Primary Submission Category: Causal Inference and SUTVA/Consistencies Violations
Low-degree Outcomes and Clustered Designs: A Combined Approach for Causal Inference under Interference
Authors: Samir Khan, Johan Ugander, Matthew Eichhorn, Christina Lee Yu,
Presenting Author: Matthew Eichhorn*
One line of work in causal inference under interference develops estimators that are low variance under parametric outcome models; another develops experimental designs that reduce variance under assumptions on the interference graph. Recent work on low-degree outcome models and pseudoinverse (PI) estimators exemplifies the former, while work on graph cluster randomization exemplifies the latter. In this work, we explore the intersection of these two by studying the interplay between low-degree models and clustered designs.
We extend the analysis of PI estimators for low-degree models beyond Bernoulli designs, characterizing unbiasedness and giving variance bounds. For clustered designs, we show that the variance of the PI estimator scales like the minimum of the variance bound guaranteed by either cluster randomization or low-degree modeling on their own. Thus, the PI estimator has consistently less variance than the Horvitz-Thompson (HT) estimator when the clustering is fixed, a fact we verify empirically.
In contrast, for randomized clustered designs, which were based on the variance structure of the HT estimator, we find that the PI estimator may have higher variance than the HT estimator. Thus the PI estimator is appropriate when using clustered designs, but not necessarily when using randomized clustered designs; as such our results provide initial answers to open questions about the alignment between design and estimator in causal inference under interference.