The log-likelihood in terms of the fitted mean response.
Parameters: | endog : array-like
mu : array-like
freq_weights : array-like
scale : float, optional
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Returns: | llf : float
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Notes
If the link is the identity link function then the loglikelihood function is the same as the classical OLS model.
llf = -nobs / 2 * (\log(SSR) + (1 + \log(2 \pi / nobs)))
where
SSR = \sum_i (Y_i - g^{-1}(\mu_i))^2
If the links is not the identity link then the loglikelihood function is defined as
llf = \sum_i freq\_weights_i * ((Y_i * \mu_i - \mu_i^2 / 2) / scale- Y^2 / (2 * scale) - (1/2) * \log(2 * \pi * scale))