[R] package for measurement error models

[peter dalgaard]

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 formulate the problem as a nonlinear model and use nls(). 

-- 
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