What are chains, forks and colliders in a causal diagram?
They are the three shapes every causal map is built from. In a chain, one thing affects a second, which affects a third. In a fork, one thing affects two others. In a collider, two arrows point into the same box. Chains and forks pass association along unless you hold the middle fixed; colliders block it unless you do.
Last time: a missing arrow claims there is no direct effect, and it's the boldest claim on any map. Today: the three shapes every map is built from, and how association travels through each one. The first shape is a chain: one thing affects a second, which affects a third. Spray zinc on the leaves, zinc builds up in the leaf, and some of it moves into the grain. Along a chain, association flows. Sprayed fields will tend to have more grain zinc, and that's the effect we're after.
Now hold the middle fixed. Compare only plants with the same leaf zinc, and whether they were sprayed tells you nothing more about the grain. The route ran through the leaf, and you've blocked it. Remember that. It comes back when we meet mediators. The second shape is a fork: one thing affects two others.
Remember the farm where grain zinc tracked fibre almost perfectly across five wheat samples? Here's one possible reason. Zinc and fibre are both concentrated in the outer layers of the grain, the bran. A sample with more bran will tend to have more of both.
So zinc and fibre move together, but neither causes the other. Bran is a common cause, and association runs out along both prongs of the fork. Hold the middle fixed. Compare only samples with the same bran fraction, and if the fork is the whole story, the link between zinc and fibre disappears. That's exactly what the published case proposes to check, by measuring bran fraction alongside the grain.
And when a common cause also drives a treatment, it has a name you already know from the prologue: a confounder. The third shape is the odd one out: a collider, where two arrows point into the same box. Suppose farmers send grain to the lab when something looks promising: either the soil is unusually good, or they've tried a new treatment and want to see whether it worked.
Out in the fields, soil quality and the new treatment have nothing to do with each other. Now look only at the samples that reached the lab. If a sample came from ordinary soil, it was probably sent because of the treatment. If it wasn't treated, the soil was probably good. So among lab samples, treated fields tend to have poorer soil. A link has appeared from nowhere.
At a collider, association is blocked until you hold the collider fixed; then it opens. Choosing which samples to study is one way of holding it fixed, and it's how many real data sets get built. So here's the whole rule in one line. Chains and forks let association through, unless you hold the middle fixed. Colliders block it, unless you hold the middle fixed.
Every map, however tangled, is made of these three shapes. To know which routes between a treatment and an outcome are open, you trace each one, shape by shape. Next: how to use these shapes to find, and close, the routes that would fool you. They're called back doors.
Both are concentrated in the outer layers of the grain, the bran, so a sample with more bran tends to have more of both. Bran is a common cause: a fork. Compare samples with the same bran fraction and, if the fork is the whole story, the link between zinc and fibre disappears.
If farmers send grain to the lab when the soil is unusually good or when they’ve tried a new treatment, the lab sample is a collider. Among lab samples, one from ordinary soil was probably sent because of the treatment, so treated fields seem to have poorer soil, although out in the fields the two have nothing to do with each other.
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