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Fitting Richards' curve

10 messages · Christofer Bogaso, PIKAL Petr, Peter Dalgaard +3 more

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Hi Christofer

Try FlexParamCurve or maybe drc package.

Cheers
Petr
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Shouldn't be hard to set up with nls(). (I kind of suspect that the Richards curve has more flexibility than data can resolve, especially the subset (Q,B,nu) seems highly related, but hey, it's your data...)

-pd

  
    
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The Richards' curve is analytic, so nlsr::nlxb() should work better than nls() for getting derivatives --
the dreaded "singular gradient" error will likely stop nls(). Also likely, since even a 3-parameter
logistic can suffer from it (my long-standing Hobbs weed infestation problem below), is
that the Jacobian will be near-singular. And badly scaled. Nonlinear fitting problems essentially
have different scale in different portions of the parameter space.

You may also want to "fix" or mask one or more parameters to reduce the dimensionality of the problem,
and nlsr::nlxb() can do that.

The Hobbs problem has the following 12 data values for time points 1:12

# Data for Hobbs problem
ydat  <-  c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443,
          38.558, 50.156, 62.948, 75.995, 91.972) # for testing
tdat  <-  seq_along(ydat) # for testing

An unscaled model is

eunsc  <-   y ~ b1/(1+b2*exp(-b3*tt))

This problem looks simple, but has given lots of software grief over nearly 5 decades. In 1974 an
extensive search had all commonly available software failing, which led to the code that evolved
into nlsr, though there are plenty of cases where really awful code will luckily find a good
solution. The issue is getting a solution and knowing it is reasonable. I suspect a Richards'
model will be more difficult unless the OP has a lot of data and maybe some external information
to fix or constrain some parameters.

JN
On 2020-05-13 5:41 a.m., Peter Dalgaard wrote:
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John, have you ever looked at interval optimization as an alternative since it can lead to provably global minima?

Bernard
Sent from my iPhone so please excuse the spelling!"
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Many moons ago (I think early 80s) I looked at some of the global optimizers,
including several based on intervals. For problems of this size, your suggestion
makes a lot of sense, though it has been so long since I looked at those techniques
that I will avoid detailed comment.

I've not looked to see if there are any such solvers for R, but would be happy
to learn (probably best off-list). Also I'm willing to work at a modest pace on
developing one. A starting point might be nls2 package.

Best, JN
On 2020-05-13 11:05 a.m., Bernard Comcast wrote:
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Also, in the full curve referenced on Wikpedia, the parameters Q And M are confounded - you only need one or the other But not both. If you are using both and trying to estimate them both you will have problems.

I have fitted these curves quite easily using the Solver in Excel.

Bernard
Sent from my iPhone so please excuse the spelling!"
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Hi Christofer,

This doesn't really answer your question.
But if the goal is to fit an S-shaped curve to data, with increased
flexibility...
(I'm assuming that's the goal).

...then I'd like to note the option of splines (or smoothing), subject
to shape constraints...

My guess, is it's probably easier to model the inverse of a growth
curve this way, than to model the growth curve directly.
In which case, a 4-piece to 10-piece spline should give considerably flexibly.

It's possible that Martin's package, cobs, can do this, but not sure,
I haven't tried it.
And there may be other R packages for fitting splines/smoothers to
data, subject to shape constraints.

If not, I'm guessing it wouldn't be too difficult to implement, via
extensions to the quadprog package, for quadratic programming.


On Wed, May 13, 2020 at 9:26 PM Christofer Bogaso
<bogaso.christofer at gmail.com> wrote:
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Further to my previous post.
I read through the documentation for the cobs package.
And (someone please correct me if I'm wrong) I don't think it can
produce a smoother with an S-shaped shape constraint.
I found two other packages for smoothing under shape constraints, but
doesn't look like they can either.

I have code that could be adapted for this purpose.
But one it's incomplete, two it (currently) requires the user to
specify a smoothness parameter, and three doesn't produce any kind of
inference...
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I have been using nlsr() to fit s curves to Covid-19 data over the past few weeks and I have not had any issues.

Bernard
Sent from my iPhone so please excuse the spelling!"