On Tue, 10 Aug 2010, Carrie Li wrote:
Thank you both!
I found that the model with both x and y have measurement errors should be
pretty common in practice. But it seems to me that there is no a simple
solution for it...(I mean, a ready-to-use package or program handing this
model fitting problem. )
Hmm, have you actually looked at my reference? We provided a program
in 1987.
One more question, is any reference that considers weighted measurement
error models (use the known variance of measurement errors as weights) ?
That's not really how you use known variances, which is the main case
covered in our paper.
(I've search on google..got nothing...)
Thanks for your sharing opinions again! I appreciate!
Carrie--
On Tue, Aug 10, 2010 at 7:54 AM, Prof Brian Ripley <rip...@stats.ox.ac.uk>
wrote:
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
--
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
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