[RsR] How does "rlm" in R decide its "w" weights for each IRLSiteration?

 set.seed(123)
 xr=rpois(100,lambda=3)
 xn=rnorm(100)
 xf =as.factor(xr)
 yn=rnorm(100)+xn+xr
 form=yn~xn+xf
library(MASS)

rlm(form,method="MM")

rlm(form,method="M")

lmrob(form,method="MM")

rlm includes an MM estimator.

S Ellison 

-----Original Message-----
From: Maheswaran Rohan [mailto:mrohan at doc.govt.nz] 
Sent: 22 July 2012 23:08
To: Valentin Todorov; S Ellison
Cc: r-sig-robust at r-project.org; r-help
Subject: RE: [RsR] How does "rlm" in R decide its "w" weights 
for each IRLSiteration?

Hi Valentin,

If the contamination is mainly in the response direction, 
M-estimator provides good estimates for parameters and rlm 
can be used.

Rohan

-----Original Message-----
From: r-sig-robust-bounces at r-project.org
[mailto:r-sig-robust-bounces at r-project.org] On Behalf Of 
Valentin Todorov
Sent: Saturday, 21 July 2012 6:57 a.m.
To: S Ellison
Cc: r-sig-robust at r-project.org; r-help
Subject: Re: [RsR] How does "rlm" in R decide its "w" weights 
for each IRLSiteration?

Hi Michael, S Ellison,

I do not actually understand what you want to achieve with 
the M estimates of rlm in MASS, but why you do not give a try 
of lmrob in 'robustbase'. Please have a llok in the 
references (?lmrob) about the advantages of MM estimators 
over the M estimators.

Best regards,
Valentin




On Fri, Jul 20, 2012 at 5:11 PM, S Ellison <S.Ellison at lgcgroup.com>
wrote:

-----Original Message-----
Subject: [RsR] How does "rlm" in R decide its "w" weights for each 
IRLS iteration?
I am also confused about the manual:

           a.  The input arguments:

wt.method are the weights case weights (giving the relative 
importance of case, so a weight of 2 means there are two of
these) or the inverse of the variances, so a weight of two 

means this 

error is half as variable?

When you give rlm weights (called 'weights', not 'w' on 

input, though
you can abbreviate to 'w'), you need to tell it which of 
these two possibilities you used.

If you gave it case numbers, say wt.method="case"; if you gave it

inverse variance weights, say wt.method="inv.var".

The default is "inv.var".

The input argument "w" is used for the initial values of 

the rlm IRLS 

weighting and the output value "w" is the converged "w".

There is no input argument 'w' for rlm (see above).
The output w are a  calculated using the psi function, so between 0

and 1.

The effective weights for the final estimate would then be something

like w*weights, using the full name of the input argument 
(and if I haven't forgotten a square root somewhere). At 
least, that would work for a simple location estimate (eg rlm(x~1)).

If my understanding above is correct, how does "rlm" 

decide its "w" 

for each IRLS iteration then?

It uses the given psi functions to calculate the iterative weights

based on the scaled residuals.

Any pointers/tutorials/notes to the calculation of these "w"'s in 
each IRLS iteration?

Read the cited references for a detailed guide. Or, of 

course, MASS -
the package is, after all, intended to support the book, not 
replace it.

S Ellison

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