statsmodels.genmod.families.family.NegativeBinomial.loglike_obs

NegativeBinomial.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 Negative 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

Defined as:

\[llf = \sum_i var\_weights_i / scale * (Y_i * \log{(\alpha * \mu_i / (1 + \alpha * \mu_i))} - \log{(1 + \alpha * \mu_i)}/ \alpha + Constant)\]

where \(Constant\) is defined as:

\[Constant = \ln \Gamma{(Y_i + 1/ \alpha )} - \ln \Gamma(Y_i + 1) - \ln \Gamma{(1/ \alpha )}\]

constant = (special.gammaln(endog + 1 / self.alpha) -

special.gammaln(endog+1)-special.gammaln(1/self.alpha))

return (endog * np.log(self.alpha * mu / (1 + self.alpha * mu)) -

np.log(1 + self.alpha * mu) / self.alpha + constant) * var_weights / scale