I'm repeatedly running into an issue in causal interpretation of SEM models. I'm not sure what to make of it, so I want to ask everybody what they think.
Suppose one knows A and B to be highly correlated in the world, but one doesn't know whether there is causality between them.
In an experiment, one stages an intervention. Manipulation X causes a difference in levels of A between the control and treatment groups.
Here's the tricky part. Suppose one analyses the data gleaned from this experiment using SEM. One makes an SEM with paths X -> A -> B. Each path is statistically significant. This is presented as a causal model indicating that manipulation X causes changes in A, which in turn cause changes in B.
|Paths X->A and A->B are significant, but X->B is not. Is a causal model warranted?|
However, if one tests the linear models A = b1×X and B = b2×X, we find that b1 is statistically significant, but b2 is not. (Note that I am not referring to the indirect effect of X on B after controlling for A. Tather, the "raw" effect of X on B is not statistically significant.)
This causes my colleagues and I to wonder: Does the SEM support the argument that, by manipulation of X, one can inflict changes in A, causing downstream changes in B? Or does this inject new variance in A that is unrelated to B, but the SEM fits because of the preexisting large correlation between A and B?
Can you refer me to any literature on this issue? What are your thoughts?
Thanks for any help you can give, readers.