Zack M. Davis summarizes collider bias as follows:
The explaining-away effect (or, collider bias; or, Berkson’s paradox) is a statistical phenomenon in which statistically independent causes with a common effect become anticorrelated when conditioning on the effect.
In the language of d-separation, if you have a causal graph X → Z ← Y, then conditioning on Z unblocks the path between X and Y.
… if you have a sore throat and cough, and aren’t sure whether you have the flu or mono, you should be relieved to find out it’s “just” a flu, because that decreases the probability that you have mono. You could be inflected with both the influenza and mononucleosis viruses, but if the flu is completely sufficient to explain your symptoms, there’s no additional reason to expect mono.[1]
Wikipedia gives a further example:
Suppose Alex will only date a man if his niceness plus his handsomeness exceeds some threshold. Then nicer men do not have to be as handsome to qualify for Alex’s dating pool. So, among the men that Alex dates, Alex may observe that the nicer ones are less handsome on average (and vice versa), even if these traits are uncorrelated in the general population. Note that this does not mean that men in the dating pool compare unfavorably with men in the population. On the contrary, Alex’s selection criterion means that Alex has high standards. The average nice man that Alex dates is actually more handsome than the average man in the population (since even among nice men, the ugliest portion of the population is skipped). Berkson’s negative correlation is an effect that arises within the dating pool: the rude men that Alex dates must have been even more handsome to qualify.
No crazy psychoanalysis, just a simple statistical artifact. (On a meta level, perhaps attractive people are meaner for some reason, but a priori, doesn’t collider bias explain away the need for other explanations?)
This seems like it could be everywhere. Most things have more than one causal parent; if it has many parents, there’s probably a pair which is independent. Then some degree of collider bias will occur for almost all probability distributions represented by the causal diagram, since collider bias will exist if (in the linked formalism). And if we don’t notice it unless we make a serious effort to reason about the causal structure of a problem, then we might spend time arguing about statistical artifacts, making up theories to explain things which don’t need explaining!
In The Book of Why, Judea Pearl speculates (emphasis mine):
Our brains are not wired to do probability problems, but they are wired to do causal problems. And this causal wiring produces systematic probabilistic mistakes, like optical illusions. Because there is no causal connection between [ and in ], either directly or through a common cause, [people] find it utterly incomprehensible that there is a probabilistic association. Our brains are not prepared to accept causeless correlations, and we need special training—through examples like the Monty Hall paradox… - to identify situations where they can arise. Once we have “rewired our brains” to recognize colliders, the paradox ceases to be confusing.
But how is this done? Perhaps one simply meditates on the wisdom of causal diagrams, understands the math, and thereby comes to properly intuitively reason about colliders, or at least reliably recognize them.
This question serves two purposes:
If anyone has rewired their brain thusly, I’d love to hear how.
It’s not clear to me that the obvious kind of trigger-action-plan will trigger on non-trivial, non-obvious instances of collider bias.
To draw attention to this potential bias, since I wasn’t able to find prior discussion on LessWrong.
One idea: make a list of situations in which you trade off against 2+ qualities, notice if you’ve formed a collider bias, and explain to yourself what’s going on. I’ll try two:
Food can be tasty and healthy. Why is food that’s tasty so often unhealthy, and vice versa? Insofar as the collider effect is the explanation, then it’s because I have a tastiness + healthiness threshold. Foods don’t need to be as tasty if they’re healthy enough, and they don’t need to be as healthy if they’re tasty enough. Also, there’s some set of foods that simply aren’t tasty + healthy enough to eat, like American cheese, out-of-season tomatoes, and Chips Ahoy.
Vacations can be relaxing and interesting. Why are interesting vacations so often stressful, and relaxing vacations so often boring? The collider effect strikes again! I don’t want to go on vacations that are neither relaxing nor interesting, such as a trip to Cancun or Ibiza.
Food can have more virtues. It can be cheap, easy to prepare, and different from what I’ve eaten recently. Weirdly enough, this means that the more potential virtues something has, the more likely you’re going to consume something that entirely lacks a certain virtue. If I go to a single-price restaurant, where price, ease of preparation, and variety are held constant, tastiness and healthiness are the only ways I can make a selection and will be more important. By contrast, if I’m at home, how tasty and healthy the meal is can more often take a back seat to these other factors.
However, I’d also note that the reason we may not think too often about “collider bias” may be that most things are correlated. Price correlates with all the other virtues in just about everything you can consume. Excitement and stress seem likely to be correlated.
If X->Z<-Y, then X and Y are independent unless you’re conditioning on Z. A relevant TAP might thus be:
Trigger: I notice that X and Y seem statistically dependent
Action: Ask yourself “what am I conditioning on?”. Follow up with “Are any of these factors causally downstream of both X and Y?” Alternatively, you could list salient things causally downstream of either X or Y and check the others.
This TAP unfortunately abstract because “things I’m currently conditioning on” isn’t an easy thing to list, but it might help.
One way to “rewire” your brain is to wire in a quick check- how does selection/stratification/conditioning matter here?
But perhaps most important is to think causally. Sure, you can open up associations, but, theoretically, do they make sense? Why would obesity, conditional on having cardiovascular disease, reduce mortality? Addressing why rather than leaping to a bivariate causal conclusion is important. This is why scientists look for mechanisms and mechanism-implicating boundary conditions.
I call this subcategory of Berkson’s paradox issues the conservation of virtue effect: when there is a filter somewhere for something like a sum of good qualities, then all good qualities are negatively correlated. Another major subcategory is the “if you observe something which has multiple possible explanations, those explanations are negatively correlated” effect. I don’t think these two subtypes cover all the instances, but they do seem to cover a large fraction, and they aren’t too difficult to internalize.