# st: RE: RE: RE: adding to X to make ln(X) nonmissing [was BTSCS and Non-linear MLE programming]

 From "Nick Cox" To Subject st: RE: RE: RE: adding to X to make ln(X) nonmissing [was BTSCS and Non-linear MLE programming] Date Fri, 2 Feb 2007 14:58:03 -0000

```Thanks for the suggestion and the reference.

My help -transint-, referred to by Austin in his email
to which I replied, which remains in the material below, also
refers to this transformation.

I agree that in general considering quite a different
transformation is part of the possibilities, but
it isn't really a solution to the specific question
I posed myself in the pseudo-FAQ I have below.

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

Benito, Andrew

> I wld suggest looking at the following reference
>
>     Burbidge, J.B., Magee, L. and Robb, L. (1988),
> `Alternative Transformations to Handle Extreme Values of the
> Dependent Variable', Journal of the American Statistical
> Association, 83, 123-7.
>
> It suggests using an Inverse hyperbolic sine function to
> The functional form, with the dampening factor set to 1, is
> sinh⁻¹(x)=ln(n+√(1+x²)).  But more generally (ie without the
> dampening factor set in that way), it involves non-linear estimation.

Nick Cox

> Let me summarise the situation as I see it. This tries a
> slightly more general pitch than the current thread.
>
> I want to work with the logarithm of a variable, but that
> variable contains zero values. What should I do?
> ---------------------------------------------------------

< snip >

Austin Nichols

> > In re: adding alpha to X to make ln(X) nonmissing Why does this
> > operation come up so often, when it is so often a bad idea?  I have
> > seen several papers this week that add some constant to X so that
> > ln(X) can be regressed on some variables, or some variable can be
> > regressed on it.  Wouldn't you be just as well off imputing
> > 2*atan(X)-2*atan(1) or somesuch?  Is there a well-known
> good reference
> > on this subject?
> >
> > Just now, when looking up the ref for an adjacent thread on
> > I ran across Oneal & Russett (2001) which acknowledges that Beck,
> > Katz, and Tucker (1998) pointed out an error, and then replies to
> > another critique with this (p.480):
> > "
> > Before taking the logarithm [of trade volume in \$millions]
> we assigned
> > a different value to the trade variable for dyads that report no
> > trade.  Some value must be imputed because the logarithm of zero is
> > undefined.  We use \$100,000 [so really it was ln(0.1)]; Green, Kim,
> > and Yoon used \$1.  It is this that accounts for most of the
> > differences between our results and theirs.
> > "
> > Oneal, John R. and Bruce Russett. 2001. Clear and Clean: The Fixed
> > Effects of the Liberal Peace. International Organization,
> Vol. 55, No.
> > 2. (Spring, 2001), pp. 469-485.
> > C469%3ACACTFE%3E2.0.CO%3B2-A
> >
> > Green, Donald P., Soo Yeon Kim, and David H. Yoon. 2001.
> "Dirty Pool."
> > International Organization, Vol. 55, No. 2. (Spring, 2001), pp.
> > 441-468.
>
> Beck, Nathaniel, Jonathan N. Katz and Richard Tucker. 1998.
> Taking Time Seriously: Time-Series-Cross-Section Analysis
> with a Binary Dependent Variable. American Journal of
> Political Science, 42:
> 1260-1288.
>
> ssc install transint
> h transint
> http://www.stata.com/statalist/archive/2006-11/msg00294.html
>

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