statsmodels.genmod.families.family.NegativeBinomial.deviance

NegativeBinomial.deviance(endog, mu, var_weights=1.0, freq_weights=1.0, scale=1.0)

The deviance function evaluated at (endog, mu, var_weights, freq_weights, scale) for the distribution.

Deviance is usually defined as twice the loglikelihood ratio.

Parameters

endogarray_like

The endogenous response variable

muarray_like

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

var_weightsarray_like

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

freq_weightsarray_like

1d array of frequency weights. The default is 1.

scalefloat, optional

An optional scale argument. The default is 1.

Returns

Deviancendarray

The value of deviance function defined below.

Notes

Deviance is defined

$$D = 2\sum_i (freq\_weights_i * var\_weights * (llf(endog_i, endog_i) - llf(endog_i, \mu_i)))$$

where y is the endogenous variable. The deviance functions are analytically defined for each family.

Internally, we calculate deviance as:

$$D = \sum_i freq\_weights_i * var\_weights * resid\_dev_i / scale$$