[R] nls: different results if applied to normal or linearized data

[Prof Brian Ripley]

On Wed, 5 Mar 2008, Wolfgang Waser wrote:

> Dear all,
>
> I did a non-linear least square model fit
>
> y ~ a * x^b
>
> (a) > nls(y ~ a * x^b, start=list(a=1,b=1))
>
> to obtain the coefficients a & b.
>
> I did the same with the linearized formula, including a linear model
>
> log(y) ~ log(a) + b * log(x)
>
> (b) > nls(log10(y) ~ log10(a) + b*log10(x), start=list(a=1,b=1))
> (c) > lm(log10(y) ~ log10(x))
>
> I expected coefficient b to be identical for all three cases. Hoever, using my
> dataset, coefficient b was:
> (a) 0.912
> (b) 0.9794
> (c) 0.9794
>
> Coefficient a also varied between option (a) and (b), 107.2 and 94.7,
> respectively.
>
> Is this supposed to happen? Which is the correct coefficient b?

Yes.  You are fitting by least-squares on two different scales: 
differences in y and differences in log(y) are not comparable.

Both are correct solutions to different problems.  Since we have no idea 
what 'x' and 'y' are, we cannot even guess which is more appropriate in 
your context.

>
>
> Regards,
>
> Wolfgang
>
> --
> Laboratory of Animal Physiology
> Department of Biology
> University of Turku
> FIN-20014 Turku
> Finland
>
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-- 
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 272866 (PA)
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