From bates@stat.wisc.edu  Thu May  9 15:04:24 2002
From: bates@stat.wisc.edu (Douglas Bates)
Date: 09 May 2002 09:04:24 -0500
Subject: [Rd] nls (PR#1533)
In-Reply-To: <200205091346.PAA22891@pubhealth.ku.dk>
References: <200205091346.PAA22891@pubhealth.ku.dk>
Message-ID: <6ry9etto2f.fsf@franz.stat.wisc.edu>

Your results are not reproducible

> library(nls)
> x = 1:10
> y = c(0.9090909, 2.8571429, 4.7368421, 6.1538462, 7.1428571, 7.8260870, 8.3050847, 8.6486486, 8.9010989, 9.0909091)
> nls(y~a*x^m/(1+b*x^m),start=list(a=1.1,m=2.1,b=.11),trace=TRUE)
1.474151 :  1.10 2.10 0.11 
0.01060234 :  1.0092752 1.9893808 0.1012907 
5.066695e-07 :  0.9999465 2.0000191 0.0999903 
1.421765e-14 :  1.0 2.0 0.1 
1.056486e-14 :  1.0 2.0 0.1 
Nonlinear regression model
  model:  y ~ a * x^m/(1 + b * x^m) 
   data:  parent.frame 
  a   m   b 
1.0 2.0 0.1 
 residual sum-of-squares:  1.056486e-14 

You are encountering a well-known anomaly which occurs only in
artificial examples with a zero residual sum of squares.  The
statistical model to be fit with nls is y = f(x, theta) + eps
but your data are y = f(x, theta)

If there is any noise in the data, such as created from my copying and
pasting above, nls performs correctly.


scs10@st-and.ac.uk writes:

> Full_Name: Sophie Smout
> Version: 1.5.0
> OS: windows 2000, pc
> Submission from: (NULL) (138.251.190.17)
> 
> 
> I'm finding that nls iterates to the end of its iteration setting and does not
> jump out to report convergence even when it has clearly converged. It is also
> mis-reporting the number of iterations completed. These may not be
> unconnected...
> 
> This is an example:
> 
> [note - details of my computer, version etc are at the end of this message]
> 
> ##### some 'data'
> 
> 
> > x
>  [1]  1  2  3  4  5  6  7  8  9 10
> 
> > y
>  [1] 0.9090909 2.8571429 4.7368421 6.1538462 7.1428571 7.8260870 8.3050847
>  [8] 8.6486486 8.9010989 9.0909091
> 
> ### call to nls
> 
> > nls(y~a*x^m/(1+b*x^m),start=list(a=1.1,m=2.1,b=.11),trace=TRUE)
> 
> ### nls spits out
> 
> 1.474151 :  1.10 2.10 0.11 
> 0.01060234 :  1.0092752 1.9893808 0.1012907 
> 5.066689e-07 :  0.9999465 2.0000191 0.0999903 
> 3.651161e-15 :  1.0 2.0 0.1 
> 1.518557e-29 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> 8.09815e-30 :  1.0 2.0 0.1 
> Error in nls(y ~ a * x^m/(1 + b * x^m), start = list(a = 1.1, m = 2.1,  : 
>         number of iterations exceeded maximum of 5.27058e-308
> > 
> ### ??? the converged parameter values are correct
> ### but nls has not reported convergence. Instead it's just gone on iterating,
> ### but not 5.27058e-308 times, which would in any case be tricky...
> 
> 
> 
> ### try another simple example
> ### generate some data 
> 
> 
> 
> > x<-c(1:10)
> > y<-3*x^2+1
> > y
>  [1]   4  13  28  49  76 109 148 193 244 301
> > x
>  [1]  1  2  3  4  5  6  7  8  9 10
> 
> ### call to nls
> 
> 
> > nls(y~a*x^b+c,start=list(a=1,b=1,c=1))
> 
> Error in nls(y ~ a * x^b + c, start = list(a = 1, b = 1, c = 1)) : 
>         number of iterations exceeded maximum of 5.27058e-308
> 
> ### another call to nls with more details requested
> 
> > nls(y~a*x^b+c,start=list(a=1,b=1,c=1),trace=TRUE,control=nls.control(maxiter=10))
> 210232 :  1 1 1 
> 209552.9 :  0.3814959 1.4296089 1.7349535 
> 191724.4 :  0.2824096 1.9134931 1.9513585 
> 165276.9 :  0.4484658 1.9827257 1.8983138 
> 125378.7 :  0.7671348 1.9977192 1.7865044 
> 70298.31 :  1.325342 1.999960 1.589895 
> 17571.14 :  2.162671 2.000005 1.294948 
> 4.457052e-06 :  3.0000000 1.9999979 0.9999999 
> 2.200966e-17 :  3 2 1 
> 6.125505e-27 :  3 2 1 
> 6.12235e-27 :  3 2 1 
> Error in nls(y ~ a * x^b + c, start = list(a = 1, b = 1, c = 1), trace = TRUE, 
> : 
>         number of iterations exceeded maximum of 5.27058e-308
> 
> 
> 
> #### same problem!!
> ##############################################
> 
> here is what I get when I type 'version'
> to get details of computer etc.
> 
> 
> 
> platform i386-pc-mingw32
> arch     i386           
> os       mingw32        
> system   i386, mingw32  
> status                  
> major    1              
> minor    5.0            
> year     2002           
> month    04             
> day      29             
> language R   
> ###############################################
> 
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-- 
Douglas Bates                            bates@stat.wisc.edu
Statistics Department                    608/262-2598
University of Wisconsin - Madison        http://www.stat.wisc.edu/~bates/
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[Rd] nls (PR#1533)
Douglas Bates