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:¶

endogndarray

Usually the endogenous response variable.

mundarray

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.

$$llf=-nobs/2\ast (\log (SSR)+(1+\log (2\pi /nobs)))$$

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

$$l{l}_i=-1/2\sum _i\ast var\mathrm{\_}weights\ast ((Y_i-m{u}_i{)}^2/scale+\log (2\ast \pi \ast scale))$$