[Rd] nls (PR#1533)
Douglas Bates
bates@stat.wisc.edu
09 May 2002 09:04:24 -0500
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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