Nick Cox wrote:
Also, partially echoing Jeph Herrin, if everything is negative,
consider reversing signs. Sign is often a convention.
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One of the things that struck me about Woong-Tae's original post was that
the ratios weren't all negative or all positive: "My first intension is
using a log transformation of all variables but seems not to be a good idea
since all variables have negative values (around 20%) Besides, all
variables except one of independant variables are ratio, thus that idea
would make worse."
Usually when I choose to describe and interpret two measurements in terms
of their ratio, I don't expect the values of the ratio to cross over the
zero-line to the other side. When they do, it raises a question as to the
utility of the expression: it seems counterproductive to express two
measurements as their ratio in order to facilitate description or
interpretation if the numerator measurement, the denominator measurement or
both measurements can take on negative values independently of each other,
namely when comparing apples to apples, that is, in ratios where, if the
numerator can cross zero, then so can the denominator. In these cases,
simple difference values or a even series of vectors would seem to be a
better short-hand description and to be more interpretable than a series of
ratios that are 20% negative-valued.
There are exceptions that have a natural interpretation: perhaps some of
Woong-Tae's ratios are proportions, such as Percent Improvement, which takes
on a negative value when there is worsening. But then this sounds like a
response, and I would deliberate before putting something like this on the
right-hand side of a longitudinal data model or other panel data model. (Or
any model for that matter, not considering instrumental variables
regression.)
If Woong-Tae's ratios are occasionally negative because of measurement
error, then that raises another of the other assumptions about independent
variables that were left as another matter in the earlier reply.
Joseph Coveney
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