statsmodels.discrete.discrete_model.NegativeBinomial.loglike¶

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:¶

llffloat

The loglikelihood value at params

Notes

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

$$\begin{array}{rl}{\lambda }_i& =exp(X\beta )\\ \theta & =1/\alpha \\ g_i& =\theta {\lambda }_i^Q\\ w_i& =g_i/(g_i+{\lambda }_i)\\ r_i& =\theta /(\theta +{\lambda }_i)\\ ln{\mathcal{L}}_i& =ln\mathrm{\Gamma }(y_i+g_i)-ln\mathrm{\Gamma }(1+y_i)+g_{i}ln(r_i)+y_{i}ln(1-r_i)\end{array}$$

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