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Abstract:
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In paired experiments, participants are grouped into pairs with similar characteristics, and one observation from each pair is randomly assigned to treatment. Because of the design, the treatment and control groups will be balanced in expectation; however, there may still be small imbalances between the groups after treatment assignment. It may be possible to improve the precision of the treatment effect estimate by adjusting for these imbalances. Building on previous work, we propose the P-LOOP (paired leave-one-out potential outcomes) estimator for paired experiments. We leave out each pair and then impute its potential outcomes using any prediction algorithm. This imputation method is flexible; for example, we could use lasso or random forests. While similar methods exist for completely randomized experiments, covariate adjustment methods in paired experiments are relatively understudied. In addition, it can be unclear whether to factor in pair assignments when making adjustments in paired experiments. In the P-LOOP estimator, we address this issue (and potentially improve precision) by automatically deciding whether to include the pairing when imputing the potential outcomes.
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