[R] nonlinear fitting when both x and y having measurement error?

[Prof Brian Ripley]

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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