R help - Sep 2007 - question about non-linear least squares in R

Hi, everyone,
    My question is: It's not every time that you can get a converged 
result from the nls function. Is there any solution for me to get a 
reasonable result? For example:

x <- c(-0.06,-0.04,-0.025,-0.015,-0.005,0.005,0.015,0.025,0.04,0.06)

y <- 
c(1866760,1457870,1314960,1250560,1184850,1144920,1158850,1199910,1263850,1452520)

fitOup<- nls(y ~ constant + A*(x-MA)^4 + B*(x-MA)^2, 
start=list(constant=10000000, A=100000000, B=-1000000, MA=0), 
control=nls.control(maxiter=100, minFactor=1/4096), trace=TRUE)

 

 For this one, I cannot get the converged result, how can I reach it? To 
use another funtion or to modify some settings for nls?

Thank you very much!

Yours,

Warren

Below is one possibility:

If you knew MA you would get a regular linear
least-squares for parameters A,B and constant which
can be easily solved. So now you can define a function
f(MA) which returns that value. Now you must minimize
that f - a function of one argument. It can have
several local minima and so you must be careful but I
believe that minimizing (even "bad") function of one
argument should be easier than your original problem.

Regards,

Moshe.

P.S. if you do this I would be interested to know
whether this works.

--- "Yu (Warren) Wang" <yu.wang at pdf.com> wrote:
> Hi, everyone,
>     My question is: It's not every time that you can
> get a converged 
> result from the nls function. Is there any solution
> for me to get a 
> reasonable result? For example:
> 
> x <-
>
c(-0.06,-0.04,-0.025,-0.015,-0.005,0.005,0.015,0.025,0.04,0.06)
> 
> y <- 
>
c(1866760,1457870,1314960,1250560,1184850,1144920,1158850,1199910,1263850,1452520)
> 
> fitOup<- nls(y ~ constant + A*(x-MA)^4 + B*(x-MA)^2,
> 
> start=list(constant=10000000, A=100000000,
> B=-1000000, MA=0), 
> control=nls.control(maxiter=100, minFactor=1/4096),
> trace=TRUE)
> 
>  
> 
>  For this one, I cannot get the converged result,
> how can I reach it? To 
> use another funtion or to modify some settings for
> nls?
> 
> Thank you very much!
> 
> Yours,
> 
> Warren
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>

Here is one way of getting a reasonable fit:

1.  Scale your y's by dividing all values by 1e6.
2.  Plot x vs. y.  The plot looks like a quadratic function.
3.  Fit a quadratic const. + B*x^2 - this a linear regression problem so
use lm.
4.  Plot the predictions.
5.  Eyball the necessary shift - MA is around 0.01.  Refit const. +
B*(x-.01)^2.  Should get const.=1.147 and B=139.144
6.  Use start=list(const.= 1.147, A=0, B=1.147, MA=.01).  nls should
converge in 4 iterations.

In general, good starting points may be crucial to nls convergence.
Scaling the y's to reasonable values also helps.

Hope this helps,

Andy

__________________________________
Andy Jaworski
518-1-01
Process Laboratory
3M Corporate Research Laboratory
-----
E-mail: apjaworski at mmm.com
Tel:  (651) 733-6092
Fax:  (651) 736-3122


                                                                           
             "Yu (Warren)                                                  
             Wang"                                                         
             <yu.wang at pdf.com>                                         
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                                                                   Subject 
             09/05/2007 02:51          [R] question about non-linear least 
             AM                        squares in R                        
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           




Hi, everyone,
    My question is: It's not every time that you can get a converged
result from the nls function. Is there any solution for me to get a
reasonable result? For example:

x <- c(-0.06,-0.04,-0.025,-0.015,-0.005,0.005,0.015,0.025,0.04,0.06)

y <-
c(1866760,1457870,1314960,1250560,1184850,1144920,1158850,1199910,1263850,1452520)


fitOup<- nls(y ~ constant + A*(x-MA)^4 + B*(x-MA)^2,
start=list(constant=10000000, A=100000000, B=-1000000, MA=0),
control=nls.control(maxiter=100, minFactor=1/4096), trace=TRUE)



 For this one, I cannot get the converged result, how can I reach it? To
use another funtion or to modify some settings for nls?

Thank you very much!

Yours,

Warren

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.