>Controlling for a collider leads to correlation<p>This is a big one that most people are not aware of. Quite often, in economics, medicine, and epidemiology, you'll see researchers adjust for everything in their regression model: income, physical activity, education, alcohol consumption, BMI, ... without realizing that they could easily be inducing collider bias.<p>A much better, but rare, approach is to sit down with some subject matter experts and draft up a DAG - directed acyclic graph - that makes your assumptions about the causal structure of the problem explicit. Then determine what needs to be adjusted for in order to get a causal estimate of the effect. When you're explicit about your causal assumptions, it makes it easier for other researchers to propose different causal structures, and see if your results still hold up under alternative causal structures.<p>The DAGitty tool [1] has some cool examples.<p>[1] <a href="https://www.dagitty.net/dags.html" rel="nofollow">https://www.dagitty.net/dags.html</a>
At the bottom, the author mentions that by "correlation" they don't mean "linear correlation", but all their diagrams show the presence or absence of a clear linear correlation, and code examples use linear functions of random variables.<p>They offhandedly say that "correlation" means "association" or "mutual information", so why not just do the whole post in terms of mutual information? I <i>think</i> the main issue with that is just that some of these points become tautologies -- e.g. the first point, "independent variables have zero mutual information" ends up being just one implication of the definition of mutual information.
Can these seven be reduced to three basic rules?<p>- controlling for a node increases correlation among pairs where both are ancestors<p>- controlling for a node does not affect (the lack of) correlation among pairs where at least one is categorically unrelated (shares no ancestry with that node)<p>- controlling for a node decreases correlation among pairs where both are related but at least one is not an ancestor
Rule 2 (“causation creates correlation”) would be strongly disputed by a lot of people. It relies on the assumption of “faithfulness” which is not discussed until the bottom of the article.<p>This is a very innocent sounding assumption but it’s actually quite strong. In particular it may be violated when there are control systems or strategic agents as part of the system you want to study — which is often the case for causal inference. In such scenarios (eg the famous thermostat example) you could have strong causal links which are invisible in the data.
> Independent variables are not correlated<p>But it's important to remember that <i>dependent</i> variables can also be <i>not correlated</i>. That is <i>no correlation</i> does <i>not</i> imply independence.<p>Consider this trivial case:<p>X ~ Uniform(-1,1)<p>Y = X^2<p>Cor(X,Y) = 0<p>Despite the fact that Y's value is absolutely determined by the value of X.
Humble reminder of how easy R is to use. Download and install R for your operating system: <a href="https://cran.r-project.org/bin/" rel="nofollow">https://cran.r-project.org/bin/</a><p>Start it in the terminal by typing:<p><pre><code> R
</code></pre>
Copy/paste the code from the article to see it run!
Are the assumptions "No spurious correlation", "Consistency", and "Exchangeability" ever actually true? If a dataset's big enough you should generally be able to find at least one weird correlation, and the others are limits of doing statistics in the real world.
I'm keeping this link, taking a backup and handing it out whenever i can. It is succinct and effective.<p>These are concepts i find myself constantly having to explain and teach and they are critical to problem solving.
I highly suggest this paper here for a more complete view of causality that nests do-calculus (at least in economics):<p>Heckman, JJ and Pinto, R. (2024): “Econometric causality: The central role of thought experiments”, Journal of Econometrics, v.243, n.1-2.
> Rule 8: Controlling for a causal descendant (partially) controls for the ancestor<p>perhaps this is a quaint or wildly off base question, but an honest one, please forgive any ignorance:<p>Isn't this essentiallydefining the partial derivative? Should one arrive at the calculus definition of a partial derivative by following this?
This is brilliant. The whole causal inference thing is something I only came across after university, either I missed it or it is a hole in the curriculum, because it seems incredibly fundamental to our understanding of the world.<p>The thing that made be read into it was a quite interesting sentence from lesswrong, saying that actually the common idea that correlation does not imply causation is wrong. Now it's not wrong in the face-value sense, it's wrong in the sense that actually you can use correlations to learn something about causation, and there turns out to be a whole field of study here.