Questions tagged [causal-diagram]
Graphical methods for investigating causality, the related [confounder] tag, do-calculus, interventions, and counterfactuals.
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Do operator in a given DAG
The Original question is here Suppose we have a DAG in the figure.
The question to is find the decomposition for $P(Y \mid do(X), S)$. If the backdoor criteria can be applied here, then the following ...
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A question about do calculus
Suppose we have a DAG in the figure.
I want to find the formula for $P(Y \mid do(X), S)$. What I think is that: Since $W$ is the parent of $X$ then we should have
$$
P(Y \mid do(X), S) = \sum_{W} ...
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Structural equation model and latent instrumental variable approach with copulas
Consider the following structural equations:
$store sales := f(store visits, x_1, x_2)$
$store visits := f(x_1, x_2)$
Where as $x_1, x_2$ denotes promotional activity spending.
Note that $x_1, x_2$ ...
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Is survey participation a cause of survey response?
I am rewatching Statistical Rethinking 2023 - 11 - Ordered Categories
because McElreath mentions some causal assumptions about survey responses, which I am interested in. He proposes a causal diagram ...
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Constructing a structural equation model/causal graph
I would like to understand some intuitions behind the following causal graph/SCM.
Where as $X_1, X_2$ are expenditure on promotional activities.
My main interest lies in understanding the fact that ...
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Multiple covariates as treatment in double ML
I have multiple economic indicators as covariates such as employment rate, gdp growth, average wage, etc. I want to estimate each of them's effect on travel demand. I was thinking of two steps:
Make ...
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Variable selection with a theoretical DAG vs algorithmically discovered DAG
I'm analysing data from an electronic health record and determining what variables to include in a model to close back doors and omit bias.
I've read that it is important to have a subject specific ...
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Why is d-separation only for disjoint sets?
I'm reading Molak's Causal Inference and Discovery in Python: Unlock the secrets of modern causal machine learning with DoWhy, EconML, PyTorch and more and I made note that I've taken the ...
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Causal discovery on partially known causal DAG
Often in data science, we have partial knowledge of the causal DAG structure. Regarding some of the possible edges in the DAG, we are in doubt.
Are there any resources to tackle this setting? The ...
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Isn't strong ignorability an incorrect assumption in complex causal structures?
I have seen that in many papers/competitions for causal inference, the assumption of strong ignorability is made -
$P(Y^{x}\perp X\mid V)$, where $X$ is the treatment, $Y$ the outcome and $V$ ...
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Causal inference in DAGs and resulting structural equations
I am trying to understand the difference between the two modelling approaches described below that stems from the causal graphs.
Our goal is to causally measure the total treatment effect of our ...
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Can my cycle-cut algorithm sample any DAG?
I am doing some computational simulations to validate a procedure involving structural equation models and causal inference. I wanted to sample from the possible space of DAGs on $n$ vertices. I can ...
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How do I interpret the identification step logs in Causal Inference using DoWhy? [closed]
I am running Causal Inference to determine whether the mass of a vehicle affects the Co2 emissions. I understand that DoWhy follows a particular structure that is modeling-> identification -> ...
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Difference between query and distribution in causal inference
Reading the causality literature, we see the concepts of "interventional" and "counterfactual" query as well as "interventional" and "counterfactual" ...
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Selection of Competing Exposures in a DAG: How many to use?
I am trying to get my head around when and how to include Competing Exposures in DAGs. In my searching I keep finding statements that are very similar to the quote from the dagitty tutorials - "...
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Causal Inference in a Multivariate Equation
I am wondering if both the coefficients can be identified in a causal sense given the context and the resulting multiple regression equation.
Imagine a scenario where we have two investment ...
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Causal inference and the backdoor-criterion
I am trying to determine if the authors of the following report missed out on an important factor or if i am the one who have missed out on something.
In the following report: Bias Correction For Paid ...
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Testing for conditional independence with nonlinear relationships
I am reading about the IC and IC* (Inductive Causation) algorithms for discovering DAGs from observations. The first step of the algorithm is for each pair of variables a and b, search for a set of ...
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Path tracing rules for nonlinear relationships
I'm learning about Wright's path-tracing rules, and because they deal with covariances it seems like they make the assumption that relationships between variables are linear. If we have nonlinear ...
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In a causal diagram where the change score $\Delta Y=Y_1-Y_0$, does $Y_1$ cause $\Delta Y$ or does $\Delta Y$ cause $Y_1$?
In Shahar & Shahar (2010), the authors argue that in a typical pre/post observational study on two longitudinal outcomes $Y_0$ and $Y_1$:
the change score $\Delta Y=Y_1-Y_0$ causes the post-...
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Covariate adjustment for "mediated" reverse causality
I have made the following DAG in dagitty.net:
DAGitty says "The total effect cannot be estimated by covariate adjustment".
I don't understand why I can't close the backdoor path by ...
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Competitions/datasets fit for exploring Pearl's graphical causal models
Are there any competitions/challenges/datasets fit for testing Pearl's graphical causal inference methods? I do not necessarily mean live competitions.
I would expect these setups to be different than ...
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How can you rewrite the estimand in terms of propensity scores? Dowhy question
I am going through the backdoor criterion and how we get from an expression involving do to one which doesn't as below.
What i don't quite get is how to rewrite this estimand in terms of propensity ...
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DAG - why is the path open?
I have this DAG
As I understand it, the paths D <- Ed -> St -> P -> Su and D <- A -> P -> Su are both closed because the contain the collider P. If I condition on P, both these ...
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How to understand the second rule of front door criterion?
In the Definition 3.4.1 of Pearl's causal inference book (Primer), the second rule for the front door criterion is "There is no backdoor path from $X$ to $Z$". But from my understanding, ...
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Can controlling for a variable block the backdoor path opened by controlling for a collider?
I have made the following model in DAGitty:
Where X2 is controlled for.
DAGitty says:
The total effect cannot be estimated due to adjustment for an intermediate or a descendant of an intermediate.
...
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Causal counterfactual inference model comparison
When refuting two causal models, model 1 has a bigger p-value and an estimated effect closer to the new effect (compared to model 2). Both can't be refuted because they have a p-value above 0.05.
Is ...
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Noise abduction for computing counterfactuals
Given observational data $X$ and knowledge of the true causal graph structure $\mathcal{G}$. How does abduction of the exogenous noise ($U$) for computing counterfactuals work?
We don't have data ...
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Given a graph representing a NPSEM-IE, how can I show that another graph also represents one?
Good morning,
I am currently following a class on Biostatistics and am currently struggling on an exercise. I am given 2 graphs $G1$ and $G2$.
Then, assuming that $G1$ represents a NPSEM-IE, I have to ...
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Computing counterfactual query given an SCM and how it differs from computing interventional query?
Assuming we have the following structural causal model (SCM), with a confounder DAG structure, as follows:
Noise variables:
$$U_1 \sim \mathcal{N}(0,\,1)$$
$$U_2 \sim \mathcal{N}(0,\,1)$$
$$U_3 \sim \...
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Causal modeling in the presence of a latent variable
Suppose that four variables of $X$, $Y$, $L$, and $C$ have the following relationships in the form of directed acyclic graph.
$X$, $Y$, and $C$ are observable variables while $L$ is a latent (...
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What variables need to be controlled for in this causal graphical model?
I have the below graphical causal model. I thought that when we apply the intervention i.e. do calculus we get to the graph on the right - that is deleting arrows going into the treatment (drug). to ...
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Adjusting for variables outside of minimal adjustment set for total causal effect in a DAG
I have a fairly elaborate Directed Acyclic Graph (DAG) for the analysis that I am running, but I am presenting a simplified example here to clarify a few things.
Here is a DAG from dagitty.net:
...
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Understanding a "fundamentally unidentified question" example in causal inference
This is the example I'm referring to, it is taken from Mostly Harmless Econometrics: An Empiricistís Companion by Angrist and Pischke:
Suppose that we are interested in whether children do better in ...
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A graph that helps understand DGP of a mixture of Gaussians (DAG, Kruschke's DBDA style graph, etc.)?
Hastie, et al in “Elements of Statistical Learning” describe a particular DGP(Data Generating Process) or causal model on page 13.
The training data in each class (2 classes total) came from a ...
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How to modifiy regression or update equations to handle causal do-calculus type statements?
Consider $X, Y$ and suppose you have some i.i.d. observations of $Y$ and $X + \text{do}(Y)$ with observation noise $\epsilon_0$ and $\epsilon_1$ (Gaussian). So the observations of the latter should ...
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Justification of definition 2.7.1 (Potential cause) in Causality by Pearl
In Causality - Models, Reasoning And Inference by Pearl, definition 2.7.1 says -
Potential Cause definition:
A variable $X$ has a potential causal influence on another variable $Y$ (that is ...
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Conditioning on a future (post intervention/treatment and post outcome) event in a causal diagram?
My team is conducting a pre/post-intervention comparison of health outcomes in treatment and control groups, and the question came up whether it's a good idea condition/match on a deceased flag for ...
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Does a PAG (partial ancestral graph) have almost directed cycles with circular endpoints?
In https://www.jmlr.org/papers/volume9/zhang08a/zhang08a.pdf, a Maximal Ancestral Graph (MAG) is defined as:
...
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In what sense is one latent causal structure "preferred to" another? Definition 2.3.3 from Causality by Pearl
In Causality - Models, Reasoning, And Inference by Pearl, definition 2.3.3 reads as follows -
One latent structure $L$ = $\langle D,O \rangle$ is preferred to
another $L^{'}$ = $\langle D^{'},O \...
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How to analyse this set of variables using causal modelling
EDIT: edited the question slightly to keep the diagram intact but make it clear that we have an observed value and a hidden unmeasurable variable.
Here is the story. There are patients who have a ...
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How to adjust for the confounder of a confounder and how to call the confounder of a confounder within treatment effect estimation?
How do we adjust for the confounder of a confounder in order to compute unbiased estimates of the treatment effect of $A$ on $D$? See the causal graph (DAG) below:
What do we call the confounder $C$ (...
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How is strength of an arrow in graphical causal models related to variance of target variable?
From Causal Inference In Statistics, A Primer by Judea Pearl, I learnt that for linear SCMs (Structural Causal Model), the arrow strengths can be related to the appropriate linear regression ...
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What is an inducing path in causal inference?
In causal graphical models, an inducing path is defined as:
[Definition Inducing Path] An inducing path relative to L is a path on which every non-endpoint node ...
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Path analysis and the direction of effects
I'm conducting a phylogenetic path analysis (phylopath in R). As I couldn't be sure which direction one of the paths should be taking (you could hypothesise it is either), I put both options in the ...
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Confused by the notation in DAG depicting structural causal model and corresponding functional equations
Statistical Notations confuses me a lot and I get lost easily in following when the authors are talking about random variables vs observations, probabilities, probability density functions or ...
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Do-calculus and causal inference for continuous random variables
Typical treatments of do-calculus and causal inference use discrete random variables. For example, the first rule of do-calculus in Pearl states:
I'm curious about how the do-calculus and causal ...
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Is treatment conditionally independent from outcome in Single Experiment Design?
I'm reading this slides.
At slide 10 there is written that in "Single Experiment Design" we assume "Randomization of treatment", that is:
$ \{ Y_i(t,m),M_i(t') \} \perp T_i \lvert ...
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Related variables but no causal link: how to analyze it?
I'm doing my first formal causal analysis and I'm a bit puzzled by what and how to include it.
I've read a few questions and guides about how to do it but I have no theoretical background (I haven't ...
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In covariate-specific effect - $P(Y=y|do(X=x),Z=z)$ - is $Z=z$ pre- or post-treatment measure?
Causal Inference In Statistics by Pearl, section 3.5, page 70 clearly mentions that -
This effect, written $P(Y=y|do(X=x),Z=z)$, measures the distribution
of $Y$ in a subset of the population for ...