Can I ask a follow-up question? about matchit HOT 3 CLOSED

Basically yes. I'll explain how matching is implemented.

One treated unit at a time, we check which controls are eligible to be matched with that treated unit. If matching without replacement, any previously matched control units are ineligible. If exact matching, any control units not in the same stratum as the treated unit are ineligible. If a caliper is present, any control units outside the caliper are ineligible. What remains is a pool of remaining eligible control units for that treated unit. If that pool is empty, the treated unit does not get a match. If the pool is not empty, the control unit in the pool that is closest to the treated unit gets matched to that treated unit. Then we move on to the next treated unit.

This is the same way matching occurred in the older versions of MatchIt, except that the bolded sentence would read "If the pool is not empty, a randomly selected control unit in the pool gets matched to that treated unit". You can see how the new behavior improves the quality of matches and enhances replicability moving forward.

I'm pretty sure the set of matched controls with a caliper is a subset of the set of matched controls without a caliper, but they will not necessarily be matched to the same treated units.

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It's great to get confirmation from you. Super helpful!
Thank you so much!

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Glad it was helpful! Feel free to ask if anything else comes to mind.

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