statsmodels.genmod.families.family.Binomial.loglike_obs

Binomial.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)

The log-likelihood function for each observation in terms of the fitted mean response for the Binomial distribution.

Parameters:

• endog (array) – Usually the endogenous response variable.
• mu (array) – Usually but not always the fitted mean response variable.
• var_weights (array-like) – 1d array of variance (analytic) weights. The default is 1.
• scale (float) – The scale parameter. The default is 1.

Returns:

ll_i – The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below.

Return type:

float

Notes

If the endogenous variable is binary:

\[ll_i = \sum_i (y_i * \log(\mu_i/(1-\mu_i)) + \log(1-\mu_i)) * var\_weights_i\]

If the endogenous variable is binomial:

\[ll_i = \sum_i var\_weights_i * (\ln \Gamma(n+1) - \ln \Gamma(y_i + 1) - \ln \Gamma(n_i - y_i +1) + y_i * \log(\mu_i / (n_i - \mu_i)) + n * \log(1 - \mu_i/n_i))\]

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.