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Seven basic rules for causal inference

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Re: Seven basic rules for causal inference

#41

Post by kyllo »

currymj wrote: post #3

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. 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…

Indeed, causally linked variables need not be correlated in observed data; bias in the opposite direction of the causal effect may approximately equal or exceed it in magnitude and "mask" the correlation. Chapter 1 of this popular causal inference book demonstrates this with a few examples: https://mixtape.scunning.com/01-introduction#do-not-confuse-...

Re: Seven basic rules for causal inference

#43

Post by bjornsing »

abeppu wrote: post #30

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. They offhandedly say that "correlation" means "association" or "mutual information", so why not just do the whole post in terms of mutual information? I think the main issue with tha…

I’d be more interested in those tautologies nonetheless. Much better than literally untrue statements that I have to somehow decipher.

Re: Seven basic rules for causal inference

#44

Post by westurner »

jdhwosnhw wrote: post #36
abeppu wrote: post #30

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. They offhandedly say that "correlation" means "association" or "mutual information", so why not just do the whole post in terms of mutual information? I think the main issue with tha…

This isnt a correction to your post, but a clarification for other readers: correlation implies dependence, but dependence does not imply correlation. Conversely, two variables share non-zero mutual information if and only if they are dependent.

By that measure, all of these Spurious Correlations indicate insignificant dependence, which isn't of utility: https://www.tylervigen.com/spurious-correlations

Isn't it possible to contrive an example where a test of pairwise dependence causes the statistician to error by excluding relevant variables from tests of more complex relations?

Trying to remember which of these factor both P(A|B) and P(B|A) into the test

Re: Seven basic rules for causal inference

#45

Post by levocardia »

Vecr wrote: post #4

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.

Some situations guarantee certain assumptions: Randomization, for example, guarantees exchangeability.

Re: Seven basic rules for causal inference

#46

Post by joe_the_user »

BenoitP wrote: post #11
currymj wrote: post #3

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. 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…

I'd argue you both could be right. Your comment could lead to a definition of intelligence. Organisms capable of causally influencing deterministic systems to their advantage can be marked as intelligent. The complexity of which would determine the degree of intelligence. Your point is great in that it pinpoints also the notions of agency scopes. In all the causal DAGs it feels like there are implicit regions: ones w…

Two problem with this. 1. There are many other ways that correlation doesn't imply causation. 2. The phenomenon the gp describes doesn't require broad intelligence but just reactiveness - a thermostat or a guided missile could have this.

Re: Seven basic rules for causal inference

#47

Post by levocardia »

>Controlling for a collider leads to correlation

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.

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.

The DAGitty tool [1] has some cool examples.

[1] https://www.dagitty.net/dags.html

Re: Seven basic rules for causal inference

#48

Post by cubefox »

currymj wrote: post #31
cubefox wrote: post #28

Earlier quoted context omitted.

What is an appropriate measure of (in)dependence though, if not Pearson correlation? Such that you feed a scatter plot into the formula for this measure, and if the measure returns 0 dependence, the variables are independent.

it's a tough problem. there are various schemes for estimating mutual information from samples. if you do that and mutual information is very close to zero, then I guess you can claim the two rvs are independent. But these estimators are pretty noisy and also often computationally frustrating (the ones I'm familiar with require doing a bunch of nearest-neighbor search between all the points). I agree with the OP that…

Yeah. It would be simpler to talk about causal graphs if the nodes represented only events instead of arbitrary variables, because independence between events is much simpler to determine: X and Y are independent iff P(X) * P(Y) = P(X and Y). For events there also exists a measure of dependence: The so-called odds ratio. It is not influenced by the marginal probabilities, unlike Pearson correlation (called "phi coefficient" for events) or pointwise mutual information. Of course in practice events are usually not a possible simplification.

Re: Seven basic rules for causal inference

#49

Post by abeppu »

westurner wrote: post #44
jdhwosnhw wrote: post #36

Earlier quoted context omitted.

This isnt a correction to your post, but a clarification for other readers: correlation implies dependence, but dependence does not imply correlation. Conversely, two variables share non-zero mutual information if and only if they are dependent.

By that measure, all of these Spurious Correlations indicate insignificant dependence, which isn't of utility: https://www.tylervigen.com/spurious-correlations Isn't it possible to contrive an example where a test of pairwise dependence causes the statistician to error by excluding relevant variables from tests of more complex relations? Trying to remember which of these factor both P(A|B) and P(B|A) into the test

I think you're using the word "insignificant" in a possibly misleading or confusing way.

I think in this context, the issue with the spurious correlations from that site is that they're all time series for overlapping periods. Of course, the people who collected these understood that time was an important causal factor in all these phenomena. In the graphical language of this post:

T --> X_i

T --> X_j

Since T is a common cause to both, we should expect to see a mutual information between X_i, X_j. In the paradigm here, we could try to control for T and see if a relationship persists (i.e. perhaps in the same month, collect observations for X_i, X_j in each of a large number of locales), and get a signal on whether some the shared dependence on time is the only link.

Re: Seven basic rules for causal inference

#50

Post by chrsig »

> Rule 8: Controlling for a causal descendant (partially) controls for the ancestor

perhaps this is a quaint or wildly off base question, but an honest one, please forgive any ignorance:

Isn't this essentiallydefining the partial derivative? Should one arrive at the calculus definition of a partial derivative by following this?

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