# [R] proportional weights

John Fox jfox at mcmaster.ca
Thu Feb 6 20:57:11 CET 2014

Dear Marco,

> -----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 12:41 PM
> To: R help
> Subject: Re: [R] proportional weights
>
>
> > I think we can blame Tim Hesterberg for the confusion:
> >
> > He writes
> >
> > "
> > * inverse-variance weights, where var(y for observation) = 1/weight
> (as opposed to just being inversely proportional to the weight) *
> > "
> >
> > And, although I'm not a native English speaker, I think there's a
> spurious comma in there. The intention was clearly to have this as a
> 4th type of weight which is a special case of inverse-variance weights,
> not as an elaboration on the definition of inv.var. weights.
> >
> > I.e., it is the difference between
> >
> > Motorists who are reckless drivers...
> >
> > and
> >
> > Motorists, who are reckless drivers...
> >
> > -pd
> In fact, that wasn't what caused the confusion as I have understood
> what
> he meant despite the problem with the comma.
>
> But I got the idea now, R uses weighted least squares and:
>
> "Var[\epsilon | X] = \Omega" (equal, not proportion)
> (https://en.wikipedia.org/wiki/Generalized_least_squares) (since WLS is
> just a special case of GLS)
>
> "The weights should, ideally, be equal to the reciprocal of the
> variance
> of the measurement."
> (https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)#Weigh
> ted_linear_least_squares)
>
> I guess I need to find another strategy to use proportional weights
> (weights know up to a constant, as John says).

No, you are perfectly fine using WLS. The constant of proportionality is the
estimated error variance, i.e., the square of the residual standard error
(as I think I said earlier).

John

>
> So, thank you much to you all, and sorry the inconvenience I caused.
>
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