statsmodels.discrete.discrete_model.NegativeBinomial.loglike

method

NegativeBinomial.loglike(params)

Loglikelihood for negative binomial model

Parameters

paramsarray-like

The parameters of the model. If loglike_method is nb1 or nb2, then the ancillary parameter is expected to be the last element.

Returns

llffloat

The loglikelihood value at params

Notes

Following notation in Greene (2008), with negative binomial heterogeneity parameter \(\alpha\):

\[\begin{split}\lambda_i &= exp(X\beta) \\ \theta &= 1 / \alpha \\ g_i &= \theta \lambda_i^Q \\ w_i &= g_i/(g_i + \lambda_i) \\ r_i &= \theta / (\theta+\lambda_i) \\ ln \mathcal{L}_i &= ln \Gamma(y_i+g_i) - ln \Gamma(1+y_i) + g_iln (r_i) + y_i ln(1-r_i)\end{split}\]

where :math`Q=0` for NB2 and geometric and \(Q=1\) for NB1. For the geometric, \(\alpha=0\) as well.