Cloak and DAG: A response to the comments on our comment

Our original comment (Lindquist and Sobel, 2011) made explicit the types of assumptions neuroimaging researchers are making when directed graphical models (DGMs), which include certain types of structural equation models (SEMs), are used to estimate causal effects. When these assumptions, which many researchers are not aware of, are not met, parameters of these models should not be interpreted as effects. Thus it is imperative that neuroimaging researchers interested in issues involving causation, for example, effective connectivity, consider the plausibility of these assumptions for their particular problem before using SEMs. In cases where these additional assumptions are not met, researchers may be able to use other methods and/or design experimental studies where the use of unrealistic assumptions can be avoided. Pearl does not disagree with anything we stated. However, he takes exception to our use of potential outcomes' notation, which is the standard notation used in the statistical literature on causal inference, and his comment is devoted to promoting his alternative conventions. Glymour's comment is based on three claims that he inappropriately attributes to us. Glymour is also more optimistic than us about the potential of using directed graphical models (DGMs) to discover causal relations in neuroimaging research; we briefly address this issue toward the end of our rejoinder.