What is an effect modifier?
An effect modifier changes how big an effect is. In Ghana, the typical maize response to fertiliser was 2.8 tonnes a hectare in the Sudan Savannah and 0.9 in the Forest–Savannah Transition. You don’t adjust a modifier away and report one number; you report the effect for each group, because a national average would be wrong almost everywhere.
Last time's quick check: a treatment that keeps weak animals alive changes who reaches slaughter, so the treated survivors include animals that would otherwise have died. Today: the last of the cast, and the cause nobody measured. Not every variable is something to adjust away. Some tell you who benefits.
In Ghana, researchers analysed 2,854 yields from randomised fertiliser trials. The typical maize response was 2.8 tonnes a hectare in the Sudan Savannah, and 0.9 in the Forest–Savannah Transition. Same fertiliser, about three times the response. The Italian olive study found the same pattern by size: the efficiency gain was largest on small farms.
Zone, there, is an effect modifier: it changes how big the effect is. You don't "control for" a modifier and report one number. You report the effect for each group, because a national average would be wrong almost everywhere. Two cautions. A map shows which way influence flows, not how strongly, so "for whom?" is a question you ask alongside it. And the trials randomised the fertiliser, not the zone: the zones show where the effect differs, not why.
Next, a role that lets you measure an effect from outside. An instrument pushes the treatment around but has no other route to the outcome. In Module 1 we met Philip Wright, who in 1928 used conditions that shifted the supply of flaxseed to measure the demand for it.
Here's a farm version. A cow's genes partly set how much milk she gives, and genes are dealt out before any farmer makes a decision, a little like a lottery. So comparing cows by their milk-yield genes is like comparing cows assigned at random to higher or lower yield.
Researchers did this with tens of thousands of Holstein cows and found evidence that higher milk yield itself raises the risk of mastitis. The method is called Mendelian randomisation. The catch is the second condition. If the same genes affect mastitis some other way, say through the shape of the udder, the instrument leaks and the answer is biased. An instrument is only as good as the case that it has no back route.
Finally, the variables you can't measure properly, or at all. A proxy is a stand-in. Disease risk on arrival at a feedlot is hard to measure, so arrival weight stands in for part of it. A lab result stands in for the true composition of the grain. Proxies help, but they leave some confounding behind. On a map, the proxy hangs off the thing it measures.
Some causes are never recorded at all: the grower's skill, the stockperson's eye. On a map, an unmeasured confounder is drawn as a dashed box. Drawing it is honest. It shows the back door you can't close by adjustment. Then there are three options. Randomise, so the hidden cause can't line up with the treatment. Find a design that sidesteps it, like an instrument. Or work out how strong it would have to be to change your conclusion: the sensitivity analysis from the prologue. What you must not do is leave it off the map and hope.
That completes the cast. Next: putting it all together on a real case, and seeing how a map changes what you do next.
Using genes as a natural lottery. A cow’s genes partly set how much milk she gives, and they are dealt out before any farmer makes a decision, so comparing cows by their milk-yield genes is like comparing cows assigned at random to higher or lower yield. It works only if the genes have no other route to the outcome, such as udder shape.
Draw it on the map as a dashed box, so the back door you can’t close is visible. Then randomise, so the hidden cause can’t line up with the treatment; find a design that sidesteps it, such as an instrument; or work out how strong it would need to be to change your conclusion. Never leave it off the map and hope.
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