R help - Feb 2011 - nls not solving

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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By the way, sorry about the reposts. I subscribed but wasn't sure what was
happening. Hopefully this worked.

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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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> 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.
>
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
Bert Gunter
Genentech Nonclinical Biostatistics

I am not sure how you simplified the model to:
y = a + b(1 - exp(kl)) - b exp(-kx) 

I tried simplifying it but only got to:
y = a + b - b * exp(kl) * exp(-kx)

I agree that the model must not be identifiable. That makes sense,
especially given that removing either a or l makes the model work. Can you
please further explain the math though as I am not understanding it? I do
not see you obtained your equation and when I tried to solve using your
equation I got quite different numbers. Thank you.

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