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

[Nick Cox <njcoxstata@gmail.com>]

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


On 19 November 2013 01:43, David Hoaglin <dchoaglin@gmail.com> wrote:
> Dear Steven,
>
> The presence of extreme values (relative to the variation in the bulk
> of the data) suggests that the variable does not have a normal
> distribution.  Do you have a mixture of some sort?
>
> What is the source of the negative values of CEO wealth?
>
> A variable that has both positive and negative values is often the
> result of taking the difference between two positive quantities.  If
> some sort of transformation seems likely to be useful, it is usually a
> good idea to transform the variables that are the basis for the
> difference.
>
> Regards,
>
> David Hoaglin
>
> On Mon, Nov 18, 2013 at 6:21 PM, Steven Delbright
> <steven.delbright@gmail.com> wrote:
>> Dear Austin:
>>
>> Thanks so much for the quick response! I indeed struggle with a
>> "wealth" dependent variable (CEO wealth to be exact). Do you have some
>> sample citations for academic work transforming wealth variables (not
>> necessarily in management but also other fields).
>>
>> Also, I found your comment regarding using a different link. I never
>> considered this option before but always transformed my DV. What link
>> would I use for untransformed wealth variables with fat tails?
>>
>> Thanks much!
>> Steven
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