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

Sun Dec 2 22:06:47 CET 2007

OK.  Since the model is linear except for A lets use brute force to
repeatedly evaluate the sum of squares for values of A between
-2 and 2 proceeding in steps of .01 solving the other parameters using
lm. That will give us better starting values and we should be able to
use nls on that.
> x <- seq(-2, 2, .01)
> ss <- sapply(x, function(A) sum(resid(lm(richness ~ I(area^A)))^2))
> plot(ss ~ x)
> x[which.min(ss)]
[1] -0.45
> model.lm <- lm(richness ~ I(area^-0.45))
> # use starting values based on lm and A = -0.45
> st <- c(Const = coef(model.lm)[[1]], B = coef(model.lm)[[2]], A = x[which.min(ss)])
> nls(richness ~ Const+B*(area^A), st = st)
Nonlinear regression model
  model:  richness ~ Const + B * (area^A)
   data:  parent.frame()
   Const        B        A
 33.9289 -33.4595  -0.4464
 residual sum-of-squares: 8751

Number of iterations to convergence: 2
Achieved convergence tolerance: 3.368e-06

Note that our A value is suspiciously close to A = -0.5 and sqrt(area)
is length so I wonder if there is an argument based on units of
measurement that might support a model of the form:

richness = Const + B / sqrt(area)


On Dec 2, 2007 3:39 PM, Milton Cezar Ribeiro <milton_ruser at yahoo.com.br> wrote:
>
> Dear Gabor,
>
> Thank you for your reply.
> In fact I am ajusting several models at same time, like linear, log-linear,
> log-log, piecewise etc. One of the models are the power model. I really need
> to fit a power model because it one of the hypothesis which have been
> suggested on literature.
>
> In addition, there are other variables which are beeing tested as
> explanatory.
>
> Kind regards,
>
> miltinho
> ----- Mensagem original ----
> De: Gabor Grothendieck <ggrothendieck at gmail.com>
> Para: Milton Cezar Ribeiro <milton_ruser at yahoo.com.br>
> Cc: R-help <r-help at stat.math.ethz.ch>
> Enviadas: Domingo, 2 de Dezembro de 2007 17:28:23
> Assunto: Re: [R] fitting "power model" in nls()
>
>
>
> Is that really the model we want?  When we have problems sometimes
> its just a sign that the model is not very good in the first place.
>
> plot(richness ~ area)
>
> shows most of the points crowded the left and just a few points out to
> the right.  This
> does not seem like a very good pattern for model fitting.
>
> plot(richness ~ log(area))
> plot(log(richness) ~ log(area))
>
> both look nicer.
>
> On Dec 2, 2007 2:08 PM, Milton Cezar Ribeiro <milton_ruser at yahoo.com.br>
> 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.
> >
> >
> >
> >  para armazenamento!
> >
> >        [[alternative HTML version deleted]]
> >
> >
> > ______________________________________________
> > 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.
> >
> >
>
>
>
> ________________________________
> Abra sua conta no Yahoo! Mail, o único sem limite de espaço para
> armazenamento!