R help - Aug 2006 - nls convergence problem

I'm having problems getting nls to agree that convergence has occurred in a 
toy problem.

nls.out never gets defined when there is an error in nls.  Reaching the 
maximum number of iterations is alway an error, so nls.out never gets 
defined when the maximum number of iterations is reched.
>From ?nls.control:
  tol: A positive numeric value specifying the tolerance level for
          the relative offset convergence criterion.
>From some S-Plus documentation I found online via Google:
http://www.uni-muenster.de/ZIV/Mitarbeiter/BennoSueselbeck/s-html/helpfiles/nls.control.html

tolerance:
tolerance for the relative offset convergence criterion in the algorithm. 
Default 0.001. Note that the convergence test used in nls() is strictly 
relative. Therefore if the solution to a problem turned out to be a perfect 
fit (unlikely except in artificial examples), convergence is not guaranteed 
to be recognized by the algorithm.


Here's my toy problem:
> ?nls.control
> ?nls
> # Method 2
> X <- 0:15
> Y <- 9.452 * exp(-0.109*X) + 5.111   # Toy problem
>
> nls.out <- nls(Y ~ a*exp(b*X)+c,
+                start=list(a=6,b=-0.5,c=1),
+                control=nls.control(maxiter=15, tol=0.01),  # nothing makes 
sense here
+                trace=TRUE)
1016.507 :   6.0 -0.5  1.0
143.5807 :   6.1680290 -0.1506021  4.4013020
7.306365 :   9.10093164 -0.09114858  5.44620298
0.0342703 :   9.2801070 -0.1109063  5.2795803
3.001985e-05 :   9.4506654 -0.1089749  5.1122982
1.918531e-14 :   9.452 -0.109  5.111
6.894644e-28 :   9.452 -0.109  5.111
2.208811e-29 :   9.452 -0.109  5.111
7.888609e-30 :   9.452 -0.109  5.111
7.888609e-30 :   9.452 -0.109  5.111
7.099748e-30 :   9.452 -0.109  5.111
3.155444e-30 :   9.452 -0.109  5.111
3.155444e-30 :   9.452 -0.109  5.111
3.155444e-30 :   9.452 -0.109  5.111
3.155444e-30 :   9.452 -0.109  5.111
3.155444e-30 :   9.452 -0.109  5.111
Error in nls(Y ~ a * exp(b * X) + c, start = list(a = 6, b = -0.5, c = 1), 
:
        number of iterations exceeded maximum of 15

There is near-perfect convergence after 12 iterations, but I cannot figure 
out a way for R to recognize it.

What does "relative offset convergence criterion" mean?  How can
nls.control
be used to say this problem has converged, and have nls exit without an 
error?

Should the R documentation be modified to explain what "relative offset 
convergence criterion" means?  Should the R documentation be expanded to 
include the comment from the S-Plus: "Therefore if the solution to a
problem
turned out to be a perfect fit (unlikely except in artificial examples), 
convergence is not guaranteed to be recognized by the algorithm".  If this 
is true, this seems like a suboptimal design.

Thanks for any insight about this.

efg

Earl F. Glynn
Scientific Programmer
Stowers Institute for Medical Research

Earl F. Glynn <efg <at> stowers-institute.org> writes:
> 
> Here's my toy problem:
> > ?nls.control
> > ?nls
> > # Method 2
> > X <- 0:15
> > Y <- 9.452 * exp(-0.109*X) + 5.111   # Toy problem
> >
> > nls.out <- nls(Y ~ a*exp(b*X)+c,
> +                start=list(a=6,b=-0.5,c=1),
> +                control=nls.control(maxiter=15, tol=0.01),  # nothing
makes
> sense here
> +                trace=TRUE)
This toy problem is exactly what the warning is for:

Warning
Do not use nls on artificial "zero-residual" data. 

Add some noise and try again.

Dieter Menne

Yours truly <dieter.menne <at> menne-biomed.de> writes:
...
> Recently, a colleague fitted gastric emptying
> curves using GraphPad, with 100% success, and
> nls failed for one third of  these.  When we
> checked GraphPads output more closely, some of
> the coefficients looked like 2.1 with a confidence
> interval in the range  -27128 ... 314141. Nobody
> forces you to look at these, though, when using
> GraphPad.
>
Since my comment has stirred a bit of an uproar, I should add
that this is not the fault of GraphPad, but that most non-linear
fitting programs, including those in the big SXXX, give the same
results. Harvey Motulsky from Graphpad/Prism informed me that
they were going to add special tests in the new versions. Their
pdf-manual on nonlinear fitting is worth a look anyway if
Bates/Watts is over your head.

And if anyone want to see sample data:

http://www.menne-biomed.de/gastempt/gastempt1.html
> I only wish nls were a little bit more polite in telling me what went
wrong.
I stand corrected:

I only wish nls were less politically correct, but rather inform me
WHY it faltered.

Dieter