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MathGroup Archive 1998

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nonlinear regress on multiple data sets?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14528] nonlinear regress on multiple data sets?
  • From: "Rajdeep S. Kalgutkar" <rajdeep at chem.nwu.edu>
  • Date: Thu, 29 Oct 1998 04:33:25 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Hello everybody!

I have a question about nonlinear regression over multiple data sets. Is
it possible using Mathematica? My problem is formulated like this:

x*(y1*Eigenvec1+f(y1)*Eigenvec2) +
(1-x)*(y2*Eigenvec1+f(y2)*Eigenvec2) = Obs. Data

where:
x can be from 0. - 1.;
y1 and y2 are usually in a narrow range whose values depend on the data
sets and eigenvectors under consideration; f(y1) and f(y2) are
functions of y1 and y2 respectively; Eigenvec1 and Eigenvec2 are 2
eigenvectors (60 - 200 element vectors) by which I want to express my
observed data (Obs. Data, same dimensions as eigenvectors).

Now, I have multiple obs'd data. Usually I use
Statistics`NonlinearRegress` to fit each individual data set. The
values of y1 and y2 (and so f(y1) and f(y2)) should be the same for all
the data sets and only x should change. Apart from minor variations the
answers that I get for y1 and y2 are consistent for all data sets.
However, it would be better if I could fit all the data sets
simulataneously in a some sort of global fashion so as to obtain a
global y1 and y2 with individual x's. Is this possible under
Mathematica 3.0? Is so, how? I would really appreciate any help on this
issue!

rajdeep kalgutkar
dept of chem
nothwestern univ.
rajdeep at chem.nwu.edu 


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