[R] nl regression with 8 parameters, help!

Peter Dalgaard p.dalgaard at biostat.ku.dk
Wed Mar 23 18:08:35 CET 2005

Arne Henningsen <ahenningsen at email.uni-kiel.de> writes:

> Does this error always occur independently of the starting values that you 
> provide? I guess so, because I think that the parameters in your equation are 
> not identifiable, since the first term (a1 to a4) is identical to the second 
> term (b1 to b4) with a1 = b1, -a2 = b2, a3 = -b3, and a4 = b4 .
> Do you really want to have the same explanatory variable ("Tl") in both terms?

That's not necessarily a problem. There will of course always be two
solutions, but the algorithm may still converge to one of them. This
happens all the time with biexponential curves, e.g.. However, in this
case we have a local unidentifiability too: if you multiply a1 and a4
by a constant and divide b1 and b4 by the same constant, you get the
same fitted values. This is reflected in the singular gradient.

> On Wednesday 23 March 2005 16:28, Guillaume STORCHI wrote:
> > I'm doing a non linear regression with 8 parameters to be fitted:
> >
> > J.Tl.nls<-nls(Gw~(a1/(1+exp(-a2*Tl+a3))+a4)*(b1/(1+exp(b2*Tl-b3))+b4),data=
> >Enveloppe, start=list(a1=0.88957,a2=0.36298,a3=10.59241,a4=0.26308,
> >
> > b1=0.391268,b2=1.041856,b3=0.391268,b4=0.03439))

   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

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