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If there is no duplicated observations in each level of covariates, then we cannot use Pearson or deviance residuals. An alternative is to use DARMA residuals in R (where we generate the Ys using the different covariates). Could someone intuitively explain why this procedure work?

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Assuming the model is correct, for each value of the covariate, you simulate the response y for a certain number of times (e.g. 10 times). Then you constructive the cumulative distribution of y for this value of covariate. Then you evaluate the cumulative distribution evaluated at the observed y. For example, if all the y you generate are smaller than the observed y, then you will see an residual of 0 for the cumulative distribution. If half the y you generate are smaller than the observed y, then you will see an residual of 0.5 for the cumulative distribution. So given a correct model, the residuals should follow a uniform distribution. These residuals can then be reflected in a QQ plot to detect a potential deviation from the uniform distribution.

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