Fully Latent Principal Stratification With Measurement Models

TL;DR

This paper introduces Fully-Latent Principal Stratification (FLPS), a new framework combining principal stratification with latent measurement models to analyze how treatment effects vary among subjects with different implementation behaviors.

Contribution

It develops FLPS models integrating item-response-theory measurement, demonstrating their feasibility and application in behavioral intervention studies.

Findings

FLPS models successfully estimated treatment effect heterogeneity.

Simulation studies confirmed model feasibility.

Application to math tutor data revealed variation in hint usage effects.

Abstract

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.