MatchBalance {Matching} | R Documentation |
This function provides a variety of balance statistics useful for
determining if balance exists in any unmatched dataset and
in matched datasets produced by the Match
function. Matching is performed by the Match
function,
and MatchBalance
is used to determine if Match
was successful in achieving balance on the observed covariates.
MatchBalance(formul, data = NULL, match.out = NULL, ks = TRUE, mv = FALSE, nboots=500, nmc=nboots, maxit = 1000, weights=rep(1,nrow(data)), digits=5, verbose=1, paired=TRUE, ...)
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. |
mv |
A logical flag for whether multivariate balance tests (the
Kolmogorov-Smirnov and Chi-Square tests) should be calculated. If
this flag is TRUE , then the formula provided to
MatchBalance will be used to estimate a logistic regression.
And the multivariate tests will be conducted on the predicted
probabilities of treatment for both treated and control based on the
formula. The predicted probability densities for both treated and
control should be indistinguishable if balance has been
achieved. The model defined by this formula is estimated separately
for the matched and unmatched datasets. |
maxit |
The maximum number of iterations for the glm logistic procedure. |
weights |
A 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. |
nmc |
This option is only used if the mv flag is
TRUE . The number of Monte Carlo simulations to be conducted
for each multivariate Kolmogorov-Smirnov test calculated. Monte
Carlo simulations are highly recommended because the usual
Kolmogorov-Smirnov test is not consistent when the densities being
compared contain point masses. At least 500 nmc (preferably
1000) are recommended for publication quality p-values. Also see the
nboots option. |
digits |
The number of significant digits that should be displayed. |
verbose |
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. |
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. |
... |
Further arguments passed to balanceMV . |
This function can be used to determine if matching was successful in
achieving balance. Both pre- and post-matching balance statistics are
provided. Difference of means between treatment and control
groups are provided as well as a variety of summary statistics for the
empirical-QQ (eQQ) plot between the two groups. The first set of eQQ
results are the standardized mean, median and maximum differences.
The second set of eQQ results are summaries of the raw differences.
Two univariate tests are also provided: the t-test and the bootstrap
Kolmogorov-Smirnov (KS) test. These tests should not be treated as
hypothesis tests in the usual fashion because we wish to maximize
balance without limit. The bootstrap KS test is highly
recommended (see the ks
and nboots
options) because the
bootstrap KS is consistent even for non-continuous distributions.
Before matching, the two sample t-test is used; after matching, the
paired t-test is used.
Two multivariate tests are provided. The KS and Chi-Square null deviance tests. The KS test is to be preferred over the Chi-Square test because the Chi-Square test is not testing the relevant hypothesis. The null hypothesis for the KS test is equal balance in the estimated probabilities between treated and control. The null hypothesis for the Chi-Square test, however, is all of the parameters being insignificant; a comparison of residual versus null deviance. If the covariates being considered are discrete, this KS test is asymptotically nonparametric as long as the logit model does not produce zero parameter estimates.
NA
's are handled by the na.action
option. But it
is highly recommended that NA
's not simply be deleted, but
one should checked to make sure that missingness is balanced.
mv |
A return object from a call to balanceMV |
uv |
A return object from a call to balanceUV . The
univariate tests performed on the last variable in formul are
returned. For the other variables call balanceUV
directly. Note that the univariate test results for all of the
variables in formul are printed if verbose > 0 . |
Jasjeet S. Sekhon, UC Berkeley, sekhon@berkeley.edu, http://sekhon.berkeley.edu/.
Sekhon, Jasjeet S. 2007. ``Multivariate and Propensity Score Matching Software with Automated Balance Optimization.'' Working Paper. http://sekhon.berkeley.edu/papers/MatchingJSS.pdf
Sekhon, Jasjeet S. 2006. ``Alternative Balance Metrics for Bias Reduction in Matching Methods for Causal Inference.'' Working Paper. http://sekhon.berkeley.edu/papers/SekhonBalanceMetrics.pdf
Diamond, Alexis and Jasjeet S. Sekhon. 2005. ``Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies.'' Working Paper. http://sekhon.berkeley.edu/papers/GenMatch.pdf
Abadie, Alberto. 2002. ``Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models.'' Journal of the American Statistical Association, 97:457 (March) 284-292.
Hall, Peter. 1992. The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag.
Wilcox, Rand R. 1997. Introduction to Robust Estimation. San Diego, CA: Academic Press.
William J. Conover (1971), Practical nonparametric statistics. New York: John Wiley & Sons. Pages 295-301 (one-sample "Kolmogorov" test), 309-314 (two-sample "Smirnov" test).
Shao, Jun and Dongsheng Tu. 1995. The Jackknife and Bootstrap. New York: Springer-Verlag.
Also see Match
, GenMatch
, balanceMV
,
balanceUV
, qqstats
, ks.boot
,
GerberGreenImai
, lalonde
# # 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 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)