Avi Feller, Evan Greif, Nhat Ho, Luke Miratrix, and Natesh Pillai write:

Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to estimate these quantities. Unfortunately, standard estimators of mixture parameters, like the MLE, are known to exhibit pathological behavior. We study this behavior in a simple but fundamental example, a two-component Gaussian mixture model in which only the component means and variances are unknown, and focus on the setting in which the components are weakly separated. . . . We provide diagnostics for all of these pathologies and apply these ideas to re-analyzing two randomized evaluations of job training programs, JOBS II and Job Corps.

The paper’s all about maximum likelihood estimates and I don’t care about that at all, but the general principles are relevant to understanding causal inference with intermediate outcomes and fitting such models in Stan or whatever.