Non linear Regression: "singular gradient matrix at initial parameter estimates"

Hi,

I am using nls to fit a non linear function to some data but R keeps giving
me "singular gradient matrix at initial parameter estimates" errors.
For testing purposes I am doing this:

### R code ###

x<- 0:140
y<- 200 / (1 + exp(17 - x)/2) * exp(-0.02*x) # creating 'perfect' samples
with fitting model
yeps<- y + rnorm(length(y), sd = 2) # adding noise

# results in above error
fit = nls(yeps ~ p1 / (1 + exp(p2 - x) / p3) * exp(p4 * x))

###

From what I've found in this list I think that my model is over-parameterized.

How can I work around that?

Take out p3; it's redundant.

Peter Ehlers

Thanks,

Felix

	[[alternative HTML version deleted]]

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

An embedded and charset-unspecified text was scrubbed...
Name: not available
URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20110412/3f039609/attachment.pl>

Use a more realistic starting point instead of the default one:

fit <- nls(yeps ~ p1 / (1 + exp(p2 - x)) * exp(p4 * x), 
start=list(p1=410,p2=18,p4=-.03))

This works for me:
 > fit
Nonlinear regression model
   model:  yeps ~ p1/(1 + exp(p2 - x)) * exp(p4 * x)
    data:  parent.frame()
        p1        p2        p4
199.48276  16.28664  -0.01987
  residual sum-of-squares: 560.6

Number of iterations to convergence: 5
Achieved convergence tolerance: 5.637e-07

Ciao!
                         mario

fit = nls(yeps ~ p1 / (1 + exp(p2 - x)) * exp(p4 * x))

Ing. Mario Valle
Data Analysis and Visualization Group            | http://www.cscs.ch/~mvalle
Swiss National Supercomputing Centre (CSCS)      | Tel:  +41 (91) 610.82.60
v. Cantonale Galleria 2, 6928 Manno, Switzerland | Fax:  +41 (91) 610.82.82

An embedded and charset-unspecified text was scrubbed...
Name: not available
URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20110412/a37bea03/attachment.pl>