statsmodels.regression.linear_model.GLS.loglike¶

GLS.loglike(params)[source]¶

Compute the value of the Gaussian log-likelihood function at params.

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

Parameters:¶

paramsarray_like

The model parameters.

Returns:¶

float

The value of the log-likelihood function for a GLS Model.

Notes

The log-likelihood function for the normal distribution is

\[-\frac{n}{2}\log\left(\left(Y-\hat{Y}\right)^{\prime} \left(Y-\hat{Y}\right)\right) -\frac{n}{2}\left(1+\log\left(\frac{2\pi}{n}\right)\right) -\frac{1}{2}\log\left(\left|\Sigma\right|\right)\]

Y and Y-hat are whitened.