In a recent post (and papers), Anders Huitfeldt and co-authors have discussed ways of achieving external validity in the presence of “effect heterogeneity.” These results are not immediately inferable using a standard (non-parametric) selection diagram, which has led them to conclude that selection diagrams may not be helpful for "thinking more closely about effect heterogeneity" and, thus, might be "throwing the baby out with the bathwater."
Taking a closer look at the analysis of Anders and co-authors, and using their very same examples, we came to quite different conclusions. In those cases, transportability is not immediately inferable in a fully nonparametric structural model for a simple reason: it relies on functional constraints on the structural equation of the outcome. Once these constraints are properly incorporated in the analysis, all results flow naturally from the structural model, and selection diagrams prove to be indispensable for thinking about heterogeneity, for extrapolating results across populations, and for protecting analysts from unwarranted generalizations. See details in the note we post here for discussion.