NegativeBinomial.loglike()

statsmodels.discrete.discrete_model.NegativeBinomial.loglike

NegativeBinomial.loglike(params) [source]

Loglikelihood for negative binomial model

Parameters:

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`

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.

Links:

http://statsmodels.sourceforge.net/stable/generated/statsmodels.discrete.discrete_model.NegativeBinomial.loglike.html

doc_statsmodels

2017-01-18 16:12:43

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