In propensity score matching, we can match on variables exactly. For example, we can match males with other males only. Additionally, the variable can be specified in the model. Here's some SAS code showing an example with 2:1 matching (control:treatment) using the logit of the propensity score:
proc psmatch data = data_to_match; class gender; model treated = gender IQ; match method = greedy (k = 2) exact = (gender) stat = lps; output out (obs = match) = matched_data matchid = match_id; run;
Note how gender is used in the EXACT= option and in the MODEL statement. I assume R and other statistical packages offer the same types of options.
Is it necessary to use gender in both places?
I could see it both ways:
- Yes, because you get a more accurate propensity score.
- No, because you did an exact match, which should no longer impact the outcome and therefore should not impact the propensity score.
The examples on the SAS support site include gender in both positions, leading me to think that is the correct specification.