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

[Austin Nichols <austinnichols@gmail.com>]

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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