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Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear relation.

I'm trying to prove this to myself via simulation, and am wondering if anyone might have any insight.

I'm imagining the following relations between three covariates (which I think should suffice):

  1. Z ~ E1
  2. X ~ Z + E2
  3. Y ~ Z + X + E3

(Ei being error terms)

I'm just wondering if anyone can shed some insight as to how I might generate data that yield relations such that Y~X appears linear, Y~X|Z appears non-linear.

Apologies for any ambiguity.

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