statsmodels.genmod.families.family.NegativeBinomial.resid_dev¶

NegativeBinomial.resid_dev(endog, mu, scale=1.0)[source]¶

Negative Binomial Deviance Residual

Parameters:

endog : array-like

endog is the response variable

mu : array-like

mu is the fitted value of the model

scale : float, optional

An optional argument to divide the residuals by scale

Returns:

resid_dev : array

The array of deviance residuals

Notes

resid_dev = sign(endog-mu) * sqrt(piecewise)

where piecewise is defined as

If $Y_i = 0$ :

$piecewise_i = 2*log(1+alpha*mu)/alpha$

If $Y_i > 0$ :

$piecewise_i = 2*Y*log(Y/\mu) - 2/\alpha * (1 + \alpha * Y) * \log((1 + \alpha * Y)/(1 + \alpha * \mu))$