R help - Apr 2011 - Multi-dimensional non-linear fitting - advice on best method?

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?

Many thanks,

   Julian

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

On Apr 24, 2011, at 02:38 , 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 believe the gnls function in the nlme package is your friend. It's a bit
involved but the basic idea is to stack the two response variables and use a
weights argument with a varIdent structure with variance depending on whether it
is a y1 or a y2 observation. You can also specify a within-pair correlation.
> 
> Many thanks,
> 
>   Julian
> 
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-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
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Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com