What is a causal map, or DAG?
A causal map, or directed acyclic graph, draws each thing that varies as a box and each direct effect as an arrow. It has no numbers or equations: it shows which way influence can flow. Drawn before the data are analysed, it puts assumptions where agronomists, vets, nutritionists and farmers can check them.
Module 1's last quick check: Cornfield asked how strong a hidden cause would need to be to explain the pattern. Now, back to the ladder from the prologue: seeing, doing, imagining. To climb from seeing to doing without an experiment, you need a model of how the world works, written down before you look at the data.
This module is about the simplest, most useful way to write it down: a causal map. A causal map has two ingredients. Each thing that varies, like a zinc spray or the zinc in the grain, is a box. Statisticians call it a node. An arrow from one box to another says: this directly affects that. That's all.
No numbers, no equations. The map doesn't say how big an effect is, or even whether it helps or harms. It says which way influence can flow. The idea is a century old. Around 1920, Sewall Wright, a geneticist at the US Department of Agriculture, drew arrows between the causes of traits in guinea pigs.
Today the formal version has a name: a DAG. D for directed: every arrow points one way, from cause to effect. A for acyclic: no route of arrows leads back to where it started. G for graph: boxes and arrows. Farming is full of feedback. Healthy soil grows a bigger crop, the crop leaves residue, and the residue feeds the soil. Isn't that a loop?
It is, but only if you ignore time. Soil this year affects yield this year, and the residue affects the soil next year. Drawn season by season, the loop becomes a line, and the map stays acyclic. Time is how a map handles feedback. Here's the part people find surprising. The strongest claim on a map isn't an arrow. It's an arrow that isn't there.
Draw an arrow and you're saying "this might have an effect". That's cautious. Leave one out and you're saying "no direct effect at all", and the analysis will lean on it. Leave out an arrow from earthworms to grain zinc, and you're claiming earthworms affect zinc only through the routes you've drawn, such as soil chemistry.
If that's wrong, the answer will be wrong however much data you collect. So every missing arrow is a question for the experts in the room: are we sure? Here's a real map, simplified, from a wheat case study published on vitagri.org. The question: could a foliar zinc spray change the zinc in the grain?
Five boxes. Foliar zinc, the treatment. Grain composition, the outcome. A laboratory result, which is how the grain gets measured. And two more: baseline soil and soil chemistry. The arrows say baseline soil can affect whether a field is sprayed and, through soil chemistry, what ends up in the grain.
Without the map, you'd compare sprayed and unsprayed fields and call the difference the spray's effect. With it, you can see straight away that soil might explain the difference instead. Before anyone runs a model, the map has told you what you need to measure.
And this is a selected extract. The complete map behind a case like this is much larger, and it stays private. Because it's just boxes and arrows, people who aren't statisticians can check it: an agronomist, a vet, a nutritionist, a farmer. They know which arrows belong. A map turns their knowledge into something the analysis has to respect. Next: every map, however large, is built from just three shapes. Learn them and you can read any map.
By adding time. Healthy soil grows a bigger crop, the crop leaves residue, and the residue feeds the soil, which looks like a loop. But soil this year affects yield this year, and the residue affects the soil next year. Drawn season by season, the loop becomes a line and the map stays acyclic.
Drawing an arrow says only that something might have an effect, which is cautious. Leaving one out says there is no direct effect at all, and the analysis will lean on it. If that claim is wrong, the answer will be wrong however much data you collect, so every missing arrow is a question for the experts in the room.
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