Matching

Matching is a statistical method that can be used to estimate quantities of interest that depend on missing, that is, unobserved, values of some variable Y. (As is made clear later in this entry, the variables with missing values in causal inference applications are subtly different from the observed outcome variable, which is commonly referred to as Y.) Schematically, matching works as follows. For each observation with a missing value of Y, find another observation that does not have a missing Y value but that is otherwise maximally similar to the initial observation in question. This similar observation is said to match the observation with the missing Y value. Now use the observed Y value from the matched observation to fill in the missing Y value. Matching can be done by selecting matching observations with or without replacement from the original dataset. It is also possible to match many observations to a single missing observation, in which case the mean of Y from the matching observations is typically used to fill in the missing Y value.

Matching can be applied to a variety of missing data problems—from estimating the population mean of Y to estimating causal effects. Examples below make this clearer. Matching is not a panacea. Matching methods rely on assumptions that can only be tested given auxiliary data and/or assumptions. The key assumptions of conditional ignorability and overlap are discussed later in this entry. There are a wide variety of ways that matching can be implemented by. A discussion of particular matching methods and their statistical properties is beyond the scope of this entry.