From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Thu, 06 Mar 2008 08:24:20 +0000 (GMT)

Date: Thu, 06 Mar 2008 08:24:20 +0000 (GMT)

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
**>
**> ______________________________________________
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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) Oxford OX1 3TG, UK Fax: +44 1865 272595Received on Thu 06 Mar 2008 - 09:04:32 GMT______________________________________________ R-help_at_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.

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