Are robust weights accounted in the calculation of the Goodness-of-fit statistics, returned as the gof structure of fit function?

When using fit function with robust option activated (Robust:'Bisquare'), are robust weights actually accounted in the calculation of the Goodness-of-fit statistics, which is returned as the gof structure?

Answer 1

[Govind KM]

Hi @mila_po,

The Robust parameter is indeed taken into account in the calculation of the Goodness-of-fit statistics when using the fit function. This can be seen by comparing the gof outputs from a robust fit to those from a non-robust fit:

load census
[f,gof1] = fit(cdate,pop,'poly3','Normalize','on');
[f,gof2] = fit(cdate,pop,'poly3','Normalize','on','Robust','Bisquare');
disp(gof1)

           sse: 149.7687
       rsquare: 0.9988
           dfe: 17
    adjrsquare: 0.9986
          rmse: 2.9682

disp(gof2)

           sse: 85.5715
       rsquare: 0.9993
           dfe: 17
    adjrsquare: 0.9992
          rmse: 2.2436

This can also been seen by stepping through the code of the fit function, which can be accessed by:

edit fit

At line 413, when the Robust parameter is set, the iRobustLinearFit function is called instead of iLinearFit. The residuals are adjusted through some calculations based on the robust weights. These weighted residuals subsequently influence the calculation of the Goodness-of-fit metrics in the iGoodnessStructure function.

Hope this clarifies the issue!