statsmodels.genmod.families.family.Gaussian.loglike¶
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Gaussian.
loglike
(endog, mu, freq_weights=1.0, scale=1.0)[source]¶ The log-likelihood in terms of the fitted mean response.
Parameters: endog : array-like
Endogenous response variable
mu : array-like
Fitted mean response variable
freq_weights : array-like
1d array of frequency weights. The default is 1.
scale : float, optional
Scales the loglikelihood function. The default is 1.
Returns: llf : float
The value of the loglikelihood function evaluated at (endog,mu,freq_weights,scale) as defined below.
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))