I always wondered what exactly people mean when they say “controlling for ...” as if somehow they can tell apart cause A and cause B for the effect C.

It turns out if you can measure A and B without noise, the whole "controlling for..." business is legit, but if you only have noisy estimates A' and B' of the actual A and B, then the "controlling for..." technique used by many researchers does not work very well at all.

interesting quotes:

> The present results demonstrate that, for a very common class of incremental validity arguments, such a strategy runs a high risk of failure. The scope of the problem is considerable: literally hundreds of thousands of studies spanning numerous fields of science have historically relied on measurement-level incremental validity arguments to support strong conclusions about the relationships between theoretical constructs.

> We conclude that many previous findings in the social sciences are at high risk of having concluded that two constructs are distinct when they may not in fact be so.

Note how polite the authors are. They don't say it straight up that many (most?) multiple regression results are bullshit, they just say "at high risk of being wrong."