statsmodels.discrete.discrete_model.NegativeBinomial.loglike¶
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NegativeBinomial.loglike(params)[source]¶ 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
- llf
float The loglikelihood value at params
- llf
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.