I have tried the method proposed by Dave, and I must say it works very well.
Not to yield starting estimates for an nls-fit, but as an independent method
for calculating E (which is, by the way, the only paramater that I am
actually interested in).
The calculated values for E (Esp[3]) are on
Hi Antoon,
now that you mention trying out different methods, maybe you should consider
fitting a
sigmoidal curve to the entire dataset and not only the exponential part (which
constitutes
a very small dataset) as seems to have been the endeavour that initiated the
posting to
R-help.
One
Thanks everybody,
This has been quite helpful, the problem remains tricky but at least now
I've got a version of my script that handles all my reactions without error.
The DEoptim solution produced good starting values for a lot of reactions,
but sadly not for all. I now use scaled parameters
I thought maybe my suggestion for reparameterizing this simple problem
was ignored because I didn't supply R code for the problem.
Here it is using optim for the optimization. It converges trivially with
an initial value for E of 1000.
As I stated before, there is nothing at all difficult about
Thanks to Dennis Murphy who pointed out that ExponCycles
is undefined. It is an R gotcha. I had shortened the name but R still
remembered it so the script worked but only on my computer.
This should fix that.
ExponValues=c(2018.34,2012.54,2018.85,2023.52,2054.58,2132.61,2247.17,2468.32,27
78.47)
Kate Mullen showed one approach to this problem by using DEOptim to get
some good starting values.
However, I believe that the real issue is scaling (Warning: well-ridden
hobby-horse!).
With appropriate scaling, as below, nls does fine. This isn't saying nls
is perfect -- I've been trying to
You used starting values:
pa - c(1,2,3)
but both algorithms (port and Gauss-Newton) fail if you use the slightly
different values:
pa - c(1,2,3.5)
Scaling does not fix the underlying sensitivity to starting values.
pa[3] in particular cannot be above ~3.15 for GN and ~3.3 for port; both
Kate is correct. The parameter scaling helps quite a bit, but not enough
to render the problem nice so that many reasonable starting points
will give useful results. Indeed, a run using all.methods=TRUE in our
optimx package (on r-forge at
http://r-forge.r-project.org/R/?group_id=395) gives
Figuring out the best parameterization for this kind of model
is a bit tricky until you get the hang of it.
Let the function be
y_t = y_0 + alpha * E^t
where uppercase Y_t denotes an observed value
and lower case y_t is a predicted value.
Index the times by t_1 t_n
WLOG assume that
Hello everyone,
I have come across a bit of an odd problem: I am currently analysing data
PCR reaction data of which part is behaving exponential. I would like to fit
the exponential part to the following:
y0 + alpha * E^t
In which Y0 is the groundphase, alpha a fluorescence factor, E the
If you could reformulate your model as alpha * (y0 + E^t) then you could
use nls with alg=plinear (alpha then would be eliminated from the
nonlinear param and treated as conditionally linear) and this would help
with convergence.
Else you can try package DEoptim to get the starting values; the
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