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

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

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