# the causal factors in a subtracting relationship in directed acyclic graph

I have one variable A which is derived from subtracting C from B, i.e., A=B-C, does that mean B and C are both the causal factors of A if depicted in A DAG?

• As written, yes. But you could also rearrange your equation to get a different causal relationship: $B=A+C,$ in which case you can think of $A$ and $C$ as causing $B.$ Or $C=B-A$ is the third possibility. What you need to do is understand the underlying causal relationships among the variables. What do $A,B,$ and $C$ actually represent? And which structural causal model makes the most sense? Mar 31, 2022 at 21:38
• So B and C represent area-based measures, B is larger than C. I used a causal analyzing method called ICEFALCON which uses monozygotic twin data and GEE. previously I treated A as a spatially independent variable of B and C, and I'm interested in whether there is a causal relationship between A and C. Mar 31, 2022 at 22:30

Not necessarily. Order of terms in a math equation can be for convenience rather than causal.

Possible example:

A: Duration of stay in the hospital

B: Discharge Date/time to hospital

So A = B - C, but I would put C and A as causes of B in the DAG. Severity of injury would be most directly a cause of A, and A would probably be the most direct cause (of the 3) of things like chance of hospital acquired infection. But B and C are most likely to be in the medical record/data set with A being computed.

Another possible example:

A: Weight of cargo and passengers in a car/truck

B: Total weight of car/truck including cargo and passengers

C: Weight of car/truck

B is the sum of A and C and I think of them causing B, but it may be easiest to weigh the car/truck without cargo, then with cargo, and take the difference.

• Thanks for your answer. but I still didn't get why B or C can't be the causal factors of A from your example. is that related to how you define a causal relationship? Mar 31, 2022 at 22:44
• @Zhoufeng, generally causes occur before effects in time. Duration of hospital stay is happening throughout the time between admit and discharge. Discharge happens only at the end. You can think of duration being caused by discharge date, but time order and my thinking put it the other order. Apr 1, 2022 at 22:42