[R] A modified log transformation with real finite values for negatives and zeros?

[roger koenker]

Bickel and Doksum (JASA, 1981) discuss a modified version of the Box-Cox
transformation that looks like this:

	y -> ( sgn(y)* abs(y)^lambda -1)/lambda

and in the original Box-Cox paper there was an offset parameter that 
gives
rise to some somewhat peculiar likelihood theory as in the 3-parameter
log-normal where one gets an unbounded likelihood by letting the
threshold parameter approach the first order statistic  from below, but
for which the likeihood equations seem to provide a perfectly sensible
root.


url:	www.econ.uiuc.edu/~roger        	Roger Koenker
email	rkoenker at uiuc.edu			Department of Economics
vox: 	217-333-4558				University of Illinois
fax:   	217-244-6678				Champaign, IL 61820

On Feb 2, 2005, at 1:28 PM, Spencer Graves wrote:

>      Does anyone have any ideas (or even experience) regarding a 
> modified log transformation that would assign real finite values to 
> zeros and negative numbers?  I encounter this routinely in a couple of 
> different situations:
>      * Physical measurements that are often lognormally distributed 
> except for values that are less than additive normal measurement 
> error.  I'd like to take logarithms of the clearly positive values and 
> assign some smaller finite number(s) for values less than or equal to 
> zero.  I also might like to decompose the values into mean plus 
> variance of the logs plus variance of additive normal noise.  However, 
> that would require more machinery than is appropriate for exploratory 
> data analysis.
>      * Integers most of which are plausibly Poisson counts but include 
> a few negative values.  People in manufacturing sometimes report the 
> number of defects "added" between two steps in the process, computed 
> as the difference between the number counted before and after 
> intervening steps.  These counts are occasionally negative either 
> because defects are removed in processing or because of a miscount 
> either before or after.
>      For an example, see "www.prodsyse.com/log0".  There, you can also 
> download working R code for such a transformation along with 
> PowerPoint slides documenting some of the logic behind the code.  It's 
> not included here, because it's too much for a standard R post.
>      Comments?      Thanks,
>      spencer graves
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html