Questions tagged [causality]

The relationship between cause and effect.

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196 votes
5 answers
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How exactly does one “control for other variables”?

Here is the article that motivated this question: Does impatience make us fat? I liked this article, and it nicely demonstrates the concept of “controlling for other variables” (IQ, career, income, ...
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148 votes
9 answers
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Does causation imply correlation?

Correlation does not imply causation, as there could be many explanations for the correlation. But does causation imply correlation? Intuitively, I would think that the presence of causation means ...
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101 votes
17 answers
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Under what conditions does correlation imply causation?

We all know the mantra "correlation does not imply causation" which is drummed into all first year statistics students. There are some nice examples here to illustrate the idea. But sometimes ...
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98 votes
7 answers
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The Book of Why by Judea Pearl: Why is he bashing statistics?

I am reading The Book of Why by Judea Pearl, and it is getting under my skin1. Specifically, it appears to me that he is unconditionally bashing "classical" statistics by putting up a straw man ...
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80 votes
6 answers
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Does no correlation imply no causality?

I know that correlation does not imply causality but does an absence of correlation imply absence of causality?
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69 votes
6 answers
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Criticism of Pearl's theory of causality

In the year 2000, Judea Pearl published Causality. What controversies surround this work? What are its major criticisms?
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59 votes
3 answers
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Statistics and causal inference?

In his 1984 paper "Statistics and Causal Inference", Paul Holland raised one of the most fundamental questions in statistics: What can a statistical model say about causation? This led to his ...
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58 votes
7 answers
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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 ...
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57 votes
10 answers
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What is the difference between prediction and inference?

I'm reading through "An Introduction to Statistical Learning" . In chapter 2, they discuss the reason for estimating a function $f$. 2.1.1 Why Estimate $f$? There are two main reasons we ...
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53 votes
6 answers
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How are propensity scores different from adding covariates in a regression, and when are they preferred to the latter?

I admit I'm relatively new to propensity scores and causal analysis. One thing that's not obvious to me as a newcomer is how the "balancing" using propensity scores is mathematically different from ...
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50 votes
6 answers
113k views

What do "endogeneity" and "exogeneity" mean substantively?

I understand that the basic definition of endogeneity is that $$ X'\epsilon=0 $$ is not satisfied, but what does this mean in a real world sense? I read the Wikipedia article, with the supply and ...
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9 answers
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Correlation does not imply causation; but what about when one of the variables is time?

I know this question has been asked a billion times, so, after looking online, I am fully convinced that correlation between 2 variables does not imply causation. In one of my stats lectures today, we ...
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42 votes
3 answers
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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. ...
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40 votes
3 answers
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Does statistical independence mean lack of causation?

Two random variables A and B are statistically independent. That means that in the DAG of the process: $(A {\perp\!\!\!\perp} B)$ and of course $P(A|B)=P(A)$. But does that also mean that there's no ...
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38 votes
7 answers
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Can cross validation be used for causal inference?

In all contexts I am familiar with cross-validation it is solely used with the goal of increasing predictive accuracy. Can the logic of cross validation be extended in estimating the unbiased ...
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36 votes
4 answers
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X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?

X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant ...
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36 votes
3 answers
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What's the relation between hierarchical models, neural networks, graphical models, bayesian networks?

They all seem to represent random variables by the nodes and (in)dependence via the (possibly directed) edges. I'm esp interested in a bayesian's point-of-view.
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34 votes
5 answers
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Introduction to causal analysis

What are good books that introduce causal analysis? I'm thinking of an introduction that both explains the principles of causal analysis and shows how different statistical methods could be used to ...
32 votes
6 answers
5k views

Under which assumptions a regression can be interpreted causally?

First, don't panic. Yes, there are many similar question on this site. But I believe none gives a conclusive answer to the question below. Please bear with me. Consider a data generation process $\...
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32 votes
6 answers
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If 'correlation doesn't imply causation', then if I find a statistically significant correlation, how can I prove the causality?

I understand that correlation is not causation. Suppose we get high correlation between two variables. How do you check if this correlation is actually because of causation? Or,under what conditions, ...
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29 votes
9 answers
7k views

When can correlation be useful without causation?

A pet saying of many statisticians is "Correlation doesn't imply causation." This is certainly true, but one thing that DOES seem implied here is that correlation has little or no value. Is this ...
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27 votes
4 answers
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Is there any theory or field of study that concerns itself with modeling causation rather than correlation?

My understanding is that probability (at least from a frequentist viewpoint) is a mathematical tool for modeling correlations. So, for example, we can say that two events $X$ and $Y$ are defined to be ...
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27 votes
5 answers
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From a statistical perspective, can one infer causality using propensity scores with an observational study?

Question: From the standpoint of statistician (or a practitioner), can one infer causality using propensity scores with an observational study (not an experiment)? Please, do not want to start a ...
26 votes
1 answer
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A layman understanding of the difference between back-door and front-door adjustment

I'm referring to the back-door adjustment and front-door adjustment here: Back-door adjustment:The archetypal epidemiological problem in statistics is to adjust for the effect of a measured ...
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26 votes
2 answers
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What are the main differences between Granger's and Pearl's causality frameworks?

Recently, I ran across several papers and online resources that mention Granger causality. Brief browsing through the corresponding Wikipedia article left me with the impression that this term refers ...
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25 votes
3 answers
2k views

Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)

I'm a rookie with statistics, and I'm struggling to understand this: it is well known that a confounding factor can cause a spurious association, leading to rejecting a true null hypothesis (i.e. due ...
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25 votes
3 answers
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Representing interaction effects in directed acyclic graphs

Directed acyclic graphs (DAGs; e.g., Greenland, et al, 1999) are a part of a formalism of causal inference from the counterfactual interpretation of causality camp. In these graphs the presence of an ...
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24 votes
7 answers
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Explain in layperson's terms why predictive models aren't causally interpretable

Imagine that you are asked to infer some causal effect -- a change in an outcome $y$ in response to some variable $x$. But, the person asking for this directs you to use a predictive model to do so. ...
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24 votes
3 answers
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Difference between rungs two and three in the Ladder of Causation

In Judea Pearl's "Book of Why" he talks about what he calls the Ladder of Causation, which is essentially a hierarchy comprised of different levels of causal reasoning. The lowest is concerned with ...
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24 votes
1 answer
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Which Theories of Causality Should I know?

Which theoretical approaches to causality should I know as an applied statistician/econometrician? I know the (a very little bit) Neyman–Rubin causal model (and Roy, Haavelmo etc.) Pearl's Work on ...
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24 votes
2 answers
8k views

Structural Equation Models (SEMs) versus Bayesian Networks (BNs)

The terminology here is a mess. "Structural equation" is about as vague as "architectural bridge" and "Bayesian network" is not intrinsically Bayesian. Even better, God-of-causality Judea Pearl says ...
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23 votes
5 answers
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Are mediation analyses inherently causal?

I am interested in testing a simple mediation model with one IV, one DV, and one mediator. The indirect effect is significant as tested by the Preacher and Hayes SPSS macro, which suggests the ...
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23 votes
2 answers
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Whether to use structural equation modelling to analyse observational studies in psychology

I've noticed this issue coming up a lot in statistical consulting settings and i was keen to get your thoughts. Context I often speak to research students that have conducted a study approximately ...
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22 votes
1 answer
5k views

How does a causal tree optimize for heterogenous treatment effects?

I have a very specific question regarding how the causal tree in the causal forest/generalized random forest optimizes for heterogeneity in treatment effects. This question comes from the Athey & ...
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21 votes
6 answers
60k views

Does simple linear regression imply causation?

I know correlation does not imply causation but instead the strength and direction of the relationship. Does simple linear regression imply causation? Or is an inferential (t-test, etc.) statistical ...
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21 votes
2 answers
4k views

do(x) operator meaning?

I have seen the $do(x)$ operator everywhere in some literature review I am doing on Causality (see, for instance this wikipedia entry). However, I cannot find a formal and general definition of this ...
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21 votes
4 answers
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To what extent is the distinction between correlation and causation relevant to Google?

Context A popular question on this site is " What are common statistical sins?". One of the sins mentioned is assuming that "correlation implies causation..." link Then, in the comments with 5 ...
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20 votes
1 answer
3k views

Confounder - definition

According to M. Katz in his book Multivariable analysis (Section 1.2, page 6), "A confounder is associated with the risk factor and causally related to the outcome." Why must the confounder be ...
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19 votes
5 answers
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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 ...
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19 votes
1 answer
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Why do we do matching for causal inference vs regressing on confounders?

I'm new to the area of causal inference. From what I understand, one of the main concerns that causal inference tries to address is the effect of confounders! For the sake of reference, let's denote ...
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19 votes
1 answer
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Interpreting Granger causality test's results

I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online. I also came across a very helpful tool, the Bivariate Granger Causality - Free ...
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19 votes
2 answers
11k views

Unconfoundedness in Rubin's Causal Model- Layman's explanation

When implementing Rubin's causal model, one of the (untestable) assumptions that we need is unconfoundedness, which means $$(Y(0),Y(1))\perp T|X$$ Where the LHS are the counterfactuals, the T is the ...
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19 votes
3 answers
882 views

How is causation defined mathematically?

What is the mathematical definition of a causal relationship between two random variables? Given a sample from the joint distribution of two random variables $X$ and $Y$, when would we say $X$ causes ...
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18 votes
4 answers
3k views

Relationships between correlation and causation

From the Wikipedia page titled correlation does not imply causality, For any two correlated events, A and B, the different possible relationships include: A causes B (direct causation); B causes A (...
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18 votes
2 answers
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Can an instrumental variable equation be written as a directed acyclic graph (DAG)?

Directed acyclic graphs (DAGs) are efficient visual representations of qualitative causal assumptions in statistical models, but can they be used to present a regular instrumental variable equation (...
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18 votes
4 answers
9k views

Why does propensity score matching work for causal inference?

Propensity score matching is used for make causal inferences in observational studies (see the Rosenbaum / Rubin paper). What's the simple intuition behind why it works? In other words, why if we ...
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18 votes
3 answers
10k views

Real examples of Correlation confused with Causation

I'm looking for specific, real cases in which a causal relationship was inappropriately inferred from evidence of a correlation. Specifically, I'm interested in examples that meet the following ...
18 votes
3 answers
4k views

Understanding d-separation theory in causal Bayesian networks

I am trying to understand the d-Separation logic in Causal Bayesian Networks. I know how the algorithm works, but I don't exactly understand why the "flow of information" works as stated in the ...
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17 votes
13 answers
4k views

Can you infer causality from correlation in this example of dictator game?

I've just had en exam where we were presented with two variables. In a dictator game where a dictator is given 100 USD, and can choose how much to send or keep for himself, there was a positive ...
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17 votes
2 answers
1k views

Why is Propensity Score Matching better than just Matching?

Propensity Score Matching at a high level uses a framework of: Identify potential confounders from the co-variates i.e all factors which can potentially influence the subject being part of experiment ...
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