  Multisite trials, in which treatment is randomized separately in multiple
sites, offer a unique opportunity to disentangle treatment effect variation due
to "compositional" differences in the distributions of unit-level features from
variation due to "contextual" differences in site-level features. In
particular, if we can re-weight (or "transport") each site to have a common
distribution of unit-level covariates, the remaining effect variation captures
contextual differences across sites. In this paper, we develop a framework for
transporting effects in multisite trials using approximate balancing weights,
where the weights are chosen to directly optimize unit-level covariate balance
between each site and the target distribution. We first develop our approach
for the general setting of transporting the effect of a single-site trial. We
then extend our method to multisite trials, assess its performance via
simulation, and use it to analyze a series of multisite trials of
welfare-to-work programs. Our method is available in the balancer R package.
