Controlling for already being at a given level


Fortran must die
Say your predictor (your intervention) is income gain. You believe that increased income leads to Y going up (what Y is does not matter, this is purely theoretical on my part). But individuals who already have a certain level of that might be less influenced by income gains. How do you address this? I was thinking this was an issue of non-linear data so that the slope would change at a certain level of income gain - and you just look for that. But that does not address the fact that individuals are already at a certain income level before the intervention occurs.

Do you use a variable to measure existing income levels as a control?


Not a robit
Just give us an example of what Y could be! So y (e.g., donations) regressed on income. Well yeah if you were trying to see if a person's income is correlated with donations and suspect a non-linear relationship, I would say a generalized additive model (GAM/ splines) would be your best bet to visualize the relationship. Then you may be able to break the dataset into groups based on income using a random training and testing datasets to ensure generalizability of model (not overfitted).