# Re: [R] nls not solving

From: Bert Gunter <gunter.berton_at_gene.com>
Date: Mon, 28 Feb 2011 13:42:18 -0800

Well, since no one else has replied, let me state the obvious: The model is nonidentifiable. It is of the form:

y = a + b(1 - exp(kl)) - b exp(-kx)

Suppose you have a solution. Suppose with your solution, a + b(1 -exp(kl)) = C, say. Then a = C - b(1-exp(kl)). Hence you have generated an infinite number of pairs <a,l> by solving for one in terms of the other that give the exact same solution. That is, the model is nonidentifiable. Whence your error. Removing "a" or "l" makes the model identifiable.

• Bert

On Mon, Feb 28, 2011 at 12:23 PM, Schatzi <adele_thompson_at_cargill.com> wrote:
> I am running the following nls equation. I tried it with data that excel was
> fitting and got the error:
> singular gradient matrix at initial parameter estimates
> I thought it was due to a low number of points (6), but when I create a
> dataset, I get the same problem. If I remove the parameter "a," then it can
> find a solution. Does anyone know what I can do to fit this model?
>
> vardata<- rnorm(73,mean=0,sd=5)
> x<-0:72
> a<-1
> b<-50
> k<-0.05
> l<-5
> startt<-c(a,b,k,l)
> yf<-a+b*(1-exp(-k*(x-l)))
> y<-yf+vardata
>
> nmodel<-nls(y~a+b*(1-exp(-k*(x-l))),
> start=list(a=1,b=50,k=0.05,l=5))
>
> --
> View this message in context: http://r.789695.n4.nabble.com/nls-not-solving-tp3328647p3328647.html
> Sent from the R help mailing list archive at Nabble.com.
>
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> and provide commented, minimal, self-contained, reproducible code.
>

```--
Bert Gunter
Genentech Nonclinical Biostatistics

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