[R] fitting "power model" in nls()

[Joerg van den Hoff]

On Sun, Dec 02, 2007 at 11:08:01AM -0800, Milton Cezar Ribeiro wrote:
> Dear all,
> I am still fighting against my "power model".
> I tryed several times to use nls() but I can??t run it.
> I am sending my variables and also the model which I would like to fit. 
> As you can see, this "power model" is not the best model to be fit, but I really need also to fit it.
> 
> The model which I would like to fit is Richness = B*(Area^A)
> 
> richness<-c(44,36,31,39,38,26,37,33,34,48,25,22,44,5,9,13,17,15,21,10,16,22,13,20,9,15,14,21,23,23,32,29,20,
> 26,31,4,20,25,24,32,23,33,34,23,28,30,10,29,40,10,8,12,13,14,56,47,44,37,27,17,32,31,26,23,31,34,
> 37,32,26,37,28,38,35,27,34,35,32,27,22,23,13,28,13,22,45,33,46,37,21,28,38,21,18,21,18,24,18,23,22,
> 38,40,52,31,38,15,21)
> area<-c(26.22,20.45,128.68,117.24,19.61,295.21,31.83,30.36,13.57,60.47,205.30,40.21,
> 7.99,1.18,5.40,13.37,4.51,36.61,7.56,10.30,7.29,9.54,6.93,12.60,
> 2.43,18.89,15.03,14.49,28.46,36.03,38.52,45.16,58.27,67.13,92.33,1.17,
> 29.52,84.38,87.57,109.08,72.28,66.15,142.27,76.41,105.76,73.47,1.71,305.75,
> 325.78,3.71,6.48,19.26,3.69,6.27,1689.67,95.23,13.47,8.60,96.00,436.97,
> 472.78,441.01,467.24,1169.11,1309.10,1905.16,135.92,438.25,526.68,88.88,31.43,21.22,
> 640.88,14.09,28.91,103.38,178.99,120.76,161.15,137.38,158.31,179.36,214.36,187.05,
> 140.92,258.42,85.86,47.70,44.09,18.04,127.84,1694.32,34.27,75.19,54.39,79.88,
> 63.84,82.24,88.23,202.66,148.93,641.76,20.45,145.31,27.52,30.70)
> plot(richness~area)
> 
> I tryed to fit the following model:
> 
> m1<-nls(richness ~ Const+B*(area^A))
> 
> Thanks a lot, 
> miltinho
> Brazil.
> 

for easier notation, let y=richness, x=area, C=const in the following.

then 

nls(y~B*x^A + C, start = c(A=3.2, B=0.002, C=0))

converges alright. where's the problem (apart from this being not a very good
model for the data)? the critical point is to provide some reasonable estimate
of the parameters as starting values.

to get reasonable start values, I'd use:


y = B*x^A + C --> log(y-C) = log(B) + A*log(x) --> ly = b + a*lx,

estimate C from the x -> 0 asymptotic value (approx. 0)

and use lm(ly~lx) which yields a and b estimates which you could use in `nls'.

and, contrary to other assessments you've received, I definitely would prefer `nls'
for least squares fitting instead of using `optim' or other general minimization routines.

hth

joerg