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

From: Rolf Turner <r.turner_at_auckland.ac.nz>
Date: Thu, 06 Mar 2008 09:04:29 +1300

On 6/03/2008, at 2:53 AM, 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?

The two approaches assume two different models.

        Model (1) is y = a*x^b + E (where different errors are independent and identically

        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.

                cheers,

                        Rolf Turner

######################################################################
Attention:\ This e-mail message is privileged and confid...{{dropped:9}}

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. Received on Wed 05 Mar 2008 - 20:07:06 GMT

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.2.0, at Wed 05 Mar 2008 - 20:30:19 GMT.

Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help. Please read the posting guide before posting to the list.

list of date sections of archive