[R] Re: [S] regression with uncertainty in both variables

Prof Brian D Ripley ripley at stats.ox.ac.uk
Thu Apr 15 09:02:49 CEST 1999

[I don't think blanketing both S and R help on this is a good idea.]

On Wed, 14 Apr 1999, Matthew Wiener wrote:
> I'm trying to use some linear regression models in which both the
> dependent and independent variables are measured with some error.  To

Notation: that is not a `regression' model.

> make things worse, while the errors in the dependent variable are uniform,
> the errors in the independent (or explanatory, or "x") variables can be
> heteroskedastic.  I've been looking at the book _Measurement Error Models_
> by Fuller (1987).  I'm wondering whether anybody knows any other
> references on the subject, and whether anyone has written S or R code that
> handles these kinds of problems.  (As far as I can tell, the usual lm and
> glm functions don't; if I'm wrong, that's great.)

Well, there are of lots of other references, even one by me, but that is
the main book. If lm and glm did this they would be wrong: it is a
different statistical model. There are several Fortran solutions on statlib
in multi/leiv?

1.      Programs for best line fitting with errors in both coordinates.

2.      D. York, "Least squares fitting of a straight line", Canadian 
                 Journal of Physics, 44, 1079-1086, 1986.
        G. Fasano and R. Vio, "Fitting straight lines with errors on both
                 coordinates", Newsletter of Working Group for Modern 
                 Astronomical Methodology, No. 7, 2-7, Sept. 1988.
        B.D. Ripley and M. Thompson, "Regression techniques for the 
                 detection of analytical bias", Analyst, 112, 377-383,

and I have seen an S interface somewhere (multiv?). Today, I would take the
algorithm in the last of those papers and re-write it in S in a few
minutes. A project that has, several times, nearly made the MASS library
and one I set as a exercise in my linear models course.

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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