On Tue, 10 Aug 2010, peter dalgaard wrote:
On Aug 10, 2010, at 3:52 AM, Carrie Li wrote:
Thanks. I found the code in the link you gave me very helpful.
But, I just have few questions regarding the code.
It seems to me that in (from wikipdeia)Deming regression, it assumes that
the ratios of the variances of two measurement errors are constant for all
pairs of (x_i, y_i). However, if the ratios are not constant, (i.e. the
variances of measurement are heterogeneous) , is it still appropriate to use
Deming regression ?
In a word, no.
One way of looking at it is that as the ratio of variances varies
from 0 to infinity, the analysis goes from regression of y on x to
(inverse) regression of x on y, and those give different results,
not just numerically but also asymptotically. I.e., getting the
ratio wrong gives an inconsistent estimate; getting it wrong for
some of the data, as is bound to happen if you assume it constant
and it isn't, will also give a inconsistent estimate. Unless, that
is, you can find a definition of "average ratio" that eliminates the
bias, but I don't think it is worth the paperwork.
Rather, I'd suggest direct minimization of the SSR (from the
Wikipedia page), noting that you can plug in x_i^* as a function of
beta also if the _individual_ ratios are known. (I get the feeling
that someone must have been here before, so possibly others can fill
in the gaps?) For modest sample sizes, it might also be possible to
Yes, people have been there before. Mike Thompson and I published a
now-much-cited-in-analytical-chemistry paper in The Analyst in 1987.
A companion paper was rejected by a mainstream statistics journal as
'already known', but the journal editor was unable to get any prior
publication out of the referee.
formulate the problem as a nonlinear model and use nls().
Direct minimization is simple enough.
--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd....@cbs.dk Priv: pda...@gmail.com
--
Brian D. Ripley, rip...@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 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
