From Professor Nozer Singpurwalla, from The George Washington University:
My basic point is that since causality has not been defined, the causal calculus is a technology which could use a foundation. However, the calculus does give useful insights and is thus valuable. Finally, according to my understanding of the causal calculus, I am inclined to state that the calculus of probability is the calculus of causality, notwithstanding Dennis' [Lindley] concerns about Suppes probabilistic causality.
From Bill Shipley, Universite de Sherbrooke, (Quebec) CANADA:
In most experiments, the external manipulation consists of adding (or subtracting) some amount from X without removing pre-existing causes of X. For example, adding 5 kg/h of fertilizer to a field, adding 5 mg/l of insulin to subjects etc. Here, the pre-existing causes of the manipulated variable still exert effects but a new variable (M) is added.
… The problem that I see with the do(x) operator as a general operator of external manipulation is that it requires two things: (1) removing any pre-existing causes of x and (2) setting x to some value. This corresponds to some types of external manipulations, but not all (or even most) external manipulations. I would introduce an add(x=n) operator, meaning "add, external to the pre-existing causal process, an amount 'n' of x''. Graphically, this consists of augmenting the pre-existing causal graph with a new edge, namely M-n–>X. Algebraically, this would consist of adding a new term –n– as a cause of X.
From L. H., University of Alberta and S.M., Georgia Tech
In response to my comments (e.g., Causality, Section 5.4) that the causal interpretation of structural coefficients is practically unknown among SEM researchers, and my more recent comment that a correct causal interpretation is conspicuously absent from all SEM books and papers, including all 1970-1999 texts in economics, two readers wrote that the "unit-change" interpretation is common and well accepted in the SEM literature.
L.H. from the University of Alberta wrote:
"Page 245 of L. Hayduk, Structural Equation Modeling with LISREL: Essentials and Advances, 1986, has a chapter headed "Interpreting it All", whose first section is titled "The basics of interpretation," whose first paragraph, has a second sentence which says in italics (with notation changed to correspond to the above) that a slope can be interpreted as: the magnitude of the change in y that would be predicted to accompany a unit change in x with the other variables in the equation left untouched at their original values." … "Seems to me that O.D. Duncan, Introduction to Structural Equation Models 1975 pages 1 and 2 are pretty clear on b as causal. "More precisely, it [byx] says that a change of one unit in x … produces a change of b units in y" (page 2). I suspect that H. M. Blalock's book "Causal models in the social Sciences", and D. Heise's book "Causal analysis." probably speak of b as causal."
S.M., from Georgia Tech concurs:
"I concur with L.H. that Heise, author of Causal Analysis (1975) regarded the b of causal equations to be how much a unit change in a cause produced an effect in an effect variable. This is a well-accepted idea."