Questions tagged [causality]

The relationship between cause and effect.

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177
votes
5answers
226k views

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, ...
140
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8answers
38k views

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 ...
34
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4answers
47k views

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 ...
58
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3answers
6k views

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 ...
16
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1answer
2k 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 ...
36
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2answers
3k views

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. ...
95
votes
17answers
61k views

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 ...
9
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3answers
7k views

Transfer function in forecasting models - interpretation

I am occupied with ARIMA modelling augmented with exogenous variables for promotional modelling purposes and i have hard time explaining it to business users. In some cases software packages end up ...
10
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3answers
723 views

Regression and causality in econometrics

In regression in general and in linear regression in particular causal interpretation about parameters is sometimes permitted. At least in econometrics literature, but not only, when causal ...
14
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2answers
2k 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 ...
7
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4answers
6k views

Omitted variable bias: which predictors do I need to include, and why?

For a last couple of weeks I've been thinking about OVB (Omitted variable bias) in the context of regression and solution for that (how to avoid this problem). I am acquainted with Shalizi's lectures (...
30
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6answers
2k 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 $\...
8
votes
3answers
709 views

T-consistency vs. P-consistency

Francis Diebold has a blog post "Causality and T-Consistency vs. Correlation and P-Consistency" where he presents the notion of P-consistency, or presistency: Consider a standard linear regression ...
41
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3answers
5k views

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 ...
46
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5answers
108k 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 ...
4
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1answer
218 views

linear causal model

Currently I’m focused on linear causal model expressed as a structural equation like this: $y = \beta_1 x_1 + \beta_2 x_2 + … + \beta_k x_k + u$ where $E[u|x_1,x_2,…,x_k]=0$ (exogenous error) we ...
48
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5answers
30k views

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 ...
30
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5answers
3k views

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 ...
17
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1answer
3k views

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 ...
5
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0answers
211 views

Structural equation and causal model in economics

Structural equations is a useful language for causal analysis in economics. In Causality Pearl (2009 cap 5) we can find the best discussion about this. My question: is possible to use the concept of ...
2
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2answers
672 views

What is the actual definition of endogeneity?

I've been learning about endogeneity but after looking around online I've gotten more and more confused about what the definition is. Most pages say that in a model $y=X\beta+\epsilon$ the definition ...
3
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0answers
257 views

Regression: Causation vs Prediction vs Description

In my experience it seems me that the interpretation about regression, its meaning and its scope, are debatable and great confusion exist about those things. It seems me that confusions are not go ...
21
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2answers
1k views

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 ...
10
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2answers
1k views

Does Simpson's Paradox cover all instances of reversal from a hidden variable?

The following is a question about the many visualizations offered as 'proof by picture' of the existence of Simpson's paradox, and possibly a question about terminology. Simpson's Paradox is a fairly ...
19
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7answers
52k 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 ...
12
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3answers
2k views

Is the linearity assumption in linear regression merely a definition of $\epsilon$?

I am revising linear regression. The textbook by Greene states: Now, of course there will be other assumptions on the linear regression model, such as $E(\epsilon|X)=0$. This assumption ...
13
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1answer
253 views

How would econometricians answer the objections and recommendations raised by Chen and Pearl (2013)?

In their article, Chen and Pearl (2013), critically examined 6 econometric textbooks, among these the textbooks written by Wooldridge (2009) {the introductory book}, and Stock & Watson (2011). ...
18
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2answers
9k 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 ...
9
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4answers
2k views

Mathematical definition of causality

Let $Y$ and $X$ be random variables. $E(Y|X)$ is the conditional mean of $Y$ given $X$. We say $Y$ is not causally related to $X$ if $E(Y|X)$ does not depend on $X$, which implies it is equal to $E(Y)$...
2
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1answer
2k views

Matching with Multiple Treatments

What's the best way to use matching methods with multiple treatment groups? I'm assessing the impact of an intervention on an outcome. For my first analysis, I used the MatchIt package (see code below)...
35
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3answers
9k views

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.
17
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1answer
31k views

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 ...
8
votes
1answer
24k views

How do I interpret a “difference-in-differences” model with continuous treatment?

How do I interpret the ATE coefficient (i.e., the post-treatment indicator interacted with the continuous variable)? Does it make sense? Should I break it down into subgroups and just run a fixed ...
24
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2answers
2k views

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 ...
10
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4answers
843 views

Why isn't causal inference a simple specialized regression problem?

I am often told that the crucial difficulty in causal inference is that we only observe one value between $Y(1)$ and $Y(0)$ while we want to estimate $E[Y(1) - Y(0)]$. There is always an unobserved ...
12
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1answer
2k views

Causal effect by back-door and front-door adjustments

If we wanted to calculate the causal effect of $X$ on $Y$ in the causal graph below, we can use both the back-door adjustment and front-Door adjustment theorems, i.e., $$P(y | \textit{do}(X = x)) = \...
8
votes
1answer
1k views

Should I use a machine learning model to calculate propensity score?

In my study, running a simple linear model to calculate de propensity score for each example seemed to not be able to model my treatment choosing process correctly. My question is, does it make sense ...
7
votes
1answer
982 views

Correlation, regression and causal modeling

This is probably a blindingly obvious answer for any seasoned statistician, but I am still confused as to how correlation differs from regression, technically. I understand that one is a measure of ...
6
votes
1answer
179 views

conditional and interventional expectation

Conditional expectation $E[Y|X]$ and interventional expectation $E[Y|do(X)]$ are related but conceptually very different things. I know that if $X$ is a randomly assigned by an experiment, we have ...
5
votes
1answer
321 views

Causality: Structural Causal Model and DAG

I know that in general a structural causal model (SCM) can be written in terms of structural equations. And in a more qualitative but formal manner, we can rewrite a structural model in terms of DAG. ...
13
votes
2answers
989 views

Is a regression causal if there are no omitted variables?

A regression of $y$ on $x$ need not be causal if there are omitted variables which influence both $x$ and $y$. But if not for omitted variables and measurement error, is a regression causal? That is, ...
3
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1answer
133 views

How does propensity score matching that uses only a small proportion of eligible patients affect generalizability?

I am reviewing a paper that seeks to assess the effect of treatment on mortality using observational data about 2,985 hospitalized patients. A propensity-matched analysis ends up with 380 patients (...
63
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5answers
6k views

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?
75
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6answers
12k views

Does no correlation imply no causality?

I know that correlation does not imply causality but does an absence of correlation imply absence of causality?
38
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7answers
3k views

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 ...
18
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2answers
4k views

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 ...
18
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2answers
2k views

Can a instrument 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 instrument variable equation (or ...
12
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4answers
35k views

Is there a test for omitted variable bias in OLS?

I am aware of the Ramsey Reset test which may detect nonlinear dependencies. However, if you just throw out one of the regression coefficients (merely linear dependencies), you may get a bias, ...
16
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3answers
3k 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 ...
14
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1answer
5k views

The difference between average and marginal treatment effect

I have been reading some papers, and I am unclear about the specific definitions of Average Treatment Effect (ATE), and Marginal Treatment Effect (MTE). Are they the same? According to Austin... A ...