There is a scattered literature on the dangers, or otherwise, of using
ratios in correlational analyses.
I have read what looks like a nonobfuscatory paper on this topic by
Firebaugh and Gibbs "User's Guide to Ratio Variables" from American
Sociological Review, Vol.50, No.5 (1985) pp.713722.
On page 721 the authors state: "Avoid mixed methods (part ratio, part
component). If Z is controlled by division rather than by
residualization, all of the other variables should be divided by Z.
Should only some of the variables by divided by Z, the effect of Z is
'controlled' for some variables and not for others, and a defensible
interpretation of the results is difficult."
The reason for my interest is that I am trying to evaluate a
morphometric paper that does linear discriminant analysis on a mixture
of measurements and ratios derived from those same measurements. For
example the analysis includes (A) Length as well as Height/Length and
(B) Height and Breadth as well as Height/Breadth and Height/Length.
This paper seems to be an example of the 'mixed method' that Firebaugh
and Gibbs warn against, where data are part ratio, part measurement,
and spurious correlations are introduced into the data.
So my first question is whether I am correct in this interpretation.
My second question also concerns ratios.
In his Multivariate Statistical Methods, 2nd ed. 1994, B.F.J. Manly
suggests controlling for the effects of absolute size difference in a
PCA of pots (goblets) by expressing the measurements as "a proportion
of the sum of all measurements on that goblet."
Given that each variable is divided by the same sum, this example of
the use of ratios seems to be a case that Firebaugh and Gibbs would
not frown on.
I shall welcome any comments on these questions and any pointers to
relevant literature.
Richard

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