statsmodels.genmod.families.family.Poisson.deviance¶
- Poisson.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.
- scale
float,optional An optional scale argument. The default is 1.
- Returns:
- Deviance
ndarray The value of deviance function defined below.
- Deviance
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:
\[D = \sum_i freq\_weights_i * var\_weights * resid\_dev_i / scale\]