This function is a wrapper for the Match function which
separates the matching problem into subgroups defined by a factor.
This is equivalent to conducting exact matching on each level of a factor.
Matches within each level are found as determined by the
usual matching options. This function is much faster for large
datasets than the Match function itself. For additional
speed, consider doing matching without replacement---see the
replace option. This function is more limited than the
Match function. For example, Matchby cannot be
used if the user wishes to provide observation specific weights.
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", ...)A vector containing the outcome of interest. Missing values are not allowed.
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 "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.
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.
A scalar for the number of matches which should be
found. The default is one-to-one matching. Also see the
ties option.
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.
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.
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.
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.
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.
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.
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.
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.
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.
The level of printing. Set to '0' to turn off printing.
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.
The estimated average causal effect.
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.
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.
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,]).
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]).
The weights for each observation in the matched dataset.
The original number of observations in the dataset.
The number of observations in the matched dataset.
The number of weighted observations in the matched dataset.
The original number of treated observations.
The number of matches which were dropped because there were not enough observations in a given group and because of caliper and exact matching.
The estimand which was estimated.
The version of Match which was used.
Matchby is much faster for large datasets than
Match. But Matchby only implements a subset of
the functionality of Match. For example, the
restrict option cannot be used, Abadie-Imbens standard errors
are not provided and bias adjustment cannot be requested.
Matchby is a wrapper for the Match function which
separates the matching problem into subgroups defined by a factor. This
is the equivalent to doing exact matching on each factor, and the
way in which matches are found within each factor is determined by the
usual matching options.
Note that by default ties=FALSE although the default for
the Match in GenMatch functions is TRUE. This is
done because randomly breaking ties in large datasets often results in
a great speedup. For additional speed, consider doing matching
without replacement which is often much faster when the dataset is
large---see the replace option.
There will be slight differences in the matches produced by
Matchby and Match because of how the covariates
are weighted. When the data is broken up into separate groups (via
the by option), Mahalanobis distance and inverse variance
will imply different weights than when the data is taken as whole.
Sekhon, Jasjeet S. 2011. "Multivariate and Propensity Score Matching Software with Automated Balance Optimization.'' Journal of Statistical Software 42(7): 1-52. http://www.jstatsoft.org/v42/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. http://sekhon.berkeley.edu/papers/GenMatch.pdf
Abadie, Alberto and Guido Imbens. 2006. ``Large Sample Properties of Matching Estimators for Average Treatment Effects.'' Econometrica 74(1): 235-267.
Imbens, Guido. 2004. Matching Software for Matlab and Stata.
Also see Match,
summary.Matchby,
GenMatch,
MatchBalance,
balanceUV,
qqstats, ks.boot,
GerberGreenImai, lalonde
# NOT RUN {
#
# 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)
# }
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