[R] package for measurement error models

[Prof Brian Ripley]

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