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. The default is 1.

Returns:

resid_dev : array

The array of deviance residuals

Notes

$resid\_dev_i = sign(Y_i-\mu_i) * \sqrt{piecewise_i}$

where $piecewise_i$ is defined as

If $Y_i = 0$ :

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

If $Y_i > 0$ :

$piecewise_i = 2 * Y_i * \log(Y_i / \mu_i) - (2 / \alpha) * (1 + \alpha * Y_i) * \log((1 + \alpha * Y_i) / (1 + \alpha * \mu_i))$