# Linked Questions

102 votes
17 answers
68k 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 ...
• 54.3k
70 votes
6 answers
8k 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?
• 14.4k
21 votes
6 answers
63k 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 ...
• 211
20 votes
5 answers
3k views

### 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 ...
• 61.1k
21 votes
3 answers
13k 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 ...
• 1,139
25 votes
2 answers
5k 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 ...
• 253
16 votes
3 answers
1k views

### 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?
• 1,834
13 votes
5 answers
8k views

### 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 $(y,\vec{x})$. ...
• 462
15 votes
3 answers
8k views

### Difference Between Simultaneous Equation Model and Structural Equation Model

Can anybody please help me to understand what are the differences between Simultaneous Equation Model and Structural Equation Model (SEM)? It will be great if somebody can provide me some literature ...
• 6,174
13 votes
2 answers
1k 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, ...
• 131
15 votes
1 answer
3k 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)) = \...
• 153
12 votes
3 answers
2k views

### 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 ...
• 4,480
5 votes
2 answers
11k views

### 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 ...
4 votes
3 answers
1k views

### 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)...
• 487
8 votes
2 answers
1k views

### What is the relationship between minimizing prediction error versus parameter estimation error?

With the advent of statistical learning techniques, people are talking a lot about prediction error, while in classical statistics, one is focusing on parameter estimation error. What is the ...
• 3,025

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