All Matching Methods

1. formula: formula used to calculate the distance measure for matching. It takes the usual syntax of R formulas, treat ~ x1 + x2, where treat is a binary treatment indicator and x1 and x2 are the pre-treatment covariates. Both the treatment indicator and pre-treatment covariates must be contained in the same data frame, which is specified as data (see below). All of the usual R syntax for formulas work here. For example, x1:x2 represents the first order interaction term between x1 and x2, and I(x1 ^ 2) represents the square term of x1. See help(formula) for details.

2. data: the data frame containing the variables called in formula. You may find it helpful for the diagnostics to specify observation names in the data frame (see Section 5.2.2).

3. method: the matching method (default=nearest). Currently, exact (exact matching), full (full matching), nearest (nearest neighbor matching), optimal (optimal matching), subclass (subclassification), and genetic (genetic matching) are available. Note that within each of these matching methods, MATCHIT offers a variety of options. See Section 3 for more details.

4. distance: the method used to estimate the distance measure (default=logistic regression, logit). Before using any of these techniques, it is best to understand the theoretical groundings of these techniques and to evaluate the results. Most of these methods (such as logistic or probit regression) are estimating the propensity score, defined as the probability of receiving treatment, conditional on the covariates (Rosenbaum & Rubin (1983)). The distance measures used are the predicted probabilities from the model (the propensity scores). Currently, the following methods are available:
   • mahalanobis computes the Mahalanobis distance measure (mahalanobis() in the stats package).
   • binomial generalized linear models with various links ( glm() in the stats package); logit (logistic link), linear.logit (logistic link with linear propensity score)^4.1, probit (probit link), linear.probit (probit link with linear propensity score), cloglog (complementary log-log link), linear.cloglog (complementary log-log link with linear propensity score), log (log link), linear.log (log link with linear propensity score), cauchit (Cauchy CDF link), linear.cauchit (Cauchy CDF link with linear propensity score).

   • binomial generalized additive model with various links ( gam() in the mgcv package); GAMlogit (logistic link), GAMlinear.logit (logistic link with linear propensity score), probit (probit link), GAMlinear.probit (probit link with linear propensity score), GAMcloglog (complementary log-log link), GAMlinear.cloglog (complementary log-log link with linear propensity score), GAMlog (log link), GAMlinear.log (log link with linear propensity score), GAMcauchit (Cauchy CDF link), GAMlinear.cauchit (Cauchy CDF link with linear propensity score). Beck & Jackman (1998); Hastie & Tibshirani (1990) and many others discuss the generalized additive models.

   • nnet, neural network model (nnet() in the nnet package). King & Zeng (2002); Zeng (1999); Beck, King & Zeng (2000); White (1992); Bishop (1995) among many others discuss neural networks.

   • rpart, classification trees (rpart() in the rpart package). Ruger et al. (2003); Breiman et al. (1984) and many others discuss classification trees.

5. distance.options specifies the optional arguments that are passed to the model for estimating the distance measure. The input to this argument should be a list. For example, if the distance measure is estimated with a logistic regression, users can increase the maximum IWLS iterations by distance.options = list(maxit = 5000).

6. discard: whether to discard units that fall outside some measure of support of the distance score before matching, and not allow them to be used at all in the matching procedure (default=none). Note that discarding units may change the quantity of interest being estimated.
   • none (default) discards no units before matching. Use this option when the units to be matched are substantially similar, such as in the case of matching treatment and control units from a field experiment that was close to (but not fully) randomized (e.g., Imai 2005), when caliper matching will restrict the donor pool, or when you do not wish to change the quantity of interest and the parametric methods to be used post-matching can be trusted to extrapolate.
   • both discards all units (treated and control) that are outside the support of the distance measure. Use this option when the units to be matched are substantially different (when there is a large degree of non-overlapping support on the distance score), such as in the case of measuring the effect of democracy on economic growth.
   • control discards only control units outside the support of the distance measure of the treated units. Use this option when the average treatment effect on the treated is of most interest and when unwilling to discard non-overlapping treatment units (which would change the quantity of interest), such as possibly in the case of the effect of job training on those individuals that actually participated in a job evaluation program or a drug study where interest is in all patients treated with the drug.
   • treat discards only treated units outside the support of the distance measure of the control units. Use this option when the average treatment effect on the control units is of most interest and when unwilling to discard control units.
   • convex.hull discards control units not within the convex hull of the treated units using the method developed in (King & Zeng, 2005).

7. reestimate: whether the model for distance measure should be re-estimated after units are discarded (default=FALSE). The input must be a logical value. Re-estimation may be desirable for efficiency reasons, especially if many units were discarded and so the post-discard samples are quite different from the original samples.

8. verbose: whether or not to print out comments indicating the status of the matching (default=FALSE). The input must be a logical value.