I have been trying to figure out, under what conditions can we identify causal effects via SEMs, particularly, is there a framework similar to the Rubin Causal Model or potential outcomes framework that I can utilize in this attempt? In search of an answer I ran across the following article:
Comments and Controversies
Cloak and DAG: A response to the comments on our comment
Martin A. Lindquist, Michael E. Sobel
Neuroimage. 2013 Aug 1;76:446-9
On potential outcomes notation:
"Personally, we find that using this notation helps us to formulate problems clearly and avoid making mistakes, to understand and develop identification conditions for estimating causal effects, and, very importantly, to discuss whether or not such conditions are plausible or implausible in practice (as above). Though quite intuitive, the notation requires a little getting used to, primarily because it is not typically included in early statistical training, but once that is accomplished, the notation is powerful and simple to use. Finally, as a strictly pragmatic matter, the important papers in the literature on causal inference (see especially papers by the 3R's (Robins, Rosenbaum, Rubin, and selected collaborators)) use this notation, making an understanding of it a prerequisite for any neuroimaging researcher who wants to learn more about this subject."
The notation definitely takes a little time getting use to, and it is also true for me that it was not discussed early on in any of my biostatistics or econometrics courses. However, Angrist and Pischke's Mostly Harmless Econometrics does a good job making it more intuitive, with a little effort. Pearl and Bollen both make arguments that SEMs 'subsume' the potential outcomes framework.While this may be true, its not straightforward to me yet. But I agree it is important to understand how SEMs relate to potential outcomes and causality, or at least understand some framework to support their use in causal inference, as stated in the article:
"Our original note had two aims. First, we wanted neuroimaging researchers to recognize that when they use SEMs to make causal inferences, the validity of the conclusions rest on assumptions above and beyond those required to use an SEM for descriptive or predictive purposes. Unfortunately, these assumptions are rarely made explicit, and in many instances, researchers are not even aware that they are needed. Since these assumptions can have a major impact on the “finndings”, it is critical that researchers be aware of them, and even though they may not be testable, that they think carefully about the science behind their problem and utilize their substantive knowledge to carefully consider, before using an SEM, whether or not these assumptions are plausible in the particular problem under consideration."
I think the assumptions they provide 1-4b seem to lay a foundation in terms that make sense to me from a potential outcomes framework, and the authors hold that these are the assumptions one should think about before using SEMs for causal inference.