[R] package for measurement error models

[Prof Brian Ripley]

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 <ripley at 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.mes at cbs.dk  Priv: PDalgd at gmail.com
> 
> 
> --
> 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 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
> 
> 
> 
>

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595