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

From: Wolfgang Waser <wolfgang.waser_at_utu.fi>
Date: Wed, 05 Mar 2008 15:53:27 +0200


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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