R help - Oct 2010 - Using NLS with a Kappa function

Hi Everyone,

I am trying to use NLS to fit a dataset using a Kappa function, but I am
having problems.  Depending on the start values that I provide, I get
either:

Error in numericDeriv(form[[3L]], names(ind), env) :
Missing value or an infinity produced when evaluating the model

Or

Error in nls(FldFatRate ~ funct3(MeanDepth_m, h, k, z, a), data = data1, :
singular gradient

I think these error results from the fact that I obtained a good fit with a
logistic function and that the Kappa reduces to a logistic in the limit with
k -> 0. This causes a problem because the Kappa function has a term raised
to (1/k)th power leading the numerical singularlity for low values of k.
(Since the logistic function gave a good fit, then I am sure that best fit
value for k is very small.) If so, this problem would intractable, but I
thought I see what response I got from other users before giving up on this
track.

Here are a few lines from the command line:
> funct3
function(x, h, k, z, a) { (1 - h*(1 - k*(x - z)/a)^(1/k))^(1/h) }
> reg24 <-nls(FldFatRate ~ funct3(MeanDepth_m, h,k,z,a), data=data1,
+ start=list(h = -17, k = .05, z = 22, a = 3.7), trace=TRUE,
control=nls.control(minFactor=.00009))
24.69316 : -17.00 0.05 22.00 3.70
Error in numericDeriv(form[[3L]], names(ind), env) :
Missing value or an infinity produced when evaluating the model
> reg24 <-nls(FldFatRate ~ funct3(MeanDepth_m, h,k,z,a), data=data1,
+ start=list(h = -18, k = -.00008, z = 24, a = 3), trace=TRUE,
control=nls.control(minFactor=.00009))
19.20454 : -1.8e+01 -8.0e-05 2.4e+01 3.0e+00
Error in nls(FldFatRate ~ funct3(MeanDepth_m, h, k, z, a), data = data1, :
singular gradient

I've also tried setting algorithm to "plinear" and
"port" but still get the
same response.  I've also tried numerous possible starting values, include
large values for k and h.

I really appreciate any advice that anyone might have with this issue.

Thanks,

Ezra

	[[alternative HTML version deleted]]

Hi Ezra,

I'm not any sort of expert on this but my own attempts to get nls to
fit functions similar in form to your kappa equation have usually
provoked the same error messages.

It might be worth log transforming your dependent variable and trying
to fit this:

 -log(h) * ( -log(k) * log(1 - h * ( 1 - k *(x-z)/a))  )

Michael


On 13 October 2010 11:48, Ezra Boyd <eboyd3 at tigers.lsu.edu>
wrote:
> Hi Everyone,
>
> I am trying to use NLS to fit a dataset using a Kappa function, but I am
> having problems. ?Depending on the start values that I provide, I get
> either:
>
> Error in numericDeriv(form[[3L]], names(ind), env) :
> Missing value or an infinity produced when evaluating the model
>
> Or
>
> Error in nls(FldFatRate ~ funct3(MeanDepth_m, h, k, z, a), data = data1, :
> singular gradient
>
> I think these error results from the fact that I obtained a good fit with a
> logistic function and that the Kappa reduces to a logistic in the limit
with
> k -> 0. This causes a problem because the Kappa function has a term
raised
> to (1/k)th power leading the numerical singularlity for low values of k.
> (Since the logistic function gave a good fit, then I am sure that best fit
> value for k is very small.) If so, this problem would intractable, but I
> thought I see what response I got from other users before giving up on this
> track.
>
> Here are a few lines from the command line:
>
>> funct3
> function(x, h, k, z, a) { (1 - h*(1 - k*(x - z)/a)^(1/k))^(1/h) }
>
>> reg24 <-nls(FldFatRate ~ funct3(MeanDepth_m, h,k,z,a), data=data1,
> + start=list(h = -17, k = .05, z = 22, a = 3.7), trace=TRUE,
> control=nls.control(minFactor=.00009))
> 24.69316 : -17.00 0.05 22.00 3.70
> Error in numericDeriv(form[[3L]], names(ind), env) :
> Missing value or an infinity produced when evaluating the model
>
>> reg24 <-nls(FldFatRate ~ funct3(MeanDepth_m, h,k,z,a), data=data1,
> + start=list(h = -18, k = -.00008, z = 24, a = 3), trace=TRUE,
> control=nls.control(minFactor=.00009))
> 19.20454 : -1.8e+01 -8.0e-05 2.4e+01 3.0e+00
> Error in nls(FldFatRate ~ funct3(MeanDepth_m, h, k, z, a), data = data1, :
> singular gradient
>
> I've also tried setting algorithm to "plinear" and
"port" but still get the
> same response. ?I've also tried numerous possible starting values,
include
> large values for k and h.
>
> I really appreciate any advice that anyone might have with this issue.
>
> Thanks,
>
> Ezra
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> 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.
>

Actually it just the parameterization that is causing trouble near k=0


let u = (x-z)/a

then the problematic part of your function is

       (1- k*u)^(1/k)

take the log to get

    log(1-k*u)/k

= -(k*u +k^2*u^2/2 + ...)/k

= -(u +k u^2/2 + ..)

so your function is  exp(-u - ku^2/2 - ...)

and use that for k<eps for some small eps. You can add the right number of
terms and fix the size of eps
so that the function behaves well.