Matching
Another approach to estimation of causal effect is matching or pairing similar units, as an approximation to observing the same unit twice. If an experiment is possible, match units with identical or most similar attributes; randomly assign treatment to one and control to the other unit in each pair.
| subject | sex | blood pressure | |||
|---|---|---|---|---|---|
| Joe | male | 180 | ? | -15 | ? |
| Bob | male | 180 | -20 | ? | ? |
| James | male | 160 | -10 | ? | ? |
| Paul | male | 160 | ? | -5 | ? |
| Mary | female | 180 | 5 | ? | ? |
| Sally | female | 180 | ? | 10 | ? |
| Susie | female | 160 | 5 | ? | ? |
| Jen | female | 160 | ? | 10 | ? |
| MEAN | 170 | -5 | 0 | -5 |
If matched units are homogeneous, then they have the same causal effect. This means that they have the same average causal effect. Therefore, if all units are perfectly matched, the average causal effect equals the causal effect.
Propensity score matching is often used when there are multiple attributes.
Read more about this topic: Rubin Causal Model