[R] nls not solving

[Bert Gunter]

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))
>
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-- 
Bert Gunter
Genentech Nonclinical Biostatistics