> since the OLS and robust regressions have the same number of DFs, looking

> at the residual standard error is insightful.

Sadly not. The residual scale in a robust model is only partly indicative of goodness of fit; robust models intentionally downweight outliers. Much of the difference in scale can be due to downweighting, rather than change in model, especially where outliers are roughly symmetricaly distributed. And the degrees of freedom are not, strictly, the same. You have the same numbers of observations, but once you throw in different weights, it's debatable whether the effective df are really equal to the classical df. In any case degrees of freedom mostly matters as a distribution parameter - if you could trust the distribution to be normal, chi-squared etc you would not need robust statistics.

What you can do, to an extent, is use something like lmRob in the robustbase package to test your fixed effects; comparing the different inferences will tell you something about which effects in OLS are simply artefacts caused by outliers. lmRob uses comparatively recent developments in wald-type inference tests to put the tests on a firmer footing.

S Ellison

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