[R] Robust Non-linear Regression

[Ruben Roa]

> -----Original Message-----
> From:	r-help-bounces at stat.math.ethz.ch [SMTP:r-help-bounces at stat.math.ethz.ch] On Behalf Of Vermeiren, Hans [VRCBE]
> Sent:	Sunday, November 13, 2005 7:48 PM
> To:	'r-help at stat.math.ethz.ch'
> Subject:	[R] Robust Non-linear Regression
> 
> Hi,
>  
> I'm trying to use Robust non-linear regression to fit dose response curves.
> Maybe I didnt look good enough, but I dind't find robust methods for NON
> linear regression implemented in R. A method that looked good to me but is
> unfortunately not (yet) implemented in R is described in 
> http://www.graphpad.com/articles/RobustNonlinearRegression_files/frame.htm
> <http://www.graphpad.com/articles/RobustNonlinearRegression_files/frame.htm>
> 
> 
> in short: instead of using the premise that the residuals are gaussian they
> propose a Lorentzian distribution,
> in stead of minimizing the squared residus SUM (Y-Yhat)^2, the objective
> function is now
> SUM log(1+(Y-Yhat)^2/ RobustSD)
>  
> where RobustSD is the 68th percentile of the absolute value of the residues
>  
> my question is: is there a smart and elegant way to change to objective
> function from squared Distance to log(1+D^2/Rsd^2) ?
>  
-----------
I do not know about in-built robustness options in R but I have found that 
Dave Fournier's robust likelihood for nonlinear regression in ADMB does
a pretty good job in detecting and counter-acting the influence of outliers
(in my applications this has been used to counter-act the effect of reading 
errors in determination of the age of fish based on rings in bones). 
It relies on a likelihood function based on a mixture of a normal and another
distribution with fatter tails. You can find the documentation in the ADMB manual 
at the ADMB website: http://otter-rsch.com/admodel.htm
Ruben