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

[Martyn Plummer]

On 12-Sep-2001 Prof Brian Ripley wrote:
> 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.

Non-linear measurement error models are covered by:

Carroll, R.J., Ruppert, D. and Stefanski, L.A.  Measurement Error
in Nonlinear Models, Chapman & Hall 1995 

Martyn
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