R help - Jun 2012 - scaling of parameter errors in a weighted regression using nls

I noticed that nls treats weights as relative and that the absolute size of the
weights w in
the following script has therefore no influence on the errors of the parameters
reported in the summary

a<-1
b<-3

x<--100:100
y<-a*x+b
yeps<-y+rnorm(length(x),sd=1)
w<-rep(1,length(x))

plot(x,yeps)
lines(x,y)

fit<-nls(yeps~p1*x+p2,start=list(p1=a*1.5,p2=b*1.5),weights=w)

summary(fit)

What is the basic idea behind this behavior which is counterintuitive to me?
The weights in my example are estimates of the absolute measurement error
and I think that scaling the weights by a factor of ten should result in
parameter errors ten times as large.
How do I achieve this behaviour?

Kind regards
Florian Hengstberger


	[[alternative HTML version deleted]]

Hello Florian,

  The best fit only depends on the relative statistical errors. The
estimated parameter error is a purely statistical error and can be
estimated from the sample. Systematic parameter errors are not
estimated. Yes, parameter errors grow with measurement errors.

     Take care
     Oliver

On Fri, Jun 1, 2012 at 11:29 AM, Hengstberger Florian
<Florian.Hengstberger at ait.ac.at> wrote:
> I noticed that nls treats weights as relative and that the absolute size of
the weights w in
> the following script has therefore no influence on the errors of the
parameters reported in the summary
>
> a<-1
> b<-3
>
> x<--100:100
> y<-a*x+b
> yeps<-y+rnorm(length(x),sd=1)
> w<-rep(1,length(x))
>
> plot(x,yeps)
> lines(x,y)
>
> fit<-nls(yeps~p1*x+p2,start=list(p1=a*1.5,p2=b*1.5),weights=w)
>
> summary(fit)
>
> What is the basic idea behind this behavior which is counterintuitive to
me?
> The weights in my example are estimates of the absolute measurement error
> and I think that scaling the weights by a factor of ten should result in
parameter errors ten times as large.
> How do I achieve this behaviour?
>
> Kind regards
> Florian Hengstberger
>
>
> ? ? ? ?[[alternative HTML version deleted]]
>
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-- 
Oliver Ruebenacker
Bioinformatics Consultant (http://www.knowomics.com/wiki/Oliver_Ruebenacker)
Knowomics, The Bioinformatics Network (http://www.knowomics.com)
SBPAX: Turning Bio Knowledge into Math Models (http://www.sbpax.org)