statsmodels.regression.linear_model.GLS.loglike¶

GLS.loglike(params)[source]¶

Returns the value of the gaussian loglikelihood function at params.

Given the whitened design matrix, the loglikelihood is evaluated at the parameter vector params for the dependent variable endog.

Parameters :

params : array-like

The parameter estimates

Returns :

loglike : float

The value of the loglikelihood function for a GLS Model.

Notes

The loglikelihood function for the normal distribution is

$-\frac{n}{2}\log\left(Y-\hat{Y}\right)-\frac{n}{2}\left(1+\log\left(\frac{2\pi}{n}\right)\right)-\frac{1}{2}\log\left(\left|\Sigma\right|\right)$

Y and Y-hat are whitened.