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While there may be a more specific functional form relating the two variables to the outcome, in a DAG it is not necessary to represent that form. … A DAG is more vague (but also more flexible) since it does not require (or necessary allow) for specific function form. It might come down to the goal of drawing your DAG. …

There are seven rules of association. In the first four, $R$ and $T$ are associated with each other: $$R \rightarrow T$$ $$R \rightarrow S \rightarrow T$$ $$R \leftarrow S \rightarrow T$$ $$R \righta …

Mediator adjustment is reasonable if you are interested in the direct effect of the treatment on the outcome that does not pass through the mediator. For example, in racial disparity studies, matching …

Once you have drawn your DAG, you already assume that any variables pointing to the same outcome can modify the effect of the others pointing to the same outcome. … It is a modeling assumption, separate from the DAG, which presumes the lack of an interaction. In addition, interaction can occur without including an explicit interaction term in your model. …

If what he meant was "women with hip fractures were more likely to be selected," then one is not conditioning on hip fracture but rather on selection, which is caused by fracture, as the DAG displays. …

You are equating omitted variable bias with confounding by assuming that the DAG (which represents causal, not parametric, relationships) needs to be adjusted to capture this bias. … Therefore, there is no reason to adjust the DAG. …

I think you're missing the fact that confounding bias (nothing to do with colliders) can be of arbitrary magnitude, including equal to the treatment effect. So if the treatment effect is $\tau$ and th …

There are so many possibilities that it's impossible to enumerate them, and no DAG can distinguish among them. … The third is that the DAG is wrong in some way, and one or both of the adjustment sets is incorrect. …

In order to get the direct effect, you must adjust for $A$. The direct effect is defined by adjusting for $A$. You have no choice but to adjust for $A$. To do otherwise would be to estimate a total ef …

Ignorability, unconfoundedness, and satisfaction of the backdoor criterion mean the same thing. They all refer to there being a set of variables (possibly empty) that when conditioned on (i.e., strati …

The first is between a DAG and a parametric model. … Nothing about the DAG implies it is of this form or another. Statistical theory for causal inference does not depend on the functional form of $f(.)$ or of other relations in the DAG. …

Mediation and moderation are two unrelated concepts that can but do not always occur together. Mediation occurs when the effect of one variable on another passes through a third variable, e.g., $A \ri …

In this way, you can identifying a causal effect with an "incomplete" DAG. … If you can fully specify the causal system in the DAG, then you can use the DAG to identify adjustment sets for the effects of more than one variable. …

As @CloseToC mentioned in the comments, this is because you have a nearly pathological data scenario here. There are a few things that make this scenario "unfair" to matching (i.e., not suitable for m …