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 --- 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. cheers, Rolf Turner ###################################################################### Attention:\ This e-mail message is privileged and confid...{{dropped:9}} ______________________________________________ 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.