[R] Using NLS with a Kappa function

[Michael Bedward]

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
>
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