[R] calculating area of ellipse

Jeff Newmiller jdnewm|| @end|ng |rom dcn@d@v|@@c@@u@
Tue May 11 16:48:16 CEST 2021

```The area is a product, not a ratio. There are certainly examples out there of meaningful products of different units, such as distance * force (work) or power " time (work).

If you choose to form a ratio with the area as numerator, you could conceivably obtain the numerator with force snd distance and then meaningfully form a ratio with time (power). So this asserted requirement as to homogeneous units seems inaccurate. But without context I don't know if any of this will aid in interpretation of variance for the OP.

On May 11, 2021 7:30:22 AM PDT, John Fox <jfox using mcmaster.ca> wrote:
>Dear Stephen,
>
>On 2021-05-11 10:20 a.m., Stephen Ellison wrote:
>>> In doing meta-analysis of diagnostic accuracy I produce ellipses of
>confidence
>>> and prediction intervals in two dimensions.  How can I calculate the
>
>area of
> >> the ellipse in ggplot2 or base R?
> >
>> There are established formulae for ellipse area, but I am curious: in
>
>a 2-d ellipse with different quantities (eg coefficients for salary and
>
>age) represented by the different dimensions, what does 'area' mean?
>
>I answered James's question narrowly, but the point you raise is
>correct
>-- the area isn't directly interpretable unless the coefficients are
>measured in the same units.
>
>It still may be possible to compare areas of ellipsoids for, say,
>different regressions with the same predictors, as ratios, however,
>since these ratios would be unaffected by rescaling the coefficients.
>The generalization of this idea to ellipsoids of any dimension is the
>basis for the generalized variance-inflation factors computed by the
>vif() function in the car package.
>
>Best,
>  John
>
>John Fox, Professor Emeritus
>McMaster University
>web: https://socialsciences.mcmaster.ca/jfox/
>
> >
> > S
> >
> >
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