[R] Starting estimates for nls Exponential Fit

[Anto]

Thanks everybody,

This has been quite helpful, the problem remains tricky but at least now
I've got a version of my script that handles all my reactions without error.
The DEoptim solution produced good starting values for a lot of reactions,
but sadly not for all. I now use scaled parameters and allow more iterations
than the standard 50 (1000). I doubt it is completely stable and I think I
will run into reactions that will fail the fit, but for now everything works
fine so I won't be complaining. 

Thanks a lot,

Antoon

 



Prof. John C Nash wrote:
> 
> Kate is correct. The parameter scaling helps quite a bit, but not enough
> to render the problem "nice" so that many "reasonable" starting points
> will give useful results. Indeed, a run using "all.methods=TRUE" in our
> optimx package (on r-forge at
> http://r-forge.r-project.org/R/?group_id=395) gives
> 
>                           par  fvalues      method   fns grs itns conv
> 4   2.194931, 1.000001, 1.000027 566407.6     nlm    NA  NA   3    0
> 1 2.1949335, -9.0413113, 0.7516435 566407.6   BFGS    37   6 NULL    0
> 2  2.1950009, 0.2548318, 1.1163498 566404.6 Nelder    82  NA NULL    0
> 3     1.974226, 1.829957, 1.681338 2409.771   SANN 10000  NA NULL    0
> 6  1.9904045, 0.6151421, 1.7559401 1696.497  ucminf    51  51 NULL    0
> 5  1.9906488, 0.6012996, 1.7575365 1696.248  nlminb    80 166   51    0
>    KKT1  KKT2
> 4 FALSE FALSE
> 1  TRUE FALSE
> 2 FALSE FALSE
> 3 FALSE  TRUE
> 6 FALSE  TRUE
> 5 FALSE  TRUE
>>
> 
> A bit of a dog's dinner.
> 
> On the positive side, this is a simple but nasty problem to illustrate
> lots of the issues with nonlinear parameter estimation.
> 
> JN
> 
> 
> 
> Katharine Mullen wrote:
>> You used starting values:
>>    pa <- c(1,2,3)
>> 
>> but both algorithms (port and Gauss-Newton) fail if you use the slightly
>> different values:
>>    pa <- c(1,2,3.5)
>> 
>> Scaling does not fix the underlying sensitivity to starting values.
>> pa[3] in particular cannot be above ~3.15 for GN and ~3.3 for port; both
>> alg. also fail if there is insufficient spread (e.g., both fail for
>> pa <- c(1,1.25,1.5) ).
>> 
>> For the record, DE uses (by default at least) a random start and for bad
>> starts will sometimes fail to give good results; decrease the probability
>> this happens by increasing itermax from the default itermax=200, as in:
>> 
>> ss <- DEoptim(fun, lower=rep(0,3), upper=c(10e7, 10, 10),
>>               control=list(trace=FALSE, itermax=1000))
>> 
>> On Wed, 2 Dec 2009, Prof. John C Nash wrote:
>> 
>>> Kate Mullen showed one approach to this problem by using DEOptim to get
>>> some good starting values.
>>>
>>> However, I believe that the real issue is scaling (Warning: well-ridden
>>> hobby-horse!).
>>>
>>> With appropriate scaling, as below, nls does fine. This isn't saying nls
>>> is perfect -- I've been trying to figure out how to do a nice job of
>>> helping folk to scale their problems. Ultimately, it would be nice to
>>> has an nls version that will do the scaling and also watch for some
>>> other situations that give trouble.
>>>
>>> Cheers, JN
>>>
>>>
>>> ## JN test
>>> rm(list=ls())
>>>
>>> ExponValues <-
>>> c(2018.34,2012.54,2018.85,2023.52,2054.58,2132.61,2247.17,
>>>                  2468.32,2778.47)
>>>
>>> ExponCycles <- c(17,18,19,20,21,22,23,24,25)
>>>
>>> mod <- function(x) x[1] + x[2]*x[3]^ExponCycles
>>>
>>> modj <- function(x) (1000*x[1] + 0.001*x[2]*x[3]^ExponCycles)
>>>
>>> fun <- function(x) sum((ExponValues-mod(x))^2)
>>>
>>>
>>>
>>> pa<-c(1,2,3)
>>> lo<-c(0,0,0)
>>> up<-c(20,20,20)
>>> names(pa) <- c("Y0", "a", "E")
>>>
>>> ## fit w/port and GN
>>> Emodjn<- nls(ExponValues ~ (1000*Y0 + 0.001*a*(E^ExponCycles)),
>>>              start=pa, algorithm='port', lower=lo, upper=up,
>>>              control=list(maxiter=1000, trace=TRUE, warnOnly=TRUE))
>>>
>>> Emodjn1 <- nls(ExponValues ~ (1000*Y0 + 0.001*a*(E^ExponCycles)),
>>> start=pa,
>>>              control=list(maxiter=1000, trace=TRUE, warnOnly=TRUE))
>>>
>>> ## fit
>>> matplot(cbind(ExponValues, fitted(Emodjn), fitted(Emodjn1)),type="l")
>>>
>>> ______________________________________________
>>> R-help at r-project.org 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.
>>>
> 
> ______________________________________________
> R-help at r-project.org 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.
> 
> 

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