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

pauljohn@ukans.edu pauljohn at ukans.edu
Sat Sep 15 15:55:41 CEST 2001

I've seen the answers that point in the measurement model
direction, but I wonder if there is not a more direct approach.

In my copy of Pindyck and Rubinfeld's Econometric Models and
Economic Forecasts, it outlines an instrumental variable
approach in which the x with error is replaced by an instrument,
a predicted value from an auxiliary model in which x is
regressed on other exogenous/predetermined variables.  They
prove the parameter estimates are consistent, which (I believe)
is about the best we can hope for. 

One advantage of that strategy is that one need not assume a
specific distribution for the error terms involved, only
something general like E(e)=0 and constant variance.  The ML
approach will require the choice of a precise distribution. Not

They don't show that approach works when the relationship
between x and y is nonlinear.  Come to think of it, I don't
recall a treatment of IV applications for nonlinear equations.

This is a great question and I'm interested to hear more about
how the project works out in the end.
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.

Paul E. Johnson                       email: pauljohn at ukans.edu
Dept. of Political Science           
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66045                FAX: (785) 864-5700
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