Genetic Matching
Description
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 ttests and KolmogorovSmirnov
tests. A variety of descriptive statistics based on empiricalQQ
(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.
Usage
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=1e05,
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, ...)
Arguments
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 onetoone 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) ttests and
KolmogorovSmirnov 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
KolmogorovSmirnov (KS) test should be calculated. If the ks option
is set to true, the univariate KS test is calculated for all
nondichotomous variables. The bootstrap KS test is consistent even
for noncontinuous variables. By default, the bootstrap KS test is
not used. To change this see the nboots option. If a given
variable is dichotomous, a ttest 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 ("pvalues") 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, floatingpoint 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 observationpair.
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
value 
The fit
values at the solution. By default, this is a vector of pvalues
sorted from the smallest to the largest. There will generally be
twice as many pvalues as there are variables in
BalanceMatrix , unless there are dichotomous variables in this
matrix. There is one pvalue for each covariate in
BalanceMatrix which is the result of a paired ttest and
another pvalue for each nondichotomous variable in
BalanceMatrix which is the result of a KolmogorovSmirnov
test. Recall that these pvalues 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 .

Author(s)
Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu,
https://www.jsekhon.com.
References
Sekhon, Jasjeet S. 2011. "Multivariate
and Propensity Score Matching Software with Automated Balance
Optimization.” Journal of Statistical Software 42(7): 152.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i07")}
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.
https://www.jsekhon.com
Sekhon, Jasjeet Singh and Walter R. Mebane, Jr. 1998. "Genetic
Optimization Using Derivatives: Theory and Application to Nonlinear
Models.” Political Analysis, 7: 187210.
https://www.jsekhon.com
See Also
Also see Match
, summary.Match
,
MatchBalance
, genoud
,
balanceUV
, qqstats
,
ks.boot
, GerberGreenImai
, lalonde
Examples
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.