weighted regression (Summary)

[David L Lorenz <lorenz@usgs.gov>]

All,
  Thanks to Rolf Turner and Brian
Ripley, who responded to my question. Thanks especially to Rolf Turner,
who was gracious in answering some followup questions.
  Unfortunately, I did not express
my question the way that it should have been posed. The real situation
is that I want to use estimates from a previous regression analysis as
the response variable in a new regression. These estimates are correlated
and if any regression can be done, then it must use GLS. The problem that
has been pointed out (within our own group) is that these regression estimates
do not capture the variability of the actual data. I was hoping to get
the procedure for WLS with known variance and apply it to GLS, but that
approach does not seem to be appropriate.
  My revised question: Is there
any way to correctly use regression estimates as the response variable
is a subsequent regression analysis?
Dave

David L Lorenz <lorenz@usgs.gov>
Sent by: s-news-owner@lists.biostat.wustl.edu

12/19/2005 08:47 AM

To	Snews <s-news@wubios.wustl.edu>
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Subject	[S] weighted regression

  We have a situation where we know the variance of observations for
a linear regression problem and need confidence limits on the parameter
estimates. The documentation in the NOTES section for lm states "In
addition, S-PLUS does not currently support weighted regression when the
absolute precision of the observations is known. This situation
arises often in physics and engineering, when the uncertainty associated
with a particular measurement is known in advance due to properties of
the measuring procedure or device. If you know the absolute precision of
your observations, it is possible to supply them to the weights
argument. This computes the correct coefficients for your model, but the
standard errors and other inference tools will be incorrect."
  I have searched the web, done bibliographic searches, and even searched
the documentation for a competing product and I found nothing regarding
the solution of this problem. I would be surprised if this problem has
not been solved because it should be a high priority in physics. At least
I remember it being an issue in physics classes, if not in the engineering
classes I took. 
  Is anyone aware of an approach to estimating the confidence limits
of parameter estimates when the variance of the observations is known?
I think I can see a solution for the case of equal known variance, but
I don't know that I have the ability to apply that to unequal variances.Thanks.
Dave