Questions tagged [causality]
The relationship between cause and effect.
725
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How to understand probability of Necessity (PN) ≥ 100%, as in this example from 'Causal Inference in Statistics a primer'
In the book 'Causal Inference in Statistics A Primer' By Pearl et al. there is an example towards the end, (Ex 4.5.1 page 119) that calculates the probability of necessity PN = 1, and the authors ...
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2answers
2k views
+200
How do DAGs help to reduce bias in causal inference?
I have read in several places that the use of DAGs can help to reduce bias due to
Confounding
Differential Selection
Mediation
Conditioning on a collider
I also see the term “backdoor path” a lot.
...
4
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3answers
130 views
Controlling variables in causal diagrams
I'm reading "The book of why" by Judea Pearl and although I understand qualitatively what he is saying when it comes to the bias introduced by controlling for an incorrect variable (a collider, for ...
5
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1answer
49 views
Convincing Causal Analysis using a DAG and Backdoor Path Criterion
Teasing out the causal effect of one variable/treatment on another/outcome by blocking all the Backdoor Paths between treatment and outcome in the corresponding DAG (Directed Acyclic Graph) requires ...
7
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1answer
88 views
Reverse causality opposite definitions
I have three sources, and all of them describe different DAG structures, and yet all claim that exactly their structure is the reverse causality:
From s0:
From s1 (page 84):
From s2:
Which of ...
2
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2answers
62 views
Is there a simpler probabilistic causal model that describes this data generating process?
Consider the following data generating process:
A person with gender male or female is selected from a population with probability $\alpha$ of selecting female.
The person is offered a drug to treat ...
1
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0answers
29 views
+50
What are simple examples of Bayesian Networks that don't work as *Causal* Bayesian Networks?
I'm re-reading some of the early chapters of Pearl's seminal Causality and I'm realizing that I can't come up with more than 2 good examples of probability distribution, Bayesian Network pairs that ...
5
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1answer
59 views
Statistical relationship between the stages of a stochastic optimization problem
What exactly do the "stages" of a stochastic program say about the statistical relationship between the problem variables?
From what I understand, the stages imply both an "ordering" and "grouping" ...
0
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0answers
33 views
Should I drop variable highly correlated with independent variable? (Causal inference)
I estimate OLS:
Y = c + b1*x1 + ....+ bn*xn +err
corr (Y, x1) = 0.8, Corr(x1,err)>0
Should I drop variable x1? What kind of biases would I have in both cases: with and without x1.
3
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0answers
61 views
Mathematical details in the definition of a Structural Causal Model
Pearl defines (see Causality, Judea Pearl, 2nd ed., Definition 7.1.1) a Structural Causal Model (SCM) as a triple $(\mathscr U, \mathscr V, F)$ where $\mathscr U$ is a set of "exogenous variables," $\...
2
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0answers
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Hierarchical/Multilayer/Nested Instrumental Variable Regression
If we can view classical instrumental variable regression as "two-layer" (from instrumental variable to covariate and then to the response), is there any "hierarchical/multilayer/nested" version of ...
6
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2answers
367 views
Is it confounding variable?
Here is a snippet from here:
Consider the example of a trial studying the relationship between
coffee drinking (the exposure or “intervention”) and myocardial
infarction (the outcome). Suppose ...
0
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0answers
21 views
Non-stochastic vs Stochastic regressors and sampling distributions and causation?
I was wondering if I understand these correctly. Would an example of a stochastic regressor be weather? so when thinking about the sampling distribtuion and causality, I would think of repeated ...
1
vote
1answer
42 views
Using scatterplot before running a controlled experiment to test causality
This question is an extension of awesome thread Does causation imply correlation?.
As an example, let's say that I am running an online experiment on Stackoverflow to see whether asking more ...
1
vote
1answer
39 views
Determining which variable is the cause and which one is the effect
I'm working on my assignment and I'm a bit lost. So the assignment requires us to draw a scatter plot based on data that we collected online. The purpose of the assignment is to see if higher earnings ...
0
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0answers
25 views
Kernel Matching
I wish to estimate a treatment effect using Kernel Matching, but I'm confused about the process. From a high level, Is A or B correct? Or are both considered Kernel matching?
A
(1) Estimate ...
0
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1answer
7 views
Intervals from an underdetermined nonnegative linear system
I'm working on a problem in genomics that yields the following puzzle. Let $b\in \mathbb R^I$, $t$ and $p\in \mathbb R^J$, and $s \in \mathbb R^{I\times J}$. Suppose $t,b,p$ are known. Further suppose:...
0
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1answer
44 views
Measuring impact of 1 independent variable on 1 dependent variable
I'm trying to measure the impact of a promotional activity and want to see whether it is contributing to business performance.
Let's say there are 100 campaigns. For some campaigns, there is no ...
17
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5answers
961 views
Is it appropriate to use “time” as a causal variable in a DAG?
This question might be better suited for philosophy.SE, but I will post it here in the first instance, since it involves technical aspects that are best understood by users on this site. The title ...
0
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0answers
15 views
Never seen combination of conditional dependent variables in models - can it generalize?
Let's say i have a set of symptoms X and Set of diagnoses Y. My dataset is in the form of one symptom and one diagnose e.g {X,Y} = {Fever,Flu} , where Fever can occur for other diagnoses and Flu can ...
3
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0answers
62 views
Theory behind Targeted Maximum Likelihood Estimation (TMLE)
There are many fine how-to articles describing how to implement TMLE but they avoid the details of the underlying theory. I'm currently working my way through Targeted Learning: Causal Inference for ...
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0answers
14 views
causal inference in linear regression where regressors have causal effect on each other
I am having some issues with the concept of causality. I have seen the causal effect of one variable on another "defined" as the effect that a change would cause if other variables are kept equal. ...
0
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1answer
33 views
Causal Inference using Linear Regression
I have been reading recently on fitting linear regression to evaluate causal effect of some treatment. Let's call the variable in the model representing treatment as Xj.
From what I have read, we ...
0
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0answers
8 views
Clinically meaningful explanation of marginal treatment effect (MTE) in instrument variable study
I am working on an instrumental variable application using clinical data. We will use a so-called preference-based instrument. We may include this as a continuous variable. With a continous instrument,...
4
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2answers
184 views
What justifies adjusting for proxy variables in the DAG causal inference framework?
Consider the following hypothetical. I am an employee of Acme Inc., and I want to quantify the impact on spending (in $) of joining the Customer Loyalty Club (CLC).
Of course, only customers who ...
1
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1answer
33 views
How to test reverse causality?
Building regression models to test the impact of X on Y, but sometimes there is reserve causality between X on Y, which is Y may also have an impact on X. How can we test this hypothesis?
1
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1answer
47 views
Instrument Validity Is Not Empirically Testable
BACKGROUND
Suppose we want to use a random sample to estimate $\beta$ in the following regression model: $$Y_i=\alpha+\beta X_i+\epsilon_i.$$ The OLS estimator of $\beta$ is inconsistent if the ...
0
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1answer
34 views
Confounder real definition
In this video, I can see that confounding variable is a variable that is correlated with two other variables:
But this image tells that confounding variables is causally related to other two ...
1
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1answer
24 views
Kernel Estimation to Estimate Treatment Effect
I am trying to determine whether an estimator I came up with is just a non-parametric kernel estimator. I am performing a simulation study to estimate a treatment effect that I impose on my data.
My ...
3
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1answer
42 views
What is “selection modeling”?
Gelman & Zelizer (2014) write:
five other methods used for causal inference in observational studies: simple regression, matching, selection modeling, difference in differences, and ...
0
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0answers
6 views
Analysis of variables that can be both cause and consequence of the outcome in cross-sectional data
We are studying the risk factors for healthcare-associated infections (HAI), considering both patient and hospital-level variables.
To achieve as more as possible a causal interpretation of the ...
3
votes
2answers
54 views
Relationship between change in one variable in relation to another
I have on variable that is number of visitors. I am trying to investigate if a recent increase in another variable has caused or related to an increase in the number of visits.
I have run some ...
0
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1answer
23 views
Understanding average treatment effect estimator notation
I want to check that I understand the notation for the average treatment effect (ATE) estimator correctly, and hopefully some of you can double check this. I often try to understand formulas through ...
2
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0answers
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Causality between $X$ and $Y$ but with $X=Y$ [closed]
What is the F-value, if I am trying to check causality between X and Y but with X=Y?
0
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0answers
17 views
why causal models generated from PC algo do not show direction?
I have scenario which I do not understand why I do not get directions in the graph generated by PC algo. I have in total 7 features in my data set which I selected using feature selection mechanism. I ...
0
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1answer
20 views
How to compare the results of surveys for two different type of users
I am working on an online store as analyst. We are constantly running a satisfaction survey (rated -3 to 3). The response rate is very low (10%). We want to compare the results of surveys between ...
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1answer
34 views
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0answers
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Tree Based models vs traditional regression at identifying sub populations
Somewhat of a follow up to this question I asked. Can someone provide a good non technical explanation of why tree based methods are becoming so popular for identifying sub populations of people who ...
3
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0answers
26 views
Applying Heterogeneous treatment effects to clinical research (non technical explanation)
I'm trying to understand the hype around this estimation of heterogeneous treatment effects in the machine learning literature lately. It seems super interesting, but alot of it is beyond me. I read ...
4
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1answer
42 views
Treatment interference (causal analysis)
I am doing research on students and their perception of their grades. Specifically, I want to do an experiment where students either (a) see their actual grades in a course (as a percentage) - the ...
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0answers
9 views
Experiment design: what's the difference between diff in diff and post-stratification?
what's the difference between diff in diff and post-stratification? When should we use diff in diff and when should we use post_stratification quasi experiment design?
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7answers
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Interview question: If correlation doesn't imply causation, how do you detect causation?
I got this question:
If correlation doesn't imply causation, how do you detect causation?
in an interview.
My answer was: You do some form of A/B testing. The interviewer kept prodding me for ...
4
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0answers
25 views
How is EMSE derived for causal trees in Athey and Imbens (PNAS 2016)?
Athey and Imbens build a non-parametric matching procedure to identify and estimate causal effects. To this end, they minimize the expected mean squared error (EMSE) of their procedure, but I don't ...
0
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1answer
71 views
difference-in-difference and omitted variable bias
i have a question concerning the difference-in-differences research design:
if i can find a variable which is both correlated with the difference-in-difference estimator and the dependent variable of ...
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0answers
14 views
Derivation of Conditional Causal Probabilities
In Causal Inference in Statistics: an Overview, Pearl presents an equation describing distribution from a graphical model presented in figure 3:
The author arrives at equality (20) - see image above. ...
4
votes
3answers
136 views
Linear regression to answer causal questions
At a news agency, I want to understand whether the number of breaking news infuence the number of citations other media make relative to the news agency.
I do not measure citations of exact news, ...
0
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0answers
40 views
R Causal Impact package implementation
I'm trying to apply the CausalImpact R package and have few questions I'd like to clarify before proceeding:
Is the ...
2
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1answer
34 views
Covariance in system with lagged reverse causality
Is there an easy way to find the covariance between $x_t$ and $\epsilon_t^1$ in a system like
$$y_{t} = \beta x_{t} + \epsilon^1_{t}$$
$$x_{t} = \alpha y_{t-1} + \epsilon^2_{t},$$
potentially under ...
5
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2answers
74 views
Number of Causal Assumptions in an Overview by Pearl
In the paper Causal Inference in Statistics: an Overview by Pearl, in page 11 (106 if you go by the Journal's indexing), a graphical model is presented in figure 2(a). The text reads (picture below):
...
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0answers
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What does cointegration mean for causality?
If two series (say, y and x) are co-integrated, how can I interpret it in a DAG? Does it cause any problem to identify the causal effect of x over y? How should I draw the DAG to represent the co-...
