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 <j...@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 >Hamilton, Ontario, Canada >web: https://socialsciences.mcmaster.ca/jfox/ > > > > > S > > > > > > ******************************************************************* >> This email and any attachments are confidential. Any >use...{{dropped:8}} > > > > ______________________________________________ > > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > > >______________________________________________ >R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code. -- Sent from my phone. Please excuse my brevity. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
