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?
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)