[R] typsize and fscale arguments to nlm

John Fox jfox at mcmaster.ca
Mon Aug 5 15:15:15 CEST 2002

Dear Martin,

Thank you for answering my question. I'm impressed that you would pay 
attention to a two-week-old question. In the interim I obtained and read 
the two references in the documentation, which clarified what typsize and 
fscale are and how they are used in the algorithm (which is why I didn't 
repost the question).

With respect to the documentation, my remark was probably unfair -- it's 
not reasonable to ask for detailed documentation of such a complicated 
function. I think, though, that I would replace the word "size" here with 
"absolute value," which seems to me more precise in this context (or just 
put "absolute value" within parentheses after size as a clarification), and 
perhaps say briefly how these arguments are used in the algorithm.

It occurred to me that I could look at the source code, but I'm not a very 
good C programmer. I'd have a better chance to figure out what the code is 
doing if it were in FORTRAN -- which dates me, I guess. Even if the code 
were in FORTRAN, I'm probably not sufficiently clever to understand it 
without reading the references.

Thanks again,

At 09:56 AM 8/5/2002 +0200, you wrote:

>nobody seems to have answered this on R-help.
> >>>>> "John" == John Fox <jfox at mcmaster.ca> writes
>on July 22 :
>     John> Dear R list members, I have a question about the
>     John> proper use of the typsize and fscale arguments to nlm.
>     John> I use nlm in my sem package to fit general
>     John> structural-equation models, which entails maximizing a
>     John> multinormal likelihood with respect to parameters that
>     John> represent regression coefficients and covariances of
>     John> variables. The magnitudes of these parameters can be
>     John> very different.
>     John> The documentation for typsize is rather terse: "an
>     John> estimate of the size of each parameter at the
>     John> minimum," with the default typsize=rep(1, length(p))
>     John> [where length(p) gives the number of parameters]. Am I
>     John> correct in interpreting the "size of each parameter"
>     John> as its absolute values?
>yes ``typical absolute values''
>     John> as its absolute values? If so, is it reasonable to
>     John> specify typsize=abs(start), where start contains that
>     John> start values of the parameters?
>Yes -- unless some `start[j]' is ``untypically'' close to zero ..
>     John> I can compute start values that have generally
>     John> reasonable magnitudes (certainly more generally
>     John> reasonable than assuming that all parameters are of
>     John> the same magnitude) and that will never be identically
>     John> 0. A related question is whether typsize specifies the
>     John> relative or absolute "sizes" of the parameters.
>Note that R is open source and (if you don't have the references
>that help(nlm) mentions) you can always read the source code.
>In this case, the really relevant things are in src/appl/uncmin.c
>whose optif9() is called from  do_nlm() in  src/main/optimimze.c}.
>Note that "typsize" is "typsiz" in the C code (since that is
>translated from Fortran which had a 6-letter limitation).
>Typical lines in uncmin.c are
>    1788:        gs = fmax2(fabs(f), fscale) / fmax2(fabs(x[i]), typsiz[i]);
>    1858:        hs = fmax2(fabs(g[j]), 1.0) / fmax2(fabs(x[j]), typsiz[j]);
>where the first tells you how `fscale' is used and both show you
>how the `typsize[]' vector is.
>     John> Finally, there is another argument to nlm called
>     John> fscale which specifies "an estimate of the size of f
>     John> at the minimum" (where f is the function to be
>     John> minimized -- in my case the negative
>     John> log-likelihood). The default is fscale=1. In
>     John> experimenting with nlm I've found that using
>     John> typsize=abs(start) appears to make my sem function
>     John> more robust (e.g., less sensitive to start values when
>     John> the parameters are of very different magnitudes), but
>     John> setting fscale to the log-likelihood at the start
>     John> values for the parameters seems to create problems.
>     John> Any help, advice, or additional information would be
>     John> appreciated. (I plan to take a look at the Dennis and
>     John> Schnabel text cited in the help file for nlm but have
>     John> not yet done so.)
>     John> Thanks, John
>You're welcome.
>Could you (`in return') propose improvements to the text
>in help(nlm) ?
>My answering above should really be an incentive for people
>to start reading source code....
>     John> John Fox Department of Sociology McMaster University
>     John> Hamilton, Ontario, Canada L8S 4M4 email:
>     John> jfox at mcmaster.ca phone: 905-525-9140x23604 web:
>     John> www.socsci.mcmaster.ca/jfox
>     John> -----------------------------------------------------
>Martin Maechler <maechler at stat.math.ethz.ch>    http://stat.ethz.ch/~maechler/
>Seminar fuer Statistik, ETH-Zentrum  LEO C16    Leonhardstr. 27
>ETH (Federal Inst. Technology)  8092 Zurich     SWITZERLAND
>phone: x-41-1-632-3408          fax: ...-1228                   <><

John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox

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