[R] calculating area of ellipse

[John Fox]

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
Hamilton, Ontario, Canada
web: https://socialsciences.mcmaster.ca/jfox/

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