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

[Nick Cox <njcoxstata@gmail.com>]

Nothing depends on my one-off terminology. Perhaps "inputs" and
"outputs" capture my meaning better.

The leading examples I know of for cube roots are

volumes go to lengths

and

gammas go to Gaussians (to a good approximation; "Wilson-Hilferty" is
a known incantation here)

and everything else is a matter of "if it helps".
Nick
njcoxstata@gmail.com


On 19 November 2013 12:24, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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