# What is the stopping criterion for adding nodes to a causal DAG?

I'm currently involved in creating a causal DAG (Directed Acyclic Graph) to map causal relationships of a real industry problem. The more I think, the more ancestor nodes I add to the DAG which is getting way too big now.

Simply put, when is it enough?

What is the criterion for stopping adding more nodes to the DAG?

It feels like if one keeps thinking there will be always more parent nodes with valid causal relationships to be added to the DAG.

• Relevant. Welcome to CV, Matheus Torquato. Commented Nov 24, 2023 at 17:15
• “ Simply put, when is it enough?” This is a great question. Usually we are limited by the data that we have or are able to collect. Of course it is also good to include unobserved /unobservable variables too, which can help find unobserved confounders. I don’t know the answer. I’m my experience we continue until we have exhausted all the likely nodes. Commented Nov 24, 2023 at 17:18
• I will add, in the spirit of my late mentor Richard Levins, to @RobertLong's excellent comment that all knowledge is contingent and incomplete: science is a strategy for navigating the truth of the world, not a guarantee that our knowledge is the truth of the world. Remember that all formal systems of causal analysis (including others besides SCMs) are fundamentally analyses of beliefs about causes. Commented Nov 24, 2023 at 17:26

Simply put, when is it enough?

This is a great question. Usually we are limited by the data that we have or are able to collect. Of course it is also good to include unobserved/unobservable variables too, which can help find unobserved confounders.

I have worked on DAGs having as many as 200 nodes. It's very ugly and almost impossible to work with. The strategy we took to simplify it was based on pragmatism. One thing we did was to group similar variables together, for we might have 10 variables that are in some way a part of, or a measure of, socio-economic class, so we replaced them with a latent variable in the DAG. Obviously this works especially well if you intend to use structural equation modelling in your analysis, but it's useful for multivariable regression models too.

Another thing you can do is try to quantify the strength of your causal beliefs. These are arcs between nodes in the DAG. If you can rate them, say 1-5, where 5 is that you are almost certain of the cause and 1 is that you have a very weak belief in the causal path. Then you can easily create separate DAGs for, say, just levels 4 and 5, for example. This can make life easier for you.

One final note, one of my teachers was keen on telling us that the most important thing in specifying a DAG isn't the arcs that you draw, it's the arcs that are absent.

• Re absent arches: this primarily applies if the causal order is known from the context. Otherwise one might argue that any arch that's drawn implies the absence of an arch in the opposite direction (or other arches that would make the graph cyclic). Commented Nov 24, 2023 at 17:47
• @Scriddie I hear you but I think our teacher had his tongue firmly in cheek, what he was really saying is that how can a statistics student know how to specify causal relations for some medical outcome (we were looking at coronary heart disease) - it's a job to be done together with a clinician. As for reverse (or cyclic) causality, I have handled that by having time varying variables. It makes the DAG even more complicated but it's one way to do it, and if you're going to be using G-methods as the analysis tool it can be quite helpful. Commented Nov 24, 2023 at 17:55
• Is multivariable supposed to mean multivariate or multiple? The latter two have specific meanings in regression analysis, while the former one does not. Commented Nov 25, 2023 at 10:19
• @RichardHardy, "Is multivariable supposed to mean multivariate or multiple?". I use "multivariable" to mean multiple explanatory variables, as opposed to multivariate which I use to mean multiple outcomes. I have often seen confusion where people say "multiple regression" which some people use to mean either. Commented Nov 25, 2023 at 11:06
• @RobertLong, thank you for the explanation. I have not seen the misuse you refer to, but I understand it may well show up every now and then. Commented Nov 25, 2023 at 11:38

### What's "enough" depends on what you're intending to use the DAG for.

If your goal were to estimate a specific causal relationship, it would probably make sense to include all variables on (undirected) paths between them.

If your goal were prediction of a certain variable, the causal Markov condition states that each variable is independent of all non-descendents given its parents, so including any indirect causes would not benefit you.

As a guideline, a good idea might be to ask yourself what variables you would need to achieve your goal, and then search for any variables that might complicate or bias your outcome if you did not include them as well.