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

[David Hoaglin <dchoaglin@gmail.com>]

Dear Steve,

I'm inclined to think of your data as longitudinal (more below).

If you want to transform the data, you could consider applying a
logarithmic transformation (I would use logs base 10) to the wealth at
each time point.  (If you pursue the alternative of a GLM, a log link
seems a likely possibility.)  Negative differences on the log scale
translate readily into percentage decreases.  It would not surprise me
if percentage increases and decreases are of at least as much interest
as dollar differences.

With a log link in a GLM for a "continuous" outcome variable, a common
choice of distribution for the random component is the gamma.  Like
other assumptions, that should be checked, to see whether it
reasonably approximates the behavior of the data.

In a longitudinal analysis it would be appropriate to consider a
random effect for CEO, to account for variation among CEOs and model
(in one way) the correlation between wealth at the end of the year and
wealth at the beginning of the year.

Regards,

David Hoaglin

On Mon, Nov 18, 2013 at 9:00 PM, Steven Delbright
<steven.delbright@gmail.com> wrote:
> Dear David:
>
> Thanks for your response:
>
> The source for negative CEO wealth are decreases in stock price. I
> find that the changes in CEO wealth (stock and option portfolio)
> outweigh annual flow compensation considerably. You are also
> absolutely correct in stating that I take a difference between two
> positive values (equity portfolio at the end minus the beginning of
> the year).
>
> I was curious about how you would transform the input variables
> without creating a negative value?
>
> Thanks again!
> Steve
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