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statsmodels.discrete.discrete_model.NegativeBinomial.loglike

NegativeBinomial.loglike(params)[source]

Loglikelihood for negative binomial model

Parameters:

params : array-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

Notes

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

\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)

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

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