Fully Latent Principal Stratification With Measurement Models

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.