[R] nls() vs lm() estimates

Janne Huttunen jmhuttun at stat.berkeley.edu
Fri Jun 13 20:21:52 CEST 2008

Héctor Villalobos wrote:
> Hi,
> I'm trying to understand why the coefficients "a" and "b" for the model: W = a*L^b estimated
> via nls() differs from those obtained for the log transformed model: log(W) = log(a) + b*log(L)
> estimated via lm(). Also, if I didn't make a mistake, R-squared suggests a "better" adjustment
> for the model using coefficients estimated by lm() . Perhaps I'm doing something wrong in
> nls()?

I didn't tried your code, but in general these estimates are different: 
for the former estimate you minimize the norm of the difference W-a*L^b 
(W are ) and for the latter you minimize the norm of the difference 
log(W)-(log(a)+b*log(L)). The solution for these problems are equal. 
That which approach you should choose depends on errors, for additive 
error model the former is better choice.

Janne Huttunen
University of California
Department of Statistics
367 Evans Hall Berlekey, CA 94720-3860
email: jmhuttun at stat.berkeley.edu
phone: +1-510-502-5205
office room: 449 Evans Hall

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