[R] nonlinear least squares, multiresponse

[Douglas Bates]

Sophie Smout <scs10 at st-andrews.ac.uk> writes:

> I'm trying to fit a model to solve a biological problem.

> There are multiple independent variables, and also there are multiple
> responses. 

> Each response is a function of all the independent variables, plus a set of
> parameters. All the responses depend on the same variables and parameters -
> just the form of the function changes to define each seperate response. 

> Any ideas how I can fit parameters to my data?
> nls, as I understand it, will work for multiple independent variables, but
> not multiple responses. 

The Box-Draper criterion for multiresponse parameter estimation is
discussed in chapter 4 of Bates and Watts, "Nonlinear Regression
Analysis and Its Applications" (Wiley, 1988).  There is even a
detailed explanation there of a generalized Gauss-Newton algorithm to
optimize the criterion.  We did not implement that in the nls function
for R and, given the state of my "To Do" list, it is not likely to
happen soon.

If a skilled and energetic R/C programmer would like to undertake this
project I would be happy to provide advice on how it could be
implemented.
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