  There is wide agreement on the importance of implementation data from
randomized effectiveness studies in behavioral science; however, there are few
methods available to incorporate these data into causal models, especially when
they are multivariate or longitudinal, and interest is in low-dimensional
summaries. We introduce a framework for studying how treatment effects vary
between subjects who implement an intervention differently, combining principal
stratification with latent variable measurement models; since principal strata
are latent in both treatment arms, we call it "fully-latent principal
stratification" or FLPS. We describe FLPS models including item-response-theory
measurement, show that they are feasible in a simulation study, and illustrate
them in an analysis of hint usage from a randomized study of computerized
mathematics tutors.
