Plotting variables in transformed space

Question

Suppose $A = X_1/X_2$ and $B = X_3/X_4$. Why would one plot the data in $(\log A, \log B)$ space as opposed to $(A,B)$ space?

You don't have to, but it make make the data better behaved or more naturally interpretable. This thread is worth reading: In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? — gung - Reinstate Monica, Oct 29 '13 at 15:15

score 2 · Answer 1 · edited Oct 29 '13 at 14:50

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If one wanted to use linear regression, then the logs of A and B will be linear in the numerator and denominator. That is the usual reason to use log transforms. It also may make the sampling errors better behaved, since you are converting ratios to sums.

edited Oct 29 '13 at 14:50

Nick Cox

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answered Oct 29 '13 at 14:41

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Log ratios are generally much better behaved than ratios, always assuming that you can take logs, i.e. all components are strictly positive. This is broadly true regardless of whether regression is intended. – Nick Cox Oct 29 '13 at 16:06
@Nick Cox: Thanks for expanding on the answer. Yes, provided data is strictly positive, Logs behave like sums, which are a LOT nicer...and I speak from experience of being analytically "burned" using logs..they don't behave intuitively. Thanks again. – Oct 29 '13 at 16:22

Plotting variables in transformed space

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