Re: Simultaneous nonlinear Regression of two data sets

• To: mathgroup at smc.vnet.net
• Subject: [mg19473] Re: [mg19440] Simultaneous nonlinear Regression of two data sets
• From: "Mark E. Harder" <harderm at ucs.orst.edu>
• Date: Sat, 28 Aug 1999 15:53:03 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```To All;
Christopher, thanks for posting this.  I, too, have a global fitting
problem**  I would like NonlinearRegress to work on, & when I read the book
& the online help, I thought the idea was still worth  trying.  Alas, the
problem *seems* to be that the function can't interpret parameter symbols
and values that are lists ( which, I believe, are the most economical and
direct forms for expressing the problem.).  In my case, the function call
returned no error messages; it simply returned a slightly expanded form of
the function.
Another problem I have is that my model function has to be a Mathematica
function module, not a symbolic statement, since evaluation of my model,
given parameter values, involves iterative numerical procedures, like
root-finding; & I don't think Mathematica can handle that, even when using
the FindMinimum option.
I have been able to implement these kinds of fits in FORTRAN 77 & 90,
using the IMSL nonlinear-fitting routine where you can pass the subroutine
the name of the model function subprogram.  If you want the package routing
to use analytical derivatives, you pass it a function for evaluating
derivatives, otherwise, it uses some internal approximate numerical
algorithm for the derivatives.  This can be a little complicated, requiring
COMMON blocks or some such, and I would rather have it done in Mathematica.
I am currently working at creating simpler test cases in Mathematica
that separate these two problem variables.  If I get anywhere, I'll let you
know (don't hold your breath).  Otherwise, I, too, would welcome
enlightenment.
-mark

**- one term for the procedure of simultaneously fitting a set of models to
multiple data sets, when some of the parameters are shared among the
models -- this can be a way to make a more overdetermined system with
better-defined minimum in its error surface out of a bunch of possibly
poorly-determined individual fits.

-----Original Message-----
From: Christopher Mack <mack at tvt.tu-darmstadt.de>
To: mathgroup at smc.vnet.net
Subject: [mg19473] [mg19440] Simultaneous nonlinear Regression of two data sets

>Hello,
>
>I want to fit two (if it works, I also want to fit threee and four)
>mathematical functions to two (in future perhaps three and four) data
>sets (gaussian
>profiles); each function has eight parameters to fit, but four of them
>are the same for all functions.
>
>I first thought of using the Mathematica-Function "NonlinearRegress";
>but after reading the Online-help I assumed that it only can fit
>one function to one data set.
>
>Is there a functino implemented into Mathematica, which can solve the
>described problem ?
>
>
>Thanks,
>
>Christopher Mack,
>
>Department of Chemical Process Engineering,