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# Re: st: How to find the best transformation for each variable in 120 periods

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: How to find the best transformation for each variable in 120 periods Date Fri, 22 Feb 2013 17:55:03 +0000

```Closer to home in a couple of senses are cube roots:

http://www.stata-journal.com/article.html?article=st0223

Odd integer roots are equally well defined for arguments of any sign,
although you have to go in Stata (e.g.)

sign(x) * (abs(x))^(1/3)

I've been working with glacier advance and retreat rates. Occasionally
glaciers advance a lot or retreat a lot but most values are much
closer to zero, so cube roots are a non-standard but useful way to
plot them. Haven't tried regressions, as that is not the nature of the
problem.

Nick

On Fri, Feb 22, 2013 at 5:28 PM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Fri, Feb 22, 2013 at 10:40 AM, Xixi Lin <winnielxx@gmail.com> wrote:
>> Hi JVerkuilen,
>>
>> You are right that the key assumption is Gaussian errors, but my data
>> does not have Gaussian errors, and I wanna use t statistics, so I
>> wanna to fix the non-normal residuals by transforming the variables (I
>> don't know what else to do to fix the Gaussian errors). Is there any
>> better way to deal with it? Or Is there any papers that I can read
>
> Well as I said, the Atkinson book is excellent. What's the nature of
> the non-normality? Outliers? Are they symmetric? You can't really
> decide this without thinking of what the likely problems are.
>
> The inverse hyperbolic sine is an under-used transformation for
> long-tailed data with zero or negative values. It was originally part
> of the Johnson system of distributions, which are based on
> transformations of the Gaussian. It behaves like the log for large
> magnitudes and like the square root for smaller ones.
>
> Burbidge, John B., Lonnie Magee and A. Leslie Robb. 1988 "Alternative
> Transformations to Handle Extreme Values of the Dependent Variable."
> Journal of the American Statistical Association, vol. 83, 123-127.
>