# [R] proportional weights

John Fox jfox at mcmaster.ca
Thu Feb 6 16:04:07 CET 2014

```Dear Marco,

What I said in the 2007 r-help posting to which you refer is, "The weights
used by lm() are (inverse-)'variance weights,' reflecting the variances of
the errors, with observations that have low-variance errors therefore being
accorded greater weight in the resulting WLS regression." ?lm says,
"Non-NULL weights can be used to indicate that different observations have
different variances (with the values in weights being inversely proportional
to the variances)."

If I understand your situation correctly, you know the error variances up to
a constant of proportionality, in which case you can set the weights
argument to lm() to the inverses of these values. As I showed you in the
example I just posted, weight and 2*weight *do* produce the same coefficient
estimates and standard errors, with the difference between the two absorbed
by the residual standard error, which is the square-root of the estimated
constant of proportionality.

If this is insufficiently clear, I'm afraid that I'll have to defer to
someone with greater powers of explanation.

Best,
John

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Marco Inacio
> Sent: Thursday, February 06, 2014 9:06 AM
> To: r-help at r-project.org
> Subject: Re: [R] proportional weights
>
> Thanks for the answers.
>
> > Dear Marco and Goran,
> >
> > Perhaps the documentation could be clearer, but it is after all a
> brief help page. Using weights of 2 to lm() is *not* equivalent to
> entering the observation twice. The weights are variance weights, not
> case weights.
> >
> According to your post here:
>    http://tolstoy.newcastle.edu.au/R/e2/help/07/05/16311.html
>    there are 3 possible kinds of weights.
>
> The person in this one:
>    http://tolstoy.newcastle.edu.au/R/e2/help/07/06/18743.html
>    includes 2 others making a distinction between weights inverse
> proportional to variance and weight equal to inverse variance.
>
> (looking at other posts in the thread shows that other people also make
> confusions on this matter)
>
> So R's lm(), glm(), etc weights **are** the inverse of the variance of
> the observations, right?
> They'are not **proportional** to the inverse of variance because if
> this
> were true, then weight and 2*weight would archive the same results,
> right?
>
>
> I needed a method to use proportional weights on observations as I know
> their proportion of variance among each other.
> And it doesn't need to be a R function, just an explanation on how
> construct the likehood would be fine. If anybody know an article on the
> subject, would be of great help to.
>
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> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.

```