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I am familiar with propensity score weighting. I set up the propensity score model, and then generally check for balance and overlap in propensity score to ensure that assumptions are met. However, I'm a little confused about how entropy balancing works.

As I understand it, entropy balancing directly optimizes the weights themselves and guarantees balance on the specified moments. That's easy enough to check. But, how do we diagnose limited overlap? (I may be missing something obvious here)

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Entropy balancing enforces exact mean balance on all covariates included in the estimation of the weights and requires that the resulting weights are positive. If it is not possible to achieve mean balance with positive weights, entropy balancing will fail; the optimization will not be able to find a solution that balances the means.

When there is a lack of overlap in the covariates, it is impossible to exactly mean balance them. Personally, I don't believe lack of overlap is anything more than an extreme form of imbalance. If you have lack of overlap, then entropy balancing will fail. That is the diagnostic.

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  • $\begingroup$ Just to be clear--the entropy balancing weights are estimators of propensity scores, right? i.e., if we "reverse" the weights, then do we obtain PS estimates? I believe the answer is yes, but there seems to be some confusion about it in the literature. $\endgroup$ Dec 14, 2023 at 14:35
  • $\begingroup$ Maybe not immediately, but it is possible when targeting the ATT. Exactly identified CBPS is the same and entropy balancing for the ATT, and you get propensity scores from it, so you can use them. But entropy balancing itself doesn't directly estimate propensity scores, and doesn't estimate them at all for the treated units (they all get a weight of 1). For the ATE, the correspondence breaks down further and it might not be possible to get the propensity scores back directly. $\endgroup$
    – Noah
    Dec 14, 2023 at 18:09
  • $\begingroup$ EB weights for the ATE have an average of 1 in each treatment group, but IPW weights for the ATE are always greater than 1 for all units. So there is no immediately obvious way to back out the propensity scores for ATE EB weights. PS have no inherent value except to create weights, so there isn't much use in doing this at all; it is not valid to assess overlap using PS because poorly estimated PS can exhibit lack of overlap even when overlap is present, and vice-versa. $\endgroup$
    – Noah
    Dec 14, 2023 at 18:11

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