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In statistical models, confounding is said to occur when the apparent dependence of the response on a predictor is partially or wholly due to the dependence of both on a third variable not included in the model, or dependence on a linear combination of other variables included in the model. Confounding with a variable included in a model is often called multicollinearity. A synonym is *aliasing*, used in design of experiments.

7 votes

Is it possible to have a variable that acts as both an effect modifier and a confounder?

However, when we run the regression of $y$ on $x$ only, we also see the confounding kicking in: lm(y ~ x) Coefficients: (Intercept) x -0.258 4.856 Finally, as pointed out …
Julian Schuessler's user avatar
2 votes

Identifying a confounder

Section 6.2 of that book is called "Why There Is No Statistical Test For Confounding", which is exactly true. … One needs to either randomize or make substantive assumptions about causal mechanisms in order to rule out confounding. …
Julian Schuessler's user avatar
3 votes
Accepted

Are there any circumstances where adjusting for path variables / mediators is useful?

Your intuition is correct, although of course in reality, things are a bit more complex. Suppose you think the causal graph looks like this: Then you can estimate the average causal effect of $D$ o …
Julian Schuessler's user avatar