Match {Matching}R Documentation

Multivariate and Propensity Score Matching Estimator for Causal Inference

Description

This function preforms multivariate matching. This function is intended to be used in conjunction with the MatchBalance function which checks if the results of this function have actually achieved balance on a set of covariates. If one wants to do propensity score matching, one should estimate the propensity model before calling Match, and then send Match the propensity scores to use. The GenMatch function can be used to automatically find balance by the use of a genetic search algorithm which deterimes the optimal weight to give each covariate. Match provides principled standard errors when matching is done with covariates or a known propensity score. Ties are handled in a deterministic and coherent fashion.

Usage

Match(Y, Tr, X, Z = X, V = rep(1, length(Y)), estimand = "ATT", M = 1,
      BiasAdj = FALSE, exact = NULL, caliper = NULL,
      Weight = 1, Weight.matrix = NULL, weights = rep(1, length(Y)),
      Var.calc = 0, sample = FALSE, tolerance = 1e-05,
      distance.tolerance = 1e-05, version="fast")

Arguments

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. 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 (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 (with replacement). The default is one-to-one matching.
BiasAdj 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. Variables which are to be exactly matched on should also be given a very large weight (e.g., 1000) via the Weight.matrix option. 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. Variables for which a caliper is to be used should also be given a very large weight (e.g., 1000) via the Weight.matrix option. 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. The ecaliper object which is returned by Match shows the enforced caliper on the scale of the X variables.
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 observations 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.
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 matrix is singular.
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
version The version of the code to be used. The "fast" C/C++ version of the code is used unless the "old" (stable) version is requested.

Details

This function is intended to be used in conjunction with the MatchBalance function which checks if the results of this function have actually achieved balance. The results of this function can be summarized by a call to the summary.Match function. If one wants to do propensity score matching, one should estimate the propensity model before calling Match, and then place the fitted values in the X matrix—see the provided example.

The GenMatch function can be used to automatically find balance by the use of a genetic search algorithm which deterimes the optimal weight to give each covariate. The object returned by GenMatch can be supplied to the Weight.matrix option of Match to obtain estimates.

Three demos are included: GerberGreenImai, DehejiaWahba, and AbadieImbens. These can be run by calling the demo function such as by demo(DehejiaWahba).

Value

est The estimated average causal effect.
se The standard error. This standard error is principled 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 BiasAdj. If BiasAdj is not requested, this is the same as est.
se.naive The naive 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.naive does not. Neither se nor se.naive take into account the uncertainty of estimating a propensity score. se.naive does not take into account any BiasAdj. Summary of the naive 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 An index 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.
weights The weight for the matched dataset. If all of the observations had a weight of 1 on input, they will have a weight of 1 on output if each observation was only matched once.
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 actual observations which were dropped either because of caliper or exact matching. This number is not reliable if observation specific weights were passed in using the weights option. But ndrops.matches will always be accurate.
ndrops.matches The number of matches including ties which were dropped either because of the caliper or exact matching. Note that since this number includes ties, it is not the same as ndrops.

Author(s)

R version by Jasjeet S. Sekhon, Harvard University, jasjeet_sekhon@harvard.edu, http://jsekhon.fas.harvard.edu/

Matlab version by Guido Imbens, University of California, Berkeley, http://elsa.berkeley.edu/~imbens/.

References

Abadie, Alberto and Guido Imbens. 2004. ``Large Sample Properties of Matching Estimators for Average Treatment Effects.'' Working Paper. http://ksghome.harvard.edu/~.aabadie.academic.ksg/sme.pdf

Diamond, Alexis and Jasjeet S. Sekhon. 2005. ``Genetic Matching for Estimating Causal Effects: A New Method of Achieving Balance in Observational Studies.'' Working Paper. http://jsekhon.fas.harvard.edu/papers/GenMatch.pdf

Sekhon, Jasjeet S. 2004. ``The Varying Role of Voter Information Across Democratic Societies.'' Working Paper. http://jsekhon.fas.harvard.edu/papers/SekhonInformation.pdf

See Also

Also see summary.Match, GenMatch, MatchBalance, balanceMV, balanceUV, ks.boot, GerberGreenImai, lalonde

Examples

#
# 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)

#
# Let's check for balance
# 'nboots' and 'nmc' are 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, nmc=10)

[Package Matching version 0.96 Index]