typsize and fscale arguments to nlm

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.

absolute.

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....
Martin

    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                   <><