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

S Ellison S.Ellison at LGCGroup.com
Fri Jul 20 17:11:22 CEST 2012

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> -----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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