Following up on this and this and this , Dan Ho sent me the following discussion of the differences between his, Jasjeet Sekhon’s, and Ben Hansen’s matching programs:

Hi Andrew,

On the matching software issues there are a few other differences as
well. The main difference between the approaches is that Jas’ program
contemplates substituting conventional parametric models with an
estimator that simultaneously conducts matching and a bias adjustment.
Our alternative theory (as outlined by Cochran and Rubin in the 1970s
in a specific linear context and generalized to all parametric models
in our paper at http://gking.harvard.edu/files/matchp.pdf) is that
matching is best used as preprocessing. Following our approach, users
can employ all the knowledge about parametric models that they have
developed and merely add a preprocessing step. The result is greatly
reduced model dependence and increased accuracy of parametric
estimates.

Other differences include that:

(1) MatchIt enables analysis of any outcome model (OLS, logit, ordered
probit, etc.) and is integrated with Zelig. The AI code appears to assume
linearity for the applied bias-adjustment.

(2) MatchIt incorporates optimal matching and full matching code by Hansen
as suggested by Rosenbaum and others.

(3) MatchIt also permits subclassification, exact restrictions,
Mahalanobis-distances, etc., as documented at
http://gking.harvard.edu/matchit/

Lastly, one clarification to Jake’s point: the default in MatchIt is
not to perform exact matching with replacement. Instead, the MatchIt
default for exact matching simply assigns subclasses to all units with
the same pretreatment covariates. Matching with replacement is a
separate option incorporated into MatchIt.

Dan

Once again, I’ll refer to this paper by Rubin for an overview of propensity score matching.