[R] alternatives to traditional least squares method in linear regression ?

[Wolfgang Raffelsberger]

Dear list,

I have encountered a special case for searching a linear regression 
where I'm not satisfied with the results obtained using the traditional 
least squares method (sometimes called OLS) for estimating/optimizing 
the residues to the regression line (see code below).  Basically, a 
group of my x-y data are a bit off the diagonal line (in my case the 
diagonal represents the ideal or theoretical fit between x and y, which 
are in the same scale) and thus these points have sufficient power to 
impose a slope deviating (too much) from the diagonal. Using rlm() 
didn't help since this is not a problem of rare outliers.
 From a pragmatic point of  view using a linear regression approach does 
fit very well the nature of the data & comparison I'd like to perform, 
so that's why I'd like to stay with something linear.

Has anybody already implemented a function or package in R allowing to 
modify the exponent (of the least squares method) or more general 
allowing to define the model to be used for estimating/optimizing the 
residues ?

Thank's in advance
Wolfgang Raffelsberger


 > plot(x,y)    # x and y are my data
 > regr <- lm(y~x)
 > abline(regr)
 > # I'm not satisfied with the line since there is one group of points 
following very well the diagonal but the regression is deviated by 
another group of points ...
 >
 > sessionInfo()
R version 2.6.0 (2007-10-03)
i386-pc-mingw32

locale:
LC_COLLATE=French_France.1252;LC_CTYPE=French_France.1252;LC_MONETARY=French_France.1252;LC_NUMERIC=C;LC_TIME=French_France.1252

attached base packages:
[1] stats     graphics  grDevices datasets  tcltk     utils     methods
[8] base

other attached packages:
[1] svSocket_0.9-5 svIO_0.9-5     R2HTML_1.58    svMisc_0.9-5   svIDE_0.9-5

loaded via a namespace (and not attached):
[1] tools_2.6.0


 

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Wolfgang Raffelsberger, PhD
Laboratoire de BioInformatique et Génomique Intégratives
CNRS UMR7104, IGBMC
1 rue Laurent Fries,  67404 Illkirch  Strasbourg,  France
Tel (+33) 388 65 3300         Fax (+33) 388 65 3276
wolfgang.raffelsberger at igbmc.u-strasbg.fr