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RE: st: Treat zeros in logarithms


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Treat zeros in logarithms
Date   Tue, 26 Aug 2008 18:23:16 +0100

I concur with the spirit of Austin's posting. That is, although
Emmanouil did not attribute the words "acceptable strategy" to me, I
would not single out the trick mentioned in that way.

The first issue seems to be: Are the observed zeros 

(a) sampling or observed or non-detects, i.e. to the best of your
knowledge or belief they really are, or should be, positive 

Or 

(b) structural or essential only, i.e. they really are, or should be,
zero. 

(Every field seems to have its own jargon, but the same distinction
recurs.) 

If a researcher doesn't know it is difficult to advise. If a researcher
does know, it is still difficult to advise, but the desirability of
various strategies or tactics should surely vary according to whether
(a) or (b) holds. 

I find the implication that there must be a trick that "solves" this
problem at odds with the variety of situations in which it occurs. 

Nick 

Austin Nichols

Emmanouil <e.mentzakis@abdn.ac.uk>:
I looked in vain for the claim about your proposed approach being an
acceptable strategy. I believe you are referring to point 4(c) of
Nick's post, but the quoted sentence in situ reads
"But the appeal here is at best one of simplicity or symmetry,
does not apply beyond 2, and does not reflect a statistical argument.
More
generally, the idea is to replace the zeros by half the
smallest non-zero measurement, given some convention about
resolution of measurement (e.g. to a fixed number of decimal
places using agreed units)."
and says nothing about replacing zeros by half the smallest non-zero
measurement being an acceptable practice for interval regression.

I doubt you will find a published reference claiming it is okay, since
any such claim is easy to refute (e.g. via simulation).  But ln(0) can
be specified as a lower bound in this case... read -help intreg- for
specifying an interval  (-inf,b.

On Tue, Aug 26, 2008 at 12:57 PM, Mentzakis, Emmanouil
<e.mentzakis@abdn.ac.uk> wrote:

> I have an interval regression model and for some cases the lower bound
is zero. As I want to take the logarithm of the bounds I run into
problems.
>
> The same issue has come up previously in the list and below is the
link of a detailed answer by Nick Cox.
>
> http://www.stata.com/statalist/archive/2007-02/msg00046.html
>
> As Nick points out an acceptable strategy is "...to replace the zeros
by half the smallest non-zero measurement..."
>
> I was wondering if anyone could provide any references of published
papers that have employed such approach.

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