[R] nonlinear fitting when both x and y having measurement error?
Prof Brian Ripley
ripley at stats.ox.ac.uk
Wed Sep 12 09:03:19 CEST 2001
On Wed, 12 Sep 2001, Etsushi Kato wrote:
> Dear r-help,
> I want to conduct nonlinear fitting to a data frame having x and y
> variables. Because both x and y have measurement error, I want to
> include error term of x variable in the model. I'm not sure but I
> think ordinary nls model only consider error term of y variable.
> How can I do this kind of nonlinear fitting in R. Is there any
> examples in nls package?
That is not a least-squares problem. Even in the simple linear case (one
x one y) it's a hard problem, one that cannot be solved without more
information (for example on the ratio of the error variances, or knowing
one of them). As far as I know there is no software available in R for
that case (although it's not hard to write).
I think you need to write down a suitable likelihood and optimize it
numerically (with optim).
This topic is not well covered in regression texts, although it is in that
by Sprent, for example. There is a specialist text by W. A. Fuller (1987)
Measurement Error Models.
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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