[S] [R] confidence ellipsoid for model parameters

[John Fox]

At 01:49 PM 1/4/2002 -0500, Duncan Murdoch wrote:
>John Fox wrote:
>
> >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.
>
>Doesn't it produce a larger ellipse, not a smaller one?

No, using q > 2 produces a smaller ellipse, e.g.:

 > qf(.95, 2, 100)
[1] 3.0873
 > qf(.95, 3, 100)
[1] 2.6955
 >


>If you are just doing a confidence region for 2 parameters, then the
>other parameters can take on any values; if you are projecting a p-dim
>region onto 2, then there are still restrictions on the other p-2
>parameters which your graphic will not show.  So the projection
>corresponds to a smaller region of parameter space than an equal sized
>2-dim confidence region, hence it needs to be bigger to give the same
>confidence level.

If I understand properly what you're saying, I think that we agree.

Regards,
  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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