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RE: st: Treat zeros in logarithms


From   "Mentzakis, Emmanouil" <e.mentzakis@abdn.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Treat zeros in logarithms
Date   Tue, 26 Aug 2008 18:40:04 +0100

Dear Maarten, Austin and Nick

Thank you for your comments. I am sorry if I made it sound as if Nick was proposing it as an acceptable strategy.

I am aware of the possibility of using open-ended left bound.

However, Maarten, why do you say that it is exactly what I want? What happens in cases where the variable shouldn't take negative values?

To give more information, my variable is willingness-to-pay and so I would expect it to be zero or positive. However, as the first interval has to start at zero the problem with the logarithm appears. If the intervals were very very thin all individuals would be likely to pay a positive amount.

For this reason I thought that using the half of the smallest non-zero measurement would be "acceptable".

Thank you again

Regards
Manos




-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: 26 August 2008 18:23
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Treat zeros in logarithms

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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