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Thanks Geoffrey. Let's say we are testing a drug which ends up lowering blood pressure. However, one of the consequences of the treatment is that it also increases the likelihood users also take vitamins (sorry for the lack of imagination) and this also lowers blood pressure. If you would like to isolate the impact of the treatment vs the impact of the vitamin usage, would it make sense to condition on the vitamin usage? What are the precautions I need to take here? A lot of the literature I've read warns against controlling for post-treatment variables in regressions:
Hi Dave thanks for your response. How do you account for the fact that you can make the data as granular as you want? For instance I could measure revenue per hour or per minute. The most granular view is actually per sale. Sorry for the confusion, but the purpose of the numeric locations was just so that I could add a revenue component unique to each location. The only thing to interpret from this simulation was the location coefficient since this isn’t a real model. I’ll make an edit to clarify this
Just to clarify, for the next iteration of bootstrap, this means I would sample with replacement from the original residuals (1.2, -1.37, -0.86, 1.03) and add them to the Y values calculated in the previous bootstrap (6.13, 4.6, ...), correct?