statsmodels.genmod.families.family.Family.resid_anscombe

Family.resid_anscombe(endog, mu, var_weights=1.0, scale=1.0)

The Anscombe residuals

Parameters:

endogndarray

The endogenous response variable

mundarray

The inverse of the link function at the linear predicted values.

var_weightsarray_like

1d array of variance (analytic) weights. The default is 1.

scalefloat, optional

An optional argument to divide the residuals by sqrt(scale). The default is 1.

See also

statsmodels.genmod.families.family.Family

resid_anscombe for the individual families for more information

Notes

Anscombe residuals are defined by

$$resid\mathrm{\_}anscomb{e}_i=\frac{A(y)-A(\mu )}{A^{\prime }(\mu )\sqrt{Var[\mu ]}}\ast \sqrt{(}var\mathrm{\_}weights)$$

where $A^{\prime }(y)=v(y{)}^{-\frac{1}{3}}$ and $v(\mu )$ is the variance function $Var[y]=\frac{\varphi }{w}v(mu)$. The transformation $A(y)$ makes the residuals more normal distributed.