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I did a poisson regression by hand and want to create a diagnostic plot. Now iam not sure, should i plot deviance residuals vs fitted values or vs log(fitted values)? Why or why not?

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Against actual fitted and against the fit on the scale of the linear predictor would both be reasonable -- either should be fine as far as assessing whether the residuals deviate from flatness as the fitted values change.

Which is easier to work with may depend on a number of factors (e.g. how broad a range of predicted values is covered, the pattern of the predictors, personal preference)

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