Multi-level hierarchical matching

[nehargupta]

Hi Noah,

Nice to meet you, I'm a big fan of your vast portfolio of work.

I'm wondering if there's any way to do optimal pair or optimal distance matching while minimizing the distances according to a user-provided distance matrix, but also having this optimization be subject to some additional constraints?

For more detail - I'm working on implementing multi-level hierarchical matching with a variety of permutations for the match at each level. One example: "Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System" (Zubizarreta and Keele, 2017).

Here's how I've currently implemented with MatchIt:

1. Iterate over every pair of possible treated/control classroom pairing. Perform matching on students within each of those experimentally matched classrooms (using student-level covariates), and use the number of students matched to build a distance matrix of classrooms.
2. Match classrooms using the distance matrix (but not sure if it's possible to use classroom-level covariates when matching classrooms then!)

My understanding is that the "formula" parameter is only used when the method is computing the distance, but not when a distance matrix is supplied. Is this true? Is there any other work-arounds I could explore?

Thanks, your help is much appreciated!

[ngreifer]

Thank you fore the kind words about my work! Unfortunately I don't think I can help you here; you'll need to look into another package to do this kind of matching. The designmatch package (removed from CRAN unfortunately) by José Zubizarreta is designed for complicated matching specifications with constraints. I would reach out to the paper authors if you want to implement their method in your analysis.

It is true the the formula argument to matchit() is only used to create the distance matrix and/or the propensity score (and determine the covariates for which balance is to be assessed). Remember that MatchIt only implements a few matching methods internally; the other methods, including optimal matching, are implemented by other packages.