Obtaining sigma zero from statsmodels.WLS

Question

I've successfully run statsmodels.WLS(Y, X, weights=1/cov), where cov is a vector of squared standard errors of the observations, matching the shape of the endogenous/response variable/regressand (Y).

What I want from the results is the sigma zero value, which is the square root of (v^TWv/degrees of freedom), where v is the residuals vector, and W is the Weight matrix, but I have no idea how to get it, and the docs aren't helping me much, presumably because of the different terminology. What should I be looking for in the results object?

I know the value's in there, because results.bse gives me correct standard errors for the parameter estimates, which can't be obtained without sigma zero.

Answer 1

The weighted residual variance is available as attribute of the results instance, scale and mse_resid. see http://statsmodels.sourceforge.net/devel/generated/statsmodels.regression.linear_model.RegressionResults.html

>>> resw.scale
0.99139414802065384
>>> resw.mse_resid
0.99139414802065384

>>> np.dot(resw.wresid, resw.wresid) / resw.df_resid
0.99139414802065384

>>> (resw.resid * resw.model.weights * res.resid).sum() / resw.df_resid
0.99139414802065395

You need to take the sqrt if you want the standard deviation.