Bayesian inference for causal effects in randomized experiments with noncompliance: The role of multivariate outcomes

Principal Stratification (PS) is a principled framework for addressing noncompliance issues. Due to the latent nature of principal strata, model-based PS analysis usually involves weakly identified models and identification of causal effects relies on untestable structural assumptions, such as exclusion restriction. This article develops a Bayesian approach to exploit multivariate outcomes to sharpen inferences for weakly identified models within PS. Simulation studies are performed to illustrate the potential gains in identifiability of jointly modelling more than one outcome. The method is applied to evaluate the causal effect of a job search program on depression.