Re: st: Transformation of variable with pos/neg values via asinh

[David Hoaglin <dchoaglin@gmail.com>]

Nick,

In Steve's application the "balance" is

(end of year) - (beginning of year).

That produces the gain or loss.  I would not ordinarily illustrate a balance as

gain - loss.

John Tukey's example (page 57, not involving data) is
"profit-and-loss," which could arise from (end of year) - (beginning
of year).  He goes on to say, "Re-expression [transformation] of the
balance rarely helps, but re-expression of the amounts or counts
before the subtraction sometimes helps a lot."  I will look for
examples involving data.

I would be reluctant to transform a balance by using the cube root,
but I have not read your SJ article.  From my "upbringing" in EDA I
generally have a relaxed attitude about transformations, but I like
them to be plausible.

David Hoaglin

On Tue, Nov 19, 2013 at 5:40 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> David's suggestion that with a balance, namely
>
> balance = gain - loss
>
> you are better off with
>
> transform of gain - transform of loss
>
> than with with
>
> transform of (gain - loss)
>
> echoes John Tukey's advice in Exploratory data analysis
> (Addison-Wesley, Reading, MA, 1977). Tukey didn't give an example, and
> I don't recall ever seeing one in his work.
>
> However, this is a counsel of perfection, as often the individual gain
> and loss values are not accessible.
>
> Like Austin I've been advocating cube roots for some while. I often
> work with audiences for whom asinh is beyond esoteric; I've even
> encountered considerable resistance to cube roots. Some people seem
> reluctant to try anything not sanctioned by a hundred texts. But they
> got a puff in
>
> SJ-11-1 st0223  . . . . . . . . . . . . . . . . . . . Stata tip 96: Cube roots
>         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
>         Q1/11   SJ 11(1):149--154                                (no commands)
>         tip showing the use of the cube function and cube roots
>
> No pretence: using cube roots is distinctly ad hoc (which, in modern
> idiom, I translate freely as "fit for purpose"). So is asinh.
>
>
> Nick
> njcoxstata@gmail.com
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