statsmodels.genmod.families.family.Gaussian.loglike_obs

method

Gaussian.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)

The log-likelihood function for each observation in terms of the fitted mean response for the Gaussian distribution.

Parameters

endogarray

Usually the endogenous response variable.

muarray

Usually but not always the fitted mean response variable.

var_weightsarray-like

1d array of variance (analytic) weights. The default is 1.

scalefloat

The scale parameter. The default is 1.

Returns

ll_ifloat

The value of the loglikelihood evaluated at (endog, mu, var_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

\[ll_i = -1 / 2 \sum_i * var\_weights * ((Y_i - mu_i)^2 / scale + \log(2 * \pi * scale))\]