NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/sci/math/stat/1789

Internet Message Format | 1992-09-02 | 1.7 KB

Path: sparky!uunet!wupost!zaphod.mps.ohio-state.edu!moe.ksu.ksu.edu!kuhub.cc.ukans.edu!jeff
From: [e-mail] (Jeff Bangert)
Newsgroups: sci.math.stat
Subject: Non-linear Regression in Chemistry
Message-ID: <[e-mail]>
Date: 3 Sep 92 06:42:30 CDT
Organization: University of Kansas Academic Computing Services
Lines: 36

A chemist has asked me to solve a problem: she has data and a model
which is to be fit by 'least squares'.  It looks like non-linear
regression, except that:

    1. the model has two equations
    2. both are non-linear
    3. there are parameters common to the two equations.

I would like to know:

    1. is there a 'standard' method for solving this problem?
    2. is there literature in stat or chemistry which I could read?

Clearly, I can form the sum of squared errors for each equation and
add them together.  I have lots of methods for minimizing the result.
However, this seems to ignore the question of the weighting of the two
equations.

I solved this kind of problem several years ago by writing FORTRAN +
IMSL.  Now that it has come up again, I wish I had some backup
literature that at least suggests the 'standard' solution method.  I
don't like reinventing the wheel.

Since the current data matrix is small, 4 by 2, I'm going to use
non-linear optimization in Quattro Pro this time.  It produces nice
graphs.  But, if I stick with QP, I'll also have to calculate the
standard errors of the parameter estimates.  Right now, I'm not
looking forward to this.

Thanks for the help,
--
Jeff Bangert            [e-mail]
Computer Center            [e-mail]
University of Kansas
Lawrence, KS 66045
[phone]