Matching (statistics)

Matching is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is, for every treated unit, to find one (or more) non-treated unit(s) with similar observable characteristics against whom the effect of the treatment can be assessed. By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding.Propensity score matching, an early matching technique, was developed as part of the Rubin causal model.

Matching has been promoted by Donald Rubin. It was prominently criticized in economics by LaLonde (1986), who compared estimates of treatment effects from an experiment to comparable estimates produced with matching methods and showed that matching methods are biased. Dehejia and Wahba (1999) reevaluted LaLonde's critique and show that matching is a good solution. Similar critiques have been raised in political science and sociology journals.

When the outcome of interest is binary, the most general tool for the analysis of matched data is conditional logistic regression as it handles strata of arbitrary size and continuous or binary treatments (predictors) and can control for covariates. In particular cases, simpler tests like paired difference test, McNemar test and Cochran-Mantel-Haenszel test are available.

When the outcome of interest is continuous, estimation of the average treatment effect is performed.

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