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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
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 
> replace the log in such cases. (related to Nick's point(d)). 
> 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 
> btscs.ado, 
> > 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.
> > http://links.jstor.org/sici?sici=0020-8183%28200121%2955%3A2%3
> > 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.
> > http://links.jstor.org/sici?sici=0020-8183%28200121%2955%3A2%3
> C441%3ADP%3E2.0.CO%3B2-N
> 
> 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.
> 
> See also:
> ssc install transint
> h transint
> http://www.stata.com/statalist/archive/2006-11/msg00294.html
> 

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