Matching (version 0.53)

Match: 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. 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. 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)

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.

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. 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

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 cali

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 Maha

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

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 ma

sample

A logical flag for whether the population or sample variance is returned.

tolerance

This is a scalar which is used to determine if distances are different from zero. Values less than tolerance are deemed to be equal to zero.

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 matches dropped either because of the caliper or exact matching.

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

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 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, 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)