[S] [R] confidence ellipsoid for model parameters

[Duncan Murdoch]

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? 

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.

Duncan Murdoch

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