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When assessing a GLM fit, why is it customary to plot residuals against the linear predictor rather than the response variable? I noticed that plot(glm) defaults to using the linear predictor values, but it isn't clear to me why this is the case.

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I guess you mean why use model predictions on the linear instead of the response scale? I don't think there is a deep reason, other that points are usually more evenly distributed on the scale of the linear predictor.

What you cannot do is to plot against observed responses, because you expect residuals and observed responses to be correlated.

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