18
votes
Are directed acyclic graphs (DAGs) only used for visualization?
DAGs are used for much more than visualization
Expressing the (causal) relationships between variables as DAGs allows employing graphical criteria for finding answers to statistical or causal ...
- 2,439
18
votes
Accepted
Causal diagrams necessary in randomized controlled trials?
In short, yes there are cases where one may want to draw a DAG. I will offer a simplified example.
As you mention, (proper) randomization ensures there are no confounders so we don't need to worry ...
- 39.6k
16
votes
Causal diagrams necessary in randomized controlled trials?
Classic randomized clinical trial analysis uses the intention to treat approach in which all patients are analyzed and they are analyzed using the randomization codes. Secondary analyses may require ...
- 98.4k
15
votes
Accepted
Can we just "pre-test" the backdoor criterion?
Indeed, given the DAG, you should only see a correlation between X and Z if there is a direct link between the two, and thus you could test for a correlation directly. These and similar tests are done ...
- 8,689
12
votes
Accepted
How can I proceed when causal directions are not that clear? An example is provided
Fist, I think it is good that you are using a DAG because it requires careful thought about causality, and this is often at the heart of modelling.
adjusting for everything, age and sex, and even if ...
- 65.8k
11
votes
Accepted
DAGs: instrumental and adjusted variables
While drawing DAGs...what are instrumental and adjusted variables?
An instrumental variable is an observed variable that is often used to help obtain an unbiased estimate for a causal effect that is ...
- 65.8k
11
votes
Accepted
Do-Calculus for Causal Diagram 7.5 from "The Book of Why" (napkin problem)
I answered this once on twitter, I can reproduce the answer here.
Derivation (graphs licensing each step are provided below).
$$
\begin{align}
P(y|do(x)) &= P(y|do(x), do(z)) \qquad &\...
- 12.7k
11
votes
Accepted
Why doesn't this work as a backdoor?
Your assumption is that conditioning on a variable (i.e., $X_4$) blocks all paths through that variable, but that is not so. Conditioning on a variable opens a path between the antecedents of the ...
- 36.8k
11
votes
Accepted
Cyclicality in causal relationships
Because causes must precede effects, acyclic is preferred. Ultimately, there can be no true cycles: if event $A$ causes event $B,$ then $A$ must precede $B.$ The time $t_a$ at which $A$ occurs must be ...
- 6,039
11
votes
Accepted
Pearl, Causal Inference in Statistics Q3.5.1 (Backdoor criterion)
No you were right to begin with, you can control for any variable along the back door path so long as it doesn’t open up new such paths.
You can try it for yourself for the specific diagram here (set ...
- 4,321
11
votes
Accepted
What is the stopping criterion for adding nodes to a causal DAG?
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 ...
- 65.8k
9
votes
Accepted
Isn't strong ignorability an incorrect assumption in complex causal structures?
The assumption of strong ignorability is that there exists a set of variables $W$, possibly a subset of all measured variables $V$, such that $Y^X \perp X \mid W$. It does not say that $Y^X \perp X \...
- 36.8k
8
votes
Accepted
Representation of unconfoundedness of Rubin causal models on Pearl causal models
Yes, you can represent them in a DAG.
In the structural framework, the DAG is nothing but a visual representation of the functional arguments that enter the structural equations. For a quick review ...
- 12.7k
8
votes
What is the stopping criterion for adding nodes to a causal DAG?
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 (...
- 2,439
8
votes
Causal diagrams necessary in randomized controlled trials?
Even in an RCT, a DAG can be useful to examine colliders and mediators
In general, there are two types of variables that might might adversely impact an RCT and which may require consideration and ...
- 133k
7
votes
Causal inference - difference between blocking a backdoor path and adding a variable to regression
You're not wrong. Including $X$ in the regression is typically how you condition on a variable in the regression setting. There are other ways to condition (stratify, backdoor adjustment, frontdoor ...
- 6,039
7
votes
Accepted
causal graph - counting the number of backdoor paths in a DAG
For Example 1, you are correct. $A\leftarrow Z\to W\to M\to Y$ is a valid backdoor path with no colliders in it (which would stop the backdoor path from being a problem).
In Example 2, you are ...
- 6,039
7
votes
Causal Bayesian network, causal diagram, structural causal model and marginal structural model: what do they exactly mean?
I will give my answer based on Pearl's other book (Causality)
First, some terminology: there are 3 types of queries: observational, interventional, and counterfactual.
For observational queries, you ...
- 121
7
votes
Accepted
Simultaneity in causal diagrams
It may not be possible, or at least has not yet been worked out yet. See the discussion in section 4.3 in Guido Imbens's Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance ...
- 38.3k
7
votes
Are directed acyclic graphs (DAGs) only used for visualization?
I would say that generally DAGs are used as an explanatory tool rather than an estimation tool, so you rarely see them used for direct statistical purposes. However, while they are not the same, DAGs ...
- 18.4k
7
votes
How to make nonlinear predictions on categorical treatments in causal inferece given causal graph?
The DAG is a nonparametric device which tells you which variables influence other variables in a causal manner. Whether the effect is linear or nonlinear is not specified by the DAG. The DAG is ...
- 65.8k
6
votes
How can I proceed when causal directions are not that clear? An example is provided
If you are not sure about the direction of the arrow, this is likely because you suspect (implicitly or explicitly) some potential confounding between the two variables. Hence, you should draw all ...
- 266
6
votes
Accepted
Causal Inference - when Conditioning on a Collider is correct
This is an excellent question giving a really incisive inquiry into causal reasoning in a "simple" problem. The issue here is that when you are playing the Monty Hall game, you are making a ...
- 133k
6
votes
Accepted
How to adjust for the confounder of a confounder and how to call the confounder of a confounder within treatment effect estimation?
Thank you for including the DAG!
The answer here is pretty straight-forward: you simply condition on both $C$ and $B.$ Neither $C$ nor $B$ is part of a collider, so you're not opening up new paths by ...
- 6,039
5
votes
Mix of terms causation and dependence in 'book of why'?
This only addresses your first question, but I wanted to point out that cancellation does not have to be accidental. It can be the outcome of purposeful human behavior. This is a key point to me since ...
- 38.3k
5
votes
Mix of terms causation and dependence in 'book of why'?
I don't understand, why he says "usually". Isn't it always the case
when we have causation that we shall see some sort of dependence in
the data?
No, because you can have accidental ...
- 12.7k
5
votes
Meaning of multiple exposures in a DAG
The problem is the same estimation procedure you used in the first case, cannot be used in the second.
DAG 1:
In the first case, you rely on a very special case where the average causal effect (ACE) ...
- 2,617
5
votes
How to evaluate validity about Causal Discovery?
Often, you don't even get a complete structure, with constraint-based methods like PC or FCI, it is usually only a Markov Equivalence Class (MEC), which is a set of several possible structures (causal ...
- 11.2k
5
votes
Accepted
Causal Diagram and multiple regression
Your interpretation is correct. Conditioning on $A$ blocks the backdoor path $B\leftarrow A\to C\to D.$ Since $C$ is unavailable because it is unmeasured, you must condition on $A$ to block the ...
- 6,039
5
votes
Can we just "pre-test" the backdoor criterion?
Yes, in order to confirm a confounding relationship you may perform a regression (or Chi-squared test or other suitable model) of $Z$ on $X$ and $Z$ on $Y$. This is exactly what I'm doing right now ...
- 6,286
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