How to get R-squared for robust regression (RLM) in Statsmodels?

Question

When it comes to measuring goodness of fit - R-Squared seems to be a commonly understood (and accepted) measure for "simple" linear models. But in case of statsmodels (as well as other statistical software) RLM does not include R-squared together with regression results. Is there a way to get it calculated "manually", perhaps in a way similar to how it is done in Stata?

Or is there another measure that can be used / calculated from the results produced by sm.RLS?

This is what Statsmodels is producing:

import numpy as np
import statsmodels.api as sm

# Sample Data with outliers
nsample = 50
x = np.linspace(0, 20, nsample)
x = sm.add_constant(x)
sig = 0.3
beta = [5, 0.5]
y_true = np.dot(x, beta)
y = y_true + sig * 1. * np.random.normal(size=nsample)
y[[39,41,43,45,48]] -= 5   # add some outliers (10% of nsample)

# Regression with Robust Linear Model
res = sm.RLM(y, x).fit()
print(res.summary())

Which outputs:

                    Robust linear Model Regression Results                    
==============================================================================
Dep. Variable:                      y   No. Observations:                   50
Model:                            RLM   Df Residuals:                       48
Method:                          IRLS   Df Model:                            1
Norm:                          HuberT                                         
Scale Est.:                       mad                                         
Cov Type:                          H1                                         
Date:                 Mo, 27 Jul 2015                                         
Time:                        10:00:00                                         
No. Iterations:                    17                                         
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
const          5.0254      0.091     55.017      0.000         4.846     5.204
x1             0.4845      0.008     61.555      0.000         0.469     0.500
==============================================================================

Answer 1

Since an OLS return the R2, I would suggest regressing the actual values against the fitted values using simple linear regression. Regardless where the fitted values come from, such an approach would provide you an indication of the corresponding R2.