statsmodels.genmod.families.family.Family.resid_anscombe¶

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

The Anscombe residuals

Parameters: endog (array) – The endogenous response variable mu (array) – The inverse of the link function at the linear predicted values. var_weights (array-like) – 1d array of variance (analytic) weights. The default is 1. scale (float, optional) – An optional argument to divide the residuals by sqrt(scale). The default is 1.

statsmodels.genmod.families.family.Family
$resid\_anscombe_i = \frac{A(y)-A(\mu)}{A'(\mu)\sqrt{Var[\mu]}} * \sqrt(var\_weights)$
where $$A'(y)=v(y)^{-\frac{1}{3}}$$ and $$v(\mu)$$ is the variance function $$Var[y]=\frac{\phi}{w}v(mu)$$. The transformation $$A(y)$$ makes the residuals more normal distributed.