Matching (version 3.3-3)

MatchBalance: Tests for Univariate and Multivariate Balance

Description

This function provides a variety of univariate and multivariate metrics to determine if balance exists. The function does no matching. Matching is performed by the Match function. MatchBalance is used to determine if Match was successful in achieving balance. Multivariate balance is determined by the use of a model. This approach can be used regardless of the algorithm used to do the original matching. For example, even if Match was told NOT to use a propensity score, MatchBalance can be used to test balance.

Usage

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, ...)

Arguments

formul

A formula denoting the model for which balance should be determined. This model will be estimated by a binary logistic estimator. The dependent variable in the formula is usually the treatment indicator. Univariate balance tests will be condu

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 tests for both before and after matching

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 ev

mv

A logical flag for if multivariate balance tests (the Kolmogorov-Smirnov and Chi-Square tests) should be calculated.

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 Kolmogorov-Smirnov test only provides correct coverage when bootstrapped due to the existence of nuisance parameters.

nmc

The number of Monte Carlo simulations to be conducted for each Kolmogorov-Smirnov test calculated. Monte Carlo simulations are highly recommended because the usual Kolmogorov-Smirnov test is not consistent when the densities being compared co

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 are printing such as the number of the bootstrap sample currently being estimated.

paired

A flag for if 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 da

...

Further arguments passed to balanceMV.

Value

• 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 > 1.

Details

This function can be used to determine if matching was successful in achieving balance. 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 there is not threshold below which imbalance is not a problem and because of a variety of other issue---see citations. The bootstrap KS test is highly recommended (see the ks and nboots options) because the bootstrap KS is consistent even for non-continuous covariates, and it is more powerful than the t-test. Before matching the two sample t-test is used, and 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 of equal balance in the estimated probabilities between treated and control. The null hypothesis for the Chi-Square test, however, is of 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. The bootstrap-Monte Carlo version of the KS test is highly recommended because the usual KS test is not consistent when there are point masses in the distributions being compared, and the bootstrap is needed because parameters are being estimated in the logit model.

References

Sekhon, Jasjeet S. 2006. ``Matching: Algorithms and Software for Multivariate and Propensity Score Matching with Balance Optimization via Genetic Search.'' http://sekhon.berkeley.edu/matching/

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.

See Also

Also see Match, GenMatch, balanceMV, balanceUV, qqstats, 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);

#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)