statsmodels.genmod.families.family.NegativeBinomial.resid_dev¶
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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 \(Y_i > 0\):
\(piecewise_i = 2 * Y_i * \log(Y_i / \mu_i) - (2 / \alpha) * (1 + \alpha * Y_i) * \log((1 + \alpha * Y_i) / (1 + \alpha * \mu_i))\)