Thomas,
I think the issue of having reasonable starting values is inherent in all
nonlinear optimization problems (unless they have some additional
properties like convexity, for example). Using a different algorithm may
or may not help. In fact, a vast majority of existing algorithms
guarantees only local convergence provided that the starting point is
within a certain distance from the solution.
If you are interested in this particular model, the following procedure
seems to give reasonable starting point.
1. Take a guess at c. This is relatively easy since c is the value of y
when a=0. For your data a crude guess could be c=8.
2. For a fixed value of c your model can be linearized by the following
transformations
y1 <- log(y-8)
x1 <- log(x)
3. Do
summary(lm(y1~x1))
and obtain values for intecept and slope
4. Your starting values for nls are (a=exp(Intercept), b=slope, c=8)
Hope this helps,
Andy
__________________________________
Andy Jaworski
518-1-01
Process Laboratory
3M Corporate Research Laboratory
-----
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From:
Thomas Bschorr <[email protected]>
To:
[email protected]
Date:
04/30/2010 03:33 PM
Subject:
[R] Curve Fitting
Sent by:
<[email protected]>
I am having troubles in fitting functions of the form
y~a*x^b+c
to data, for example
x<-c(0.1,0.36,0.63,0.90,1.166,1.43, 1.70, 1.96, 2.23)
y<-c(8.09,9.0,9.62,10.11,10.53,10.9, 11.25, 11.56, 11.86)
I tried for example with nls, which did only work with really good initial
guessed values.
Any suggestion, what I should use?
Thanks a lot
Thomas
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