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. )
One more question, is any reference that considers weighted measurement
error models (use the known variance of measurement errors as weights) ?

(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@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@cbs.dk  Priv: PDalgd@gmail.com
>>
>
> --
> Brian D. Ripley,                  ripley@stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/<http://www.stats.ox.ac.uk/%7Eripley/>
> 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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