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

[Gabor Grothendieck]

Write out the objective functions that they are minimizing and it
will be clear they are different so you can't expect the same
results.

On Wed, Mar 5, 2008 at 8:53 AM, Wolfgang Waser <wolfgang.waser at utu.fi> 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?
>
>
> Regards,
>
> Wolfgang
>
> --
> Laboratory of Animal Physiology
> Department of Biology
> University of Turku
> FIN-20014 Turku
> Finland
>
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