An alternative to the usual residual (see regression diagnostics) which Anscombe proposed in 1953 for cases where the random errors in a general regression model do not have a normal distribution. The idea is to produce quantities that do have near-normal distributions, and the form for the residual depends upon the error distribution assumed.
In the case of a Poisson distribution, an Anscombe residual is given by
where
y and
ŷ are, respectively,
observed and
fitted values. In the case of a
gamma distribution the formula becomes
and in the case of an
inverse normal distribution the formula is
