st: RE: lnskew question

 From "Nick Cox" To Subject st: RE: lnskew question Date Mon, 9 Dec 2002 09:56:14 -0000

```Robert Saunders
>
> I've been tinkering with log-transforming an outcome variable for a
> regression, but I thought lnskew0 might be a good trick
> (and it was doing
> better than ln()).  However, I wonder how I could convert
> the estimates
> back to the natural units.  For example, I've seen the
> smearing technique
> for converting regression estimates scaled in ln(dollars)
> back to dollars,
> but I can't imagine what's involved in getting back from
> whatever it is
> lnskew0 creates.  Then I thought, somebody on STATAlist might
> know.  [Couldn't find anything in the list archives or manual.]

Without very much context, it is difficult to advise, but there
are issues here on various levels.

1. On a purely algebraic level, the back transformation corresponding
to t = ln(y - k) is exp(t) + k. Note that the constant k is left
behind by -lnskew0- as r(gamma).

2. Removal of bias produced by transformation is not quite so
straightforward. In the case of smearing, for example, Duan's
original paper makes clear that the smearing idea leads to a
very simple recipe for simple log transformation but typically
a messy recipe for other transformations. See

Duan, N. 1983. Smearing estimate: a nonparametric retransformation
method.  Journal, American Statistical Association 78: 605-610.

I'm aware of two Stata programs for smearing, Richard Goldstein's
-predlog- (STB-29) and my own -smear- (unpublished), but both
concentrate entirely on log transformation (and to that
extent the name -smear- of mine is a misnomer). To do smearing
as an antidote to ln(y - k), you would need to write your own
code, I believe.

3. ln(y - k) will be less skew than ln(y) in almost all cases
but I wish you luck in finding a systematic,
scientific interpretation of k. Whenever, as here, there is concern
for getting predictions in the original metric, generalised
linear models offer, in my view, a far superior approach.

Nick
n.j.cox@durham.ac.uk

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