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

[Steven Delbright <steven.delbright@gmail.com>]

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

On Mon, Nov 18, 2013 at 5:11 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Steven Delbright <steven.delbright@gmail.com>:
>
> It can't actually be normally distributed if it has fatter tails or
> unexpectedly extreme values. You might also try cube roots, or fifth
> roots, or 7th roots, etc. I have found income and wealth is often
> easier to deal with after taking an odd root.
>
> But it's usually better not to transform an outcome variable and then
> regress, instead of using a regression with an appropriate link. In
> any case, there is no problem with a bimodal outcome variable,
> especially if you have a bimodal regressor that predicts it well!
>
> On 11/18/13, Steven Delbright <steven.delbright@gmail.com> wrote:
>> Dear All:
>>
>> I frequently work with variables that have positive and negative
>> values, and that also have extreme values. Normally, I just winsorize
>> the tails and that's the end of the story.
>>
>> Recently, I frequently come across inverse hyperbolic sine function
>> (IHS) transformations (stata function asinh). The benefit of IHS is
>> that it also transforms negative values (contrary to log
>> transformations). However, the transformed variable typically has two
>> modes (aka bimodal distribution) -- even though the input variable is
>> normally distributed (although with extreme values).
>>
>> My question: Does any of you use asinh, and if so, how do you deal
>> with the bimodal distribution of the transformed variable? I realize
>> that the normality assumption of OLS does not require the DV to be
>> normally distributes (but the residuals) but it still seems strange to
>> have a DV with two modes...
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