[R] Multi-dimensional non-linear fitting - advice on best method?

[David Winsemius]

On Apr 23, 2011, at 8:38 PM, Julian Gilbey wrote:

> Hello!
>
> I have a set of data of the form (x, y1, y2) where x is the
> independent variable and (y1, y2) is the response pair.  The model is
> some messy non-linear function:
>
>  (y1, y2) = f(x; param1, param2, ..., paramk) + (y1error, y2error)
>
> where the parameters param1, ..., paramk are to be estimated, and I'll
> assume the errors to be normal for sake of simplicity.
>
> If there were only one response per input, I would use the nls()
> function, but what can I do in this case?

I wonder it would be sensible or at least informative to consider  
solving for the "inverse case". i.e. solve for:

x = f(y1, y2)

-- 
David Winsemius, MD
West Hartford, CT