statsmodels.genmod.families.family.Gaussian.loglike_obs¶
-
Gaussian.
loglike_obs
(endog, mu, var_weights=1.0, scale=1.0)[source]¶ The log-likelihood function for each observation in terms of the fitted mean response for the Gaussian distribution.
- Parameters
- endog
ndarray
Usually the endogenous response variable.
- mu
ndarray
Usually but not always the fitted mean response variable.
- var_weightsarray_like
1d array of variance (analytic) weights. The default is 1.
- scale
float
The scale parameter. The default is 1.
- endog
- Returns
- ll_i
float
The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below.
- ll_i
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
\[ll_i = -1 / 2 \sum_i * var\_weights * ((Y_i - mu_i)^2 / scale + \log(2 * \pi * scale))\]