83
votes
Accepted
How do DAGs help to reduce bias in causal inference?
Causal Inference is an important topic in statistics generally, for both observational research and controlled experiments such as clinical trials.
A DAG is a Directed Acyclic Graph.
A “Graph” is a ...
- 65.8k
46
votes
Accepted
Does statistical independence mean lack of causation?
So if that's the case, does statistical independence automatically
mean lack of causation?
No, and here's a simple counter example with a multivariate normal,
...
- 12.7k
41
votes
Does statistical independence mean lack of causation?
Suppose we have a lightbulb controlled by two switches. Let $S_1$ and $S_2$ denote the state of the switches, which can be either 0 or 1. Let $L$ denote the state of the lighbulb, which can be either ...
- 33.2k
38
votes
Accepted
A layman understanding of the difference between back-door and front-door adjustment
Let's say you are interested in the causal effect of $D$ on $Y$. The following statement are not quite precise but I think convey the intuition behind the two approaches:
Back-door adjustment: ...
- 2,395
24
votes
Representing interaction effects in directed acyclic graphs
The simple answer is that you already do. Conventional DAGs do not only represent main effects but rather the combination of main effects and interactions. Once you have drawn your DAG, you already ...
- 36.8k
23
votes
Accepted
Causal effect by back-door and front-door adjustments
The action $do(x)$ corresponds to an intervention on variable $X$ that sets it to $x$. When we intervene on $X$, this means the parents of $X$ do not affect its value anymore, which corresponds to ...
- 12.7k
20
votes
Accepted
Is it appropriate to use "time" as a causal variable in a DAG?
As a partial answer to this question, I am going to put forward an argument to the effect that time itself cannot be a proper causal variable, but it is legitimate to use a "time" variable ...
- 133k
19
votes
Accepted
Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes.
For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$.
The instrumental variable model for this DAG ...
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19
votes
Which OLS assumptions are colliders violating?
I will assume models without intercepts to have shorter notation. Say the structural causal model is
\begin{aligned}
Y&=\beta_1X+u, \\
Z&=\gamma_1X+\gamma_2Y+v, \\
X&=w
\end{aligned}
with $...
- 69.5k
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
15
votes
Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes, they surely can.
As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and ...
- 12.7k
15
votes
Accepted
What is G-computation and G-estimation in causal inference
This is a short beginner-friendly guide to g-computation for estimating the average treatment effect https://github.com/kathoffman/causal-inference-visual-guides/blob/master/visual-guides/G-...
- 194
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
How do DAGs help to reduce bias in causal inference?
This is generally a fairly elaborate topic, and may require more reading on your part for better understanding, but I will try to answer a couple of your questions in isolation and leave references ...
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
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
10
votes
Causality: Structural Causal Model and DAG
Your model statement specifies a class of DAGs, not a single DAG. That is, all DAGs in which $x_1, \dots, x_n$ are direct causes of $y$, and $e$ is exogenous are DAGs compatibles with your assumptions....
- 12.7k
10
votes
Is it appropriate to use "time" as a causal variable in a DAG?
I see no problem with this. A simple example from physics: suppose you are interested in modelling the DAG of the temperature of a glass of water. It might look something like:
Time does cause the ...
- 12.3k
10
votes
Accepted
Reverse causality opposite definitions
Reverse causality is particularly problematic for DAGs because it often implies either a reversal of a causal path, or feedback loop (which would make it a Directed Cyclic Graph) rendering the usual ...
- 65.8k
10
votes
Does information criteria (AIC, BIC and DIC...) imply "causality"?
There is nothing inherently causal about any score. A score encodes assumptions about the underlying model. If the assumptions are met, a score can yield a causal model.
Score-based causal discovery ...
- 2,439
9
votes
Which OLS assumptions are colliders violating?
It is very easy to demonstrate that all the assumptions of OLS can be satisfied and yet collider bias persists.
Here, I generate data in which $z$ is a collider for the effect of $x$ on $y$.
...
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8
votes
Which OLS assumptions are colliders violating?
The problem here is that "collider" is a causal concept while OLS regression not necessarily deal with causality. About "regression and causality" read here: Under which ...
- 5,779
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
7
votes
Accepted
Multiple minimally sufficient adjustment sets in a Directed Acyclic Graph (DAG): Which unbiased estimate should be presented?
Let's start by defining some terms. Bias is the average distance from the true parameter of effects estimated from an estimator across many repeated samples. A biased estimate is an estimate coming ...
- 36.8k
7
votes
Is it appropriate to use "time" as a causal variable in a DAG?
Whether "time" is an appropriate variable in a model depends on the phenomenon you are modeling. Thus, as you posed it, your question is about model misspecification, not a fundamental ...
- 12.7k
7
votes
Accepted
Convincing Causal Analysis using a DAG and Backdoor Path Criterion
No, we can never be sure that the DAG is correct. This is one of the fundamental principles of causal inference informed by DAGs. DAGs are a non-parametric abstraction of reality. You will find in ...
- 65.8k
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