statsmodels.genmod.families.family.Binomial.deviance¶
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Binomial.
deviance
(endog, mu, freq_weights=1, scale=1.0)[source]¶ Deviance function for either Bernoulli or Binomial data.
Parameters: endog : array-like
Endogenous response variable (already transformed to a probability if appropriate).
mu : array
Fitted mean response variable
freq_weights : array-like
1d array of frequency weights. The default is 1.
scale : float, optional
An optional scale argument. The default is 1.
Returns: deviance : float
The deviance function as defined below
Notes
If the endogenous variable is binary:
D = -2 * \sum_i freq\_weights * (I_{1,i} * \log(\mu_i) + I_{0,i} * \log(1 - \mu_i))
where I_{1,i} is an indicator function that evalueates to 1 if Y_i = 1. and I_{0,i} is an indicator function that evaluates to 1 if Y_i = 0.
If the model is ninomial:
D = 2 * \sum_i freq\_weights * (\log(Y_i / \mu_i) + (n_i - Y_i) * \log((n_i - Y_i) / n_i - \mu_i))
where Y_i and n are as defined in Binomial.initialize.