[R] nls fit to exponential decay with unknown time origin

[Robert D. Merithew]

doh!  Boy, do I feel stupid.

sorry, it's been a long day.

thanks,
--
Robert



On 14 Dec 2001, Peter Dalgaard BSA wrote:

> "Robert D. Merithew" <merithew at ccmr.cornell.edu> writes:
> 
> > I'm trying to use nls() to fit an exponential decay with an unknown offset
> > in the time (independent variable).  (Perhaps this is inherently very
> > difficult?).
> > 
> > 
> > > decay.pl <- nls (amp ~ expn(b0,b1,tau,t0,t), data = decay,
> > +                  start = c(b0=1, b1=7.5, tau=3.5, t0=0.1), trace=T)
> > Error in nlsModel(formula, mf, start) : singular gradient matrix at
> > initial parameter estimates
> > > 
> > > expn(1, 7.5, 3.5, 0.1, decay$t)
> > [1] 6.636080 5.259657 4.164661 2.797383 1.760584 1.250300
> > attr(,"gradient")
> >      b0         b1        tau         t0
> > [1,]  1 0.75147729 -0.4600881 1.61030849
> > [2,]  1 0.56795432 -0.6884997 1.21704497
> > [3,]  1 0.42195477 -0.7801858 0.90418880
> > [4,]  1 0.23965104 -0.7336256 0.51353794
> > [5,]  1 0.10141123 -0.4973290 0.21730978
> > [6,]  1 0.03337327 -0.2431481 0.07151415
> > > 
> > 
> > 
> > Is the gradient matrix really singular?  It works without the t0
> > parameter.
> > 
> 
> Yes. b1 and t0 are not simultaneously identifiable.  Shifting an
> exponential curve in time is the same as multiplying by a constant.
> 
> Try calculating the ratio of the t0 and b1 columns above.
> -- 
>    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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