Re: st: RE: Yeo-Johnson Power Transformation

[Rajiv Sabherwal <sabherwal@umsl.edu>]

Kit, Nick, and others:

Thanks for your suggestions as well as patience. I am a complete  
novice with Stata (and with this arena of  statistics -- my earlier  
work has mainly been based on SEM and case studies), and please  
excuse my ignorance.

Based on how the percentages are computed [100*(x-y)/(w+x+y)], Yeo- 
Johnson transformation does seem appropriate.

I follow most of what Kit suggested. Thanks again. However, based on   
the Weisberg paper on Yeo-Johnson transformation (www.stat.umn.edu/ 
arc/yjpower.pdf), I have a different interpretation on four aspects.

1. I believe I should be using 2-`theta' instead of 2*`theta' at both  
places toward the end of the code you suggested.
2. I believe Equation 2 on page 1 of the above PDF file is the one  
being modeled. This includes two possibilities for y<0, one when  
lambda <> 2 (I believe this captured in the line two above else in  
your suggested code), and the other when lambda = 2 (which I am don't  
think is captured).
3. There should be a negative sign prior to ( ( (abs($ML_y1)+1)^(2- 
`theta')-1)/(2-`theta' )
4. In the line after else, I believe there should be a +1 within  
parentheses.

Assuming I am right on the above points, should the last block of  
code be as follows?

qui gen double `yt' = .
if `diffL'> 1e-10 {
qui replace `yt' =( ( ($ML_y1+1)^`theta'-1)/ `theta' ) if $ML_y1 >= 0
qui replace `yt' = -( ( (abs($ML_y1)+1)^(2-`theta')-1)/(2-`theta' )  
if ($ML_y1 < 0 and `diffL' <>2)
qui replace `yt' =  -ln((abs($ML_y1)+1) if ($ML_y1 < 0 and `diffL' =2)
}
else {
qui replace `yt' = ln( $ML_y1+1 )
}

Please advise.

Thanks, and best wishes,

Rajiv

On Jan 21, 2007, at 12:20 PM, Nick Cox wrote:


> Kit Baum has already replied on the assumption that
> you want to estimate the parameter in this transformation
> by maximum likelihood, in which case his advice is in
> effect change the parts of -boxcox- that do not apply
> to this transformation until they do apply.
>
> On a quite different point: I think the assumption in
> your post is dubious. Given the percent flavour, you
> may need a generalisation of the logit-and-folded-power
> family, not a generalisation of power-and-logarithm family.
> But that depends on your data generation process.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Rajiv Sabherwal
>
> > How can I perform Yeo-Johnson Power transformation in STATA? It is
> > similar to Box-Cox transformation, but can be used with negative
> > variables as well, unlike Box-Cox transformation which can only be
> > used for positive variables. Please see
> www.stat.umn.edu/arc/yjpower.pdf and
> rweb.stat.umn.edu/R/library/alr3/html/powtran.html.
> > My dependent variable is a percentage that varies from -100 to +100,
> > and hence Box-Cox transformation would be inappropriate, but Yeo-
> > Johnson Power transformation would be perfect.
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