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
A modified log transformation with real finite values for negatives and zeros?
2 messages · Spencer Graves, 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
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