[R] using weights in lm()

Prof Brian D Ripley ripley at stats.ox.ac.uk
Tue Dec 7 15:36:55 CET 1999

On Tue, 7 Dec 1999, Wolfgang Koller wrote:

> Hello!
> When I know the vector of the variance of the disturbances (i.e. the 
> structure of heteroskedasticity), say Var(u_{i})=v_{i},
> what is the weights I should use as argument to lm(): 
> M <- lm(y~x,weigths=1/v)
>   or 
> M <- lm(y~x,weights=1/(v^0.5))   ???
> In the help pages I did not find a clear answer to this question, so 
> please could someone help me!

?lm says:

 weights: an optional vector of weights to be used in the
          fitting process.

That means it does weighted least-squares with weights w, minimizing
sum(w*e*e) where e = y - X %*% b. I assume that you want weights = 1/v,
as that gives the MLE, but what you use is a modelling decision
(and I am working in fMRI where people deliberately do not use the MLE

If it had said it did weighted least squares with weights w, would
that have been clear enough?

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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