The R Book

Residuals

After fitting a model to data, we should investigate how well the model describes the data. In particular, we should look to see if there are any systematic trends in the goodness of fit. For example, does the goodness of fit increase with the observation number, or is it a function of one or more of the explanatory variables? We can work with the raw residuals:

residuals = response variable – fitted values.

With normal errors, the identity link, equal weights and the default scale factor, the raw and standardized residuals are identical. The standardized residuals are required to correct for the fact that with non-normal errors (like count or proportion data) we violate the fundamental assumption that the variance is constant (p. 389) because the residuals tend to change in size as the mean value the response variable changes.

For Poisson errors, the standardized residuals are

For binomial errors they are

where the binomial denominator is the size of the sample from which the y successes were drawn. For Gamma errors they are

In general, we can use several kinds of standardized residuals

where the prior weights are optionally specified by you to give individual data points ...