[R] Is DUD available in nls()?

[Prof J C Nash (U30A)]

One of the reasons DUD is not available much any more is that methods 
have evolved:

- nls (and nlxb() from nlmrt as well as nlsLM from minpack.LM -- which 
are more robust but may be less efficient) can use automatic derivative 
computation, which avoids the motive for which DUD was written

- DUD came about, as Bert noted, in a period when many methods were 
being tried. I recall being at one of the first talks about DUD by Mary
Ralston. It seems to work well on the examples used to illustrate it, 
but I have never seen a good comparative test of it. I think this is 
because it was always embedded in proprietary code, so not properly 
available for scrutiny. (If I'm wrong in this, I hope to be enlightened 
as to source code. I did find a student paper, but it tests with SAS.)

- Marquardt methods, as in nlmrt and minpack.LM, generally have a better 
track record. They can be used with numerical derivative approximations 
(numDeriv, for example) with R functions rather than expressions (nlfb 
from nlmrt, and one of the other minpack.LM routines), in which case one 
gets a form of secant method.

- Ben's mention of bobyqa leads to a different derivative-free minimizer 
that approximates the surface and minimizes that.

John Nash




Date: Tue, 2 Apr 2013 07:22:33 +0000
From: Ben Bolker <bbolker at gmail.com>
To: <r-help at stat.math.ethz.ch>
Subject: Re: [R] Is DUD available in nls()?
Message-ID: <loom.20130402T091830-660 at post.gmane.org>
Content-Type: text/plain; charset="us-ascii"

Bert Gunter <gunter.berton <at> gene.com> writes:

 >
 > I certainly second all Jeff's comments.
 >
 > **HOWEVER** :
 > http://www.tandfonline.com/doi/pdf/10.1080/00401706.1978.10489610
 >
 > IIRC, DUD's provenance is old, being originally a BMDP feature.
 >

   If you want to do derivative-free nonlinear least-squares fitting
you could do something like:

library("bbmle")
dnorm2 <- function(x,mean,log=FALSE) {
    ssq <- sum((x-mean)^2)
    n <- length(x)
    dnorm(x,mean,sd=ssq/n,log=log)
}
mle2(y~dnorm2(mean=a*x^b),data=...,method="Nelder-Mead")

   This is not necessarily the most efficient/highly tuned possibility,
but it is one reasonably quick way to get going (you can substitute
other derivative-free optimizers, e.g.

library("optimx")
mle2(...,optimizer="optimx",method="bobyqa")

(I think).

   This isn't the exact algorithm you asked for, but it might serve
your purpose.

   Ben Bolker