[R] Robust measures of goodness of fit?

[Jon Olav Vik]

Dear all,

I have been using rlm() for robust regression. Could someone please  
suggest an appropriate measure of goodness-of-fit [1]? All I've found  
after trawling the web, literature databases, and previous r-help posts,  
is the "robust R^2" on pp. 362-363 of the S-plus manual, which is  
available at
http://web.mit.edu/afs/athena/software/splus_v7.0/www/statman1.pdf
(7.57 MB)

It is based on M-estimators as detailed in Chapter 11 of statman1.pdf. I  
think the s-plus method lmRobMM() returns this "robust R-squared", but I  
would like to stay within R. Implementing the abovementioned formulas in R  
was not straightforward because the definition and notation of the loss  
functions (psi,rho,Tukey's bisquare) differ between statman1.pdf and
http://spider.stat.umn.edu/R/library/MASS/html/rlm.html

I would be most grateful for any references or tips.

[1] I'm picturing my data as possibly contaminated by some other  
phenomenon than the one I'm interested in. What I think I want is a robust  
estimator of the R-squared which would be obtained in the absence of such  
contamination.

Sincerely,
Jon Olav Vik