statsmodels.genmod.families.family.Gaussian.loglike
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Gaussian.loglike(endog, mu, scale=1.0)
[source] -
Loglikelihood function for Gaussian exponential family distribution.
Parameters: endog : array-like
Endogenous response variable
mu : array-like
Fitted mean response variable
scale : float, optional
Scales the loglikelihood function. The default is 1.
Returns: llf : float
The value of the loglikelihood function evaluated at (endog,mu,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((endog-link^(-1)(mu))**2)
If the links is not the identity link then the loglikelihood function is defined as llf = sum((
endog`*`mu
-mu`**2/2)/`scale
-endog`**2/(2*`scale
) - (1/2.)*log(2*pi*`scale`))
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