[RsR] VIF for robust regression?

[Olivier Renaud]

I don't know if there is work on a robust VIF. Here are my two cents:
- What type of variable do you have ? If some of them are discrete with 
very few different values, this may cause problem to robust covariance 
matrices estimation.
- Your approach to apply the "partialling out"  of the robust matrix, as 
in the OLS case,  might or might not be correct, I don't know.
- If you believe that 1/(1-R^2_i) is a good measure, then you might want 
to compute its direct robust equivalent.  The output of lmrob does not 
provide a R^2, but the output of lmRob does. We have recently published 
a paper however that shows that the robust R-squared provided by lmRob 
is biased, sometimes to a large extent. We provide a consistent and 
robust estimator of R-squared and a version adjusted for the sample 
size.  See my previous post for an example and the code at
https://stat.ethz.ch/pipermail/r-sig-robust/2010/000290.html

Olivier

ref: Renaud, O. & Victoria-Feser, M.-P. (2010). A robust coefficient of 
determination for regression. Journal of Statistical Planning and 
Inference, 140, 1852-1862. http://dx.doi.org/10.1016/j.jspi.2010.01.008






On 31/03/2011 17:35, Nicholas Lewin-Koh wrote:
> Hi,
> I was looking at the vif function in the car package
> and it it is trivial to modify to make a version for robust
> regression. However, after trying it out I noticed  that what
> were reasonable values under ols, jumped way up.
> So my thought is that either,
> I made a coding error, and the weights attribute needs to be used
> to modify the variance covariance matrix of the coefficients
> Or, the reduced variance from the robust regression, causes peripheral
> points
> (outside the mve) to have much more influence in the r^2's for each
> predictor.
> So that the standard vif measure, 1/(1-R^2_i) is not relevant in this
> context.
> Am I off base here?
>
> Thanks
> Nicholas
>
>
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-- 
Olivier.Renaud using unige.ch               http://www.unige.ch/fapse/mad/
Methodology&  Data Analysis - Psychology Dept - University of Geneva
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