[S] [R] confidence ellipsoid for model parameters

[Eric Zivot]

Very recently a graduate student, Mohamed Taamouti, in economics at the
University of Montreal, working with Jean Marie Dufour, has derived analytic
formulas based on "quadrics" for computing projected confidence sets for
individual parameters in instrumental variables regression models. These
formulas can be used for regular regression as well. See the working paper
"Projection-Based Statistical Inference in Linear Structural Models with
Possibly Weak Instruments" Discussion paper C.R.D.E., University of
Montreal, 2000.

-----Original Message-----
From: s-news-owner at lists.biostat.wustl.edu
[mailto:s-news-owner at lists.biostat.wustl.edu]On Behalf Of John Fox
Sent: Wednesday, January 02, 2002 10:29 AM
To: renaud.lancelot at cirad.fr; S-news
Cc: R-Help
Subject: Re: [S] [R] confidence ellipsoid for model parameters


Dear Renaud,

At 10:51 PM 1/1/2002 +0000, Renaud Lancelot wrote:
>Dear all,
>
>Has anyone written functions to compute (and ideally project / plot onto
>a plane) confidence ellipsoids for q linear model parameters, q > 2 ?

(I also read the subsequent messages on this topic. I'm not sure that I
understand why you want to do what you suggest, but if I interpret the
question properly, you should be able to proceed as follows.)

The confidence ellipse for a pair of coefficients is just (with an
adjustment for size) the perpendicular shadow of the joint ellipsoid, in
the same sense that the confidence intervals for individual coefficients
are shadows of the joint ellipsoid or ellipse. The usual confidence ellipse
for 2 of q coefficients uses qf(.95, 2, df.error) to scale the ellipse; if
you want to scale the ellipse as a literal shadow of the joint confidence
region for all q coefficients, use qf(.95, q, df.error) instead (which
produces a smaller ellipse). You can do this by simply editing
confidence.ellipse.lm in car.

I hope that this helps.
  John

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
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