On Thu, 6 Mar 2008, Wolfgang Waser wrote:
Thanks for your comments!
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.
I'm fitting metabolic rate data from small fish (oxygen consumption in
nmol/min vs. body weight in g).
The b coefficient is the interesting part and is generally somewhere around
0.75.
The one calculated for my data using option (a) is therefore 'better' than
(b,c), but which one is the correct to use? Log-transformation of metabolic
rate data is (was) normally performed to be able to determine a and b by
simple linear regression (or even on paper).
The two approaches assume two different models.
Model (1) is y = a*x^b + E (where different errors are independent
and identically
--- usually normally --- distributed).
Model (2) is y = a*(x^b)*E (and you are usually tacitly assuming
that ln E is normally distributed).
The point estimates of a and b will consequently be different ---
although usually not hugely
different. Their distributional properties will be substantially
different.
So in view of my context (metabolic rate data) would Model (1) be the
appropriate model to use?
Unlikely for a rate: those are normally viewed as being on log scale (we
saya a rate is doubled, for example). But a residual analysis will show
if there are departures from assumptions in one or other model.
Usual advice: seek local statistical help, for these are conceptual and
not R issues.
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
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Brian D. Ripley, [EMAIL PROTECTED]
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)
Oxford OX1 3TG, UK Fax: +44 1865 272595
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
