**From:** Andrew Robinson (*andrewr@uidaho.edu*)

**Date:** Thu 11 Mar 2004 - 03:19:25 EST

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Message-id: <200403100819.25760.andrewr@uidaho.edu>

Dear R friends,

I know that this topic has been mulled over before, and that there is a

substantial difference between the convergence criteria for JMP and those for

R. I apologize that this is somwehat raking cold coals.

Summary:

A model/data combination achieves convergence in JMP, and survives a

reasonably rigorous examination (sensible parameter estimates, well-behaved

surface, confidence intervals exclude 0). The same combination fails to

achieve convergence in R despite starting from the estimates reported in JMP.

What can I do?

Full story:

I am collaborating on a project which presently requires the fit of a seven

parameter non-linear function to 874 observations. The function is:

freeze.d <- deriv3(~ dbh^b * u^dbh * a1 * smi^a2 * exp(a3*pbal) *

(1 + a4*exp(a5*ba)) * cr^a6 * dh5^a7,

c("a1","a2","a3","a4","a5","a6","a7","b","u"),

function(dbh, smi, pbal, ba, cr, dh5, a1, a2, a3, a4, a5, a6, a7, b, u){})

The dbh, smi, pbal, ba, cr, and dh5, are known.

The data do not require the level of intricacy reflected in the function. It

is debatable whether they support it. However, my collaborator is anxious to

avoid linear models because of their relatively poor extrapolative

properties. So, that is an ongoing discussion.

He has achieved convergence using non-linear least squares in JMP. JMP uses

the union of three criteria: small change in objective function, small change

in parameter values, and small change in gradient. He can achieve

convergence in any of the three by reducing the other two sufficiently. He

arrives at the same point of convergence from a range of different starting

values. He gets garbage solutions for other starting points, but recognizes

these as such and explores elsewhere. At the point of convergence the model

has reasonable behavior, the confidence intervals for all the parameters

exclude 0, the surface seems to fit the data just fine, and the parameter

estimates all make sense. Some of them are highly correlated (up to -0.95)

but by no means all. In short, it seems to me to be a very thorough and

careful effort.

I'm trying to reproduce the model in R using nls. The convergence criterion

is different than JMP: it's a relative-offset convergence criterion. Even if

I start with his converged parameter estimates, nls will consume as many

iterations as I allow it and produce an error, e.g. "number of iterations

exceeded maximum of 50000". I have the trace on, and for the last n-2

iterations the parameter estimates do not change, at least in the digits that

trace provides. Increasing the tolerance does not seem to help.

So, I wonder: is it possible that JMP could produce results that are garbage

but stand up to reasonable scrutiny? Alternatively, is there some further

element of the fit that I should advise him to examine? I've been reading

Bruce McCullough's work and I know that for example S-plus was one of only

two packages to declare "ns" instead of providing estimates with 0 accurate

digits. But, how does one know that is what is happening in any given

situation, if the model looks good? Finally, it's possible that I am using

nls wrongly: here is my call

freeze.nls.d.1 <-

nls(dd.5 ~ freeze.d(dbh.0, smi, pbal.0, sba.0, cr.0, dh.5,

a1, a2, a3, a4, a5, a6, a7, b, u),

data = trees, control=ctl.obj, trace=T,

start = list(b = 0.2, u = 1, a1 = 0.4, a2 = -0.1, a3 = -0.01, a4 = 3,

a5 = -0.02, a6 = 0.25, a7 = 0.40))

Any insights will be appreciated!

Andrew

-- Andrew Robinson Ph: 208 885 7115 Department of Forest Resources Fa: 208 885 6226 University of Idaho E : andrewr@uidaho.edu PO Box 441133 W : http://www.uidaho.edu/~andrewr Moscow ID 83843 Or: http://www.biometrics.uidaho.edu No statement above necessarily represents my employer's opinion.______________________________________________ R-help@stat.math.ethz.ch mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

**Next message:**Thomas Stabla: "[R] R CMD check errors"**Previous message:**Abdou Ali: "[R] numerical equation"**Next in thread:**Douglas Bates: "Re: [R] Non-linear regression problem: R vs JMP (long)"**Reply:**Douglas Bates: "Re: [R] Non-linear regression problem: R vs JMP (long)"

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