statsmodels.regression.linear_model.WLS.loglike¶

WLS.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 Y.

Parameters:¶

paramsarray_like

The parameter estimates.

Returns:¶

float

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

Notes

$$-\frac{n}{2}\log SSR-\frac{n}{2}(1+\log \left(\frac{2\pi }{n}\right))+\frac{1}{2}\log \left(\left|W\right|\right)$$

where $W$ is a diagonal weight matrix matrix, $\left|W\right|$ is its determinant, and $SSR={(Y-\hat{Y})}^{\prime }W(Y-\hat{Y})$ is the sum of the squared weighted residuals.