statsmodels.genmod.families.family.Binomial.loglike_obs¶

Binomial.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)[source]¶

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:

$$l{l}_i=\sum _i(y_i\ast \log ({\mu }_i/(1-{\mu }_i))+\log (1-{\mu }_i))\ast var\mathrm{\_}weight{s}_i$$

If the endogenous variable is binomial:

$$l{l}_i=\sum _{i}var\mathrm{\_}weight{s}_i\ast (\ln \mathrm{\Gamma }(n+1)-\ln \mathrm{\Gamma }(y_i+1)-\ln \mathrm{\Gamma }(n_i-y_i+1)+y_i\ast \log ({\mu }_i/(n_i-{\mu }_i))+n\ast \log (1-{\mu }_i/n_i))$$

where $y_i=Y_i\ast n_i$ with $Y_i$ and $n_i$ as defined in Binomial initialize. This simply makes $y_i$ the original number of successes.