statsmodels.genmod.families.family.Binomial.loglike¶
-
Binomial.
loglike
(endog, mu, freq_weights=1, scale=1.0)[source]¶ The log-likelihood function in terms of the fitted mean response.
Parameters: endog : array-like
Endogenous response variable
mu : array-like
Fitted mean response variable
freq_weights : array-like
1d array of frequency weights. The default is 1.
scale : float, optional
Not used for the Binomial GLM.
Returns: llf : float
The value of the loglikelihood function evaluated at (endog,mu,freq_weights,scale) as defined below.
Notes
If the endogenous variable is binary:
llf = scale * \sum_i (y_i * \log(\mu_i/(1-\mu_i)) + \log(1-\mu_i)) * freq\_weights_i
If the endogenous variable is binomial:
llf = scale * \sum_i freq\_weights_i * (\ln \Gamma(n+1) - \ln \Gamma(y_i + 1) - \ln \Gamma(n_i - y_i +1) + y_i * \log(\mu_i / (1 - \mu_i)) + n * \log(1 - \mu_i))
where y_i = Y_i * n_i with Y_i and n_i as defined in Binomial initialize. This simply makes y_i the original number of successes.