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statsmodels.genmod.families.family.Gaussian.loglike

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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