# RE: st: Treat zeros in logarithms

 From "Mentzakis, Emmanouil" <[email protected]> To "'[email protected]'" <[email protected]> Subject RE: st: Treat zeros in logarithms Date Tue, 26 Aug 2008 19:49:19 +0100

```Dear Sam,

Quite often such questions concern items that you need to pay for (e.g. health or public goods) and even more often they are exploratory and rhetorical. However, theoretically, WTP could be negative. Testing sensitivity, log-normal distributions are often compared to the normal ones.

Cheers
Manos

-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of SamL
Sent: 26 August 2008 18:48
To: '[email protected]'
Cc: [email protected]
Subject: RE: st: Treat zeros in logarithms

Interesting.  I always find it funny when someone says "How much are you willing to pay for . . .?"  My answer is always, "Less than zero; I want to be paid to take this item from you."  I just think the salesperson should have a sense of the value of what they're selling and, if not, they should let me set the price and I'll set it in the negative.  So, theoretically, why can't willingness to pay be negative?

Of course, this only exacerbates the logarithm problem.  JOOQ (Just out of curiosity), why are you taking logarithms?

Sam

On Tue, 26 Aug 2008, Mentzakis, Emmanouil wrote:

>
> 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: [email protected]
> [mailto:[email protected]] On Behalf Of Nick Cox
> Sent: 26 August 2008 18:23
> To: [email protected]
> 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 <[email protected]>:
> 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 <[email protected]> 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
>>
>> 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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