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Checking Balance

The goal of matching is to create a data set that looks closer to one that would result from a perfectly blocked (and possibly randomized) experiment. When we get close, we break the link between the treatment variable and the pretreatment controls, which makes the parametric form of the analysis model less relevant or irrelevant entirely. To break this link, we need the distribution of covariates to be the same within the matched treated and control groups.

A crucial part of any matching procedure is, therefore, to assess how close the (empirical) covariate distributions are in the two groups, which is known as ``balance.'' Because the outcome variable is not used in the matching procedure, any number of matching methods can be tried and evaluated, and the one matching procedure that leads to the best balance can be chosen. MATCHIT provides a number of ways to assess the balance of covariates after matching, including numerical summaries such as the ``mean Diff.'' (difference in means) or the difference in means divided by the treated group standard deviation, and summaries based on quantile-quantile plots that compare the empirical distributions of each covariate. The widely used procedure of doing t-tests of the difference in means is highly misleading and should never be used to assess balance; see ().

These balance diagnostics should be performed on all variables in $ X$ , even if some are excluded from one of the matching procedures.


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