Message-ID: <D71F5453-7A3E-46A4-BA0B-FE152039B1F0@gmail.com>
Date: 2011-04-24T22:57:46Z
From: Peter Dalgaard
Subject: Multi-dimensional non-linear fitting - advice on best method?
In-Reply-To: <20110424003813.GB9726@d-and-j.net>
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
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com