nls(): Levenberg-Marquardt, Gauss-Newton, plinear - PI curve fitting

On 6/21/05, Christfried Kunath <mailpuls at gmx.net> wrote:

Hello,

i have a problem with the function nls().

This are my data in "k":
       V1    V2
 [1,]    0 0.367
 [2,]   85 0.296
 [3,]  122 0.260
 [4,]  192 0.244
 [5,]  275 0.175
 [6,]  421 0.140
 [7,]  603 0.093
 [8,]  831 0.068
 [9,] 1140 0.043

With the nls()-function i want to fit following formula whereas a,b, and c
are variables: y~1/(a*x^2+b*x+c)

With the standardalgorithm "Newton-Gauss" the fitted curve contain an peak
near the second x,y-point.
This peak is not correct for my purpose. The fitted curve should descend
from the maximum y to the minimum y given in my data.

The algorithm "plinear" give me following error:


  phi function(x,y) {
k.nls<-nls(y~1/(a*(x^2)+b*x+c),start=c(a=0.0005,b=0.02,c=1.5),alg="plinear")
      coef(k.nls)
  }

  phi(k[,1],k[,2])

  Error in qr.solve(QR.B, cc) : singular matrix `a' in solve


I have found in the mailinglist
"https://stat.ethz.ch/pipermail/r-help/2001-July/012196.html" that is if t
he data are artificial. But the data are from my measurment.

The commercial software "Origin V.6.1" solved this problem with the
Levenberg-Marquardt algorithm how i want.
The reference results are: a = 9.6899E-6, b = 0.00689, c = 2.72982

What are the right way or algorithm for me to solve this problem and what
means this error with alg="plinear"?

Thanks in advance.

This is not a direct answer to your question but log(y) looks nearly linear
in x when plotting them together and log(y) ~ a + b*x or
y ~ a*exp(b*x) will always be monotonic.  Also, this model uses only 2
rather than 3 parameters.

res1 <- nls(1/y ~ a*x^2 + b*x + c, start = list(a=0,b=0,c=0))
res2 <- nls(y ~ 1/(a*x^2 + b*x + c), start = as.list(coef(res1)))
res2