Fixed effects regression and robust regression

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Fixed effects regression and robust regression

R help mailing list-2
Hello:
I am using R 3.0.2.  
I have panel data on countries' renewable energy net generation (and installed capacity) over time.  I am regressing these dependent variables on various socioeconomic variables, as well as binary policy variables.  I have have done basic OLS, but I wanted to explore both fixed effects models, as there are likely significant country effects (using plm) and robust regression (using rlm), as Q-Q plots indicate that there are some strong outliers.  This might be a question of apples and oranges, but how do I compare the goodness of fit of the fixed effects models with the robust regression models?  One can use F-tests to compare OLS and the fixed effects, and since the OLS and robust regressions have the same number of DFs, looking at the residual standard error is insightful.  Any help would be appreciated.
Cheers,
Michael

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Re: Fixed effects regression and robust regression

Bert Gunter
On Tue, May 19, 2015 at 1:23 PM, michael westphal via R-help
<[hidden email]> wrote:

You can't compare them (statistically -- you can of course draw
pictures). Note, from ?rlm:

" Note that the df.residual component is deliberately set to NA to
avoid inappropriate estimation of the residual scale from the residual
mean square by "lm" methods. "

Further questions should probably go to a statistics list like
stats.stackexchange.com, as statistical questions are generally
offtopic here.

Cheers,
Bert



Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll

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Re: Fixed effects regression and robust regression

S Ellison-2
In reply to this post by R help mailing list-2
> 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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