset. If all of the observations had a weight of 1 on input, then each matched-pair will have a weight of 1 on output if there are no ties.

orig.nobs

The original number of observations in the dataset.

orig.wnobs

The original number of weighted observations in the dataset.

orig.treated.nobs

The original number of treated observations (unweighted).

nobs

The number of observations in the matched dataset.

wnobs

The number of weighted observations in the matched dataset.

caliper

The caliper which was used.

ecaliper

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.

exact

The value of the exact function argument.

ndrops

The number of weighted observations which were dropped either because of caliper or exact matching. This number, unlike ndrops.matches, takes into account observation specific weights which the user may have provided via the weights argument.

ndrops.matches

The number of matches which were dropped either because of caliper or exact matching.

# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option defaults to ATT).
#
rr <- Match(Y=Y, Tr=Tr, X=X, M=1);
summary(rr)
# Let's check the covariate balance
# 'nboots' is set to small values in the interest of speed.
# Please increase to at least 500 each for publication quality p-values.
mb <- MatchBalance(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, data=lalonde, match.out=rr, nboots=10)

MatchBalance(formul, data = NULL, match.out = NULL, ks = TRUE,
 nboots=500, weights=NULL, digits=5, paired=TRUE, print.level=1)

formul

This formula does not estimate any model. The formula is simply an efficient way to use the R modeling language to list the variables we wish to obtain univariate balance statistics for. The dependent variable in the formula is usually the treatment indicator. One should include many functions of the observed covariates. Generally, one should request balance statistics on more higher-order terms and interactions than were used to conduct the matching itself.

data

A data frame which contains all of the variables in the formula. If a data frame is not provided, the variables are obtained via lexical scoping.

match.out

The output object from the Match function. If this output is included, MatchBalance will provide balance statistics for both before and after matching. Otherwise balance statistics will only be reported for the raw unmatched data.

ks

A logical flag for whether 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. See ks.boot for more details.

weights

An optional vector of observation specific weights.

nboots

The number of bootstrap samples to be run. If zero, no bootstraps are done. Bootstrapping is highly recommended because the bootstrapped Kolmogorov-Smirnov test provides correct coverage even when the distributions being compared are not continuous. At least 500 nboots (preferably 1000) are recommended for publication quality p-values.

digits

The number of significant digits that should be displayed.

paired

A flag for whether the paired t.test should be used after matching. Regardless of the value of this option, an unpaired t.test is done for the unmatched data because it is assumed that the unmatched data were not generated by a paired experiment.

print.level

The amount of printing to be done. If zero, there is no printing. If one, the results are summarized. If two, details of the computations are printed.

BeforeMatching

A list containing the before matching univariate balance statistics. That is, a list containing the results of the balanceUV function applied to all of the covariates described in formul. Note that the univariate test results for all of the variables in formul are printed if verbose > 0.

AfterMatching

A list containing the after matching univariate balance statistics. That is, a list containing the results of the balanceUV function applied to all of the covariates described in formul. Note that the univariate test results for all of the variables in formul are printed if verbose > 0. This object is NULL, if no matched dataset was provided.

BMsmallest.p.value

The smallest p.value found across all of the before matching balance tests (including t-tests and KS-tests.

BMsmallestVarName

The name of the variable with the BMsmallest.p.value (a vector in case of ties).

BMsmallestVarNumber

The number of the variable with the BMsmallest.p.value (a vector in case of ties).

AMsmallest.p.value

The smallest p.value found across all of the after matching balance tests (including t-tests and KS-tests.

AMsmallestVarName

The name of the variable with the AMsmallest.p.value (a vector in case of ties).

AMsmallestVarNumber

The number of the variable with the AMsmallest.p.value (a vector in case of ties).

#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr <- Match(Y=Y,Tr=Tr,X=X,M=1);
#Let's summarize the output
summary(rr)
# Let's check the covariate balance
# 'nboots' is set to small values in the interest of speed.
# Please increase to at least 500 each for publication quality p-values.
mb <- MatchBalance(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, data=lalonde, match.out=rr, nboots=10)

Matchby(Y, Tr, X, by, estimand = "ATT", M = 1, ties=FALSE, replace=TRUE,
 exact = NULL, caliper = NULL, AI=FALSE, Var.calc=0,
 Weight = 1, Weight.matrix = NULL, distance.tolerance = 1e-05,
 tolerance = sqrt(.Machine$double.eps), print.level=1, version="Matchby", ...)

Y

A vector containing the outcome of interest. Missing values are not allowed.

Tr

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.

X

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.

by

A "factor" in the sense that as.factor(by) defines the grouping, or a list of such factors in which case their interaction is used for the grouping.

estimand

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 (for all), and "ATC" is the sample average treatment effect for the controls.

M

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

ties

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.

replace

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 is sorted. Thus, the match(es) for the first observation will be found first and then for the second etc. Matching without replacement will generally increase bias so it is not recommended. But if the dataset is large and there are many potential matches, setting replace=false often results in a large speedup and negligible or no bias. Ties are randomly broken when replace==FALSE—see the ties option for details.

exact

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 of 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.

caliper

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 provide 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.

AI

A logical flag for if the Abadie-Imbens standard error should be calculated. It is computationally expensive to calculate with large datasets. Matchby can only calculate AI SEs for ATT. To calculate AI errors with other estimands, please use the Match function. See the Var.calc option if one does not want to assume homoscedasticity.

Var.calc

A scalar for the variance estimate that should be used. By default Var.calc=0 which means that homoscedasticity is assumed. For values of Var.calc > 0, robust variances are calculated using Var.calc matches.

Weight

A scalar for the type of weighting scheme the matching algorithm should use when weighting each of the covariates in X. The default value of 1 denotes that weights are equal to the inverse of the variances. 2 denotes the Mahalanobis distance metric, and 3 denotes that the user will supply a weight matrix (Weight.matrix). Note that if the user supplies a Weight.matrix, Weight will be automatically set to be equal to 3.

Weight.matrix

This matrix denotes the weights the matching algorithm uses when weighting each of the covariates in X—see the Weight option. This square matrix should have as many columns as the number of columns of the X matrix. This matrix is usually provided by a call to the GenMatch function which finds the optimal weight each variable should be given so as to achieve balance on the covariates.

For most uses, this matrix has zeros in the off-diagonal cells. This matrix can be used to weight some variables more than others. For example, if X contains three variables and we want to match as best as we can on the first, the following would work well:
> Weight.matrix <- diag(3)
> Weight.matrix[1,1] <- 1000/var(X[,1])
> Weight.matrix[2,2] <- 1/var(X[,2])
> Weight.matrix[3,3] <- 1/var(X[,3])
This code changes the weights implied by the inverse of the variances by multiplying the first variable by a 1000 so that it is highly weighted. In order to enforce exact matching see the exact and caliper options.

distance.tolerance

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

tolerance

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.

print.level

The level of printing. Set to '0' to turn off printing.

version

The version of the code to be used. The "Matchby" C/C++ version of the code is the fastest, and the end-user should not change this option.

...

Additional arguments passed on to Match .

est

The estimated average causal effect.

se.standard

The usual standard error. This is the standard error calculated on the matched data using the usual method of calculating the difference of means (between treated and control) weighted so that ties are taken into account.

se

The Abadie-Imbens standard error. This is only calculated if the AI option is TRUE. This standard error has correct coverage if X consists of either covariates or a known propensity score because it takes into account the uncertainty of the matching procedure. If an estimated propensity score is used, the uncertainty involved in its estimation is not accounted for although the uncertainty of the matching procedure itself still is.

index.treated

A vector containing the observation numbers from the original dataset for the treated observations in the matched dataset. This index in conjunction with index.control can be used to recover the matched dataset produced by Matchby. For example, the X matrix used by Matchby can be recovered by rbind(X[index.treated,],X[index.control,]).

index.control

A vector containing the observation numbers from the original data for the control observations in the matched data. This index in conjunction with index.treated can be used to recover the matched dataset produced by Matchby. For example, the Y matrix for the matched dataset can be recovered by c(Y[index.treated],Y[index.control]).

weights

The weights for each observation in the matched dataset.

orig.nobs

The original number of observations in the dataset.

nobs

The number of observations in the matched dataset.

wnobs

The number of weighted observations in the matched dataset.

orig.treated.nobs

The original number of treated observations.

ndrops

The number of matches which were dropped because there were not enough observations in a given group and because of caliper and exact matching.

estimand

The estimand which was estimated.

version

The version of Match which was used.

#
# Match exactly by racial groups and then match using the propensity score within racial groups
#
data(lalonde)
#
# Estimate the Propensity Score
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, family=binomial, data=lalonde)
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
# one-to-one matching with replacement (the "M=1" option) after exactly
# matching on race using the 'by' option. Estimating the treatment
# effect on the treated (the "estimand" option defaults to ATT).
rr <- Matchby(Y=Y, Tr=Tr, X=X, by=lalonde$black, M=1);
summary(rr)
# Let's check the covariate balance
# 'nboots' is set to small values in the interest of speed.
# Please increase to at least 500 each for publication quality p-values.
mb <- MatchBalance(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, data=lalonde, match.out=rr, nboots=10)

balanceUV(Tr, Co, weights = rep(1, length(Co)), exact = FALSE, ks=FALSE,
 nboots = 1000, paired=TRUE, match=FALSE,
 weights.Tr=rep(1,length(Tr)), weights.Co=rep(1,length(Co)),
 estimand="ATT")

Tr

A vector containing the treatment observations.

Co

A vector containing the control observations.

weights

A vector containing the observation specific weights. Only use this option when the treatment and control observations are paired (as they are after matching).

exact

A logical flag indicating if the exact Wilcoxon test should be used instead of the test with a correction. See wilcox.test for details.

ks

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. See ks.boot for more details.

nboots

The number of bootstrap samples to be run for the ks test. If zero, no bootstraps are done. Bootstrapping is highly recommended because the bootstrapped Kolmogorov-Smirnov test only provides correct coverage even for non-continuous covariates. At least 500 nboots (preferably 1000) are recommended for publication quality p-values.

paired

A flag for if the paired t.test should be used.

match

A flag for if the Tr and Co objects are the result of a call to Match .

weights.Tr

A vector of weights for the treated observations.

weights.Co

A vector of weights for the control observations.

estimand

This determines if the standardized mean difference returned by the sdiff object is standardized by the variance of the treatment observations (which is done if the estimand is either "ATE" or "ATT") or by the variance of the control observations (which is done if the estimand is "ATC").

sdiff

This is the standardized difference between the treated and control units multiplied by 100. That is, 100 times the mean difference between treatment and control units divided by the standard deviation of the treatment observations alone if the estimand is either ATT or ATE. The variance of the control observations are used if the estimand is ATC.

sdiff.pooled

This is the standardized difference between the treated and control units multiplied by 100 using the pooled variance. That is, 100 times the mean difference between treatment and control units divided by the pooled standard deviation as in Rosenbaum and Rubin (1985).

mean.Tr

The mean of the treatment group.

mean.Co

The mean of the control group.

var.Tr

The variance of the treatment group.

var.Co

The variance of the control group.

p.value

The p-value from the two-sided weighted t.test .

var.ratio

var.Tr/var.Co.

ks

The object returned by ks.boot .

tt

The object returned by two-sided weighted t.test .

qqsummary

The return object from a call to qqstats with standardization—i.e., balance test based on the empirical CDF.

qqsummary.raw

The return object from a call to qqstats without standardization–i.e., balance tests based on the empirical QQ-plot which retain the scale of the variable.

data(lalonde)
attach(lalonde)
foo <- balanceUV(re75[treat==1],re75[treat!=1])
summary(foo)

ks.boot(Tr, Co, nboots=1000, alternative = c("two.sided","less","greater"),
 print.level=0)

Tr

A vector containing the treatment observations.

Co

A vector containing the control observations.

nboots

The number of bootstraps to be performed. These are, in fact, really Monte Carlo simulations which are preformed in order to determine the proper p-value from the empiric.

alternative

indicates the alternative hypothesis and must be one of '"two.sided"' (default), '"less"', or '"greater"'. You can specify just the initial letter. See ks.test for details.

print.level

If this is greater than 1, then the simulation count is printed out while the simulations are being done.

ks.boot.pvalue

The bootstrap p-value of the Kolmogorov-Smirnov test for the hypothesis that the probability densities for both the treated and control groups are the same.

ks

Return object from ks.test .

nboots

The number of bootstraps which were completed.

#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
#
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)
#
# Do we have balance on 1975 income after matching?
#
ks <- ks.boot(lalonde$re75[rr$index.treated], lalonde$re75[rr$index.control], nboots=500)
summary(ks)

data(lalonde)

qqstats(x, y, standardize=TRUE, summary.func)

x

The first sample.

y

The second sample.

standardize

A logical flag for whether the statistics should be standardized by the empirical cumulative distribution functions of the two samples.

summary.func

A user provided function to summarize the difference between the two distributions. The function should expect a vector of the differences as an argument and return summary statistic. For example, the quantile function is a legal function to pass in.

meandiff

The mean difference between the QQ plots of the two samples.

mediandiff

The median difference between the QQ plots of the two samples.

maxdiff

The maximum difference between the QQ plots of the two samples.

summarydiff

If the user provides a summary.func, the user requested summary difference is returned.

summary.func

If the user provides a summary.func, the function is returned.

#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in
# Non-Experimental Studies: Re-Evaluating the Evaluation of Training
# Programs.''Journal of the American Statistical Association 94 (448):
# 1053-1062.
#
data(lalonde)
#
# Estimate the propensity model
#
glm1 <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
 hisp + married + nodegr + re74 + I(re74^2) + re75 + I(re75^2) +
 u74 + u75, family=binomial, data=lalonde)
#
#save data objects
#
X <- glm1$fitted
Y <- lalonde$re78
Tr <- lalonde$treat
#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)
#
# Do we have balance on 1975 income after matching?
#
qqout <- qqstats(lalonde$re75[rr$index.treated], lalonde$re75[rr$index.control])
print(qqout)

 ## S3 method for class 'Match'
summary(object, ... , full=FALSE, digits=5)

object

An object of class "Match", usually, a result of a call to Match .

full

A flag for whether the unadjusted estimates and naive standard errors should also be summarized.

digits

The number of significant digits that should be displayed.

...

Other options for the generic summary function.

 ## S3 method for class 'Matchby'
summary(object, ... , digits=5)

object

An object of class "Matchby", usually, a result of a call to Matchby .

digits

The number of significant digits that should be displayed.

...

Other options for the generic summary function.

 ## S3 method for class 'balanceUV'
summary(object, ..., digits=5)

object

An object of class "balanceUV", usually, a result of a call to balanceUV .

digits

The number of significant digits that should be displayed.

...

Other options for the generic summary function.

 ## S3 method for class 'ks.boot'
summary(object, ..., digits=5)

object

An object of class "ks.boot", usually, a result of a call to ks.boot .

digits

The number of significant digits that should be displayed.

...

Other options for the generic summary function.