  A new method is proposed to explore sources of cross-site impact variance in
multi-site trials of social interventions. With this approach, aggregate
reports from participants in the treatment arm about the treatment experience
are used to define potential mediators and aggregate reports from participants
in the control arm about the outcome of interest are used to remove confounding
due to unmeasured local contextual factors. Particular attention is paid to
correcting bias due to measurement error in the mediator. Asymptotic theory for
the validity of this approach is provided. Two example applications are given,
one simulated and one empirical.
