Linked Questions

105 votes
17 answers

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 ...
Rob Hyndman's user avatar
  • 57.6k
76 votes
6 answers

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?
Neil G's user avatar
  • 15.4k
22 votes
6 answers

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 ...
user4572's user avatar
  • 221
23 votes
3 answers

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 ...
RayVelcoro's user avatar
  • 1,189
21 votes
5 answers

Definition and delimitation of regression model

An embarrassingly simple question -- but it seems it has not been asked on Cross Validated before: What is the definition of a regression model? Also a support question, What is not a regression ...
Richard Hardy's user avatar
30 votes
2 answers

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 ...
Judio's user avatar
  • 303
17 votes
3 answers

Which OLS assumptions are colliders violating?

The following webpage says that: We should not control for a collider variable! Which OLS assumptions are colliders violating?
robertspierre's user avatar
9 votes
2 answers

Incorrectly Using the Word "Causal" to Describe a Regression Model?

Suppose we take the classical linear regression model: $$y_i = \beta_0 + \beta_1 x_i + \epsilon_i$$ Over the years, I have heard so many people say that such an interpretation can be drawn from this ...
stats_noob's user avatar
15 votes
5 answers

What are the differences between stochastic and fixed regressors in linear regression model?

If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
Kun's user avatar
  • 502
17 votes
3 answers

Difference Between Simultaneous Equation Model and Structural Equation Model

Can anybody please help me to understand the differences between simultaneous equations models and structural equation models (SEM)? It will be great if somebody can provide me some literature on it. ...
Beta's user avatar
  • 6,386
14 votes
2 answers

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, ...
Esha's user avatar
  • 141
18 votes
1 answer

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)) = \...
Jae's user avatar
  • 283
13 votes
3 answers

Regression and causality in econometrics

In regression in general and in linear regression in particular, causal interpretation of parameters is sometimes permitted. At least in econometrics literature, but not only, when causal ...
markowitz's user avatar
  • 5,729
6 votes
2 answers

Strict exogeneity and lagged variables

I am confused why strict exogeneity must be violated when we have lagged time series variables. My understanding of strict exogeneity is that a variable must be uncorrelated with error terms in all ...
mangofruit's user avatar
4 votes
3 answers

Conditional probability and causality

I would like to understand the link between conditional probabilities and causality. More precisely: Assume we have two variables $A=\{0,1\}$ and $B=\{0,1\}$ and we observe: $P(A=1|B=1)>P(A=1|B=0)...
user6441253's user avatar

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