On Wednesday 05 March 2008 (14:53:27), 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.
Models (a) and (b) entail different distributions of the dependent variable y and different ranges of values that y may take. (a) implies that y has, conditionally on x, a normal distribution and has a range of feasible values from -Inf to +Inf. (b) and (c) imply that log(y) has a normal distribution, that is, y has a log-normal distribution and can take values from zero to +Inf. > Is this supposed to happen? Given the above considerations, different results with respect to the intercept are definitely to be expected. > Which is the correct coefficient b? That depends - is y strictly non-negative or not ... Just my 20 cents... ______________________________________________ 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.
