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

endogndarray

Usually the endogenous response variable.

mundarray

Usually but not always the fitted mean response variable.

var_weightsarray_like

1d array of variance (analytic) weights. The default is 1.

scalefloat

The scale parameter. The default is 1.

Returns

ll_ifloat

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

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.