statsmodels.genmod.families.family.Gaussian.deviance

Gaussian.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=2i(freq_weightsivar_weights(llf(endogi,endogi)llf(endogi,μi)))

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

Internally, we calculate deviance as:

D=ifreq_weightsivar_weightsresid_devi/scale

Last update: Feb 19, 2025