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Re: st: Correction for bias in regression estimates after log transformation


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Correction for bias in regression estimates after log transformation
Date   Wed, 17 Dec 2008 09:49:01 +0000 (GMT)

--- "Loncar, Dejan" <LoncarD@unaids.org> wrote:
> I have transformed the variables using log function before
> regression.
> 
> Do you know by any chance which function in Stata or some ado file
> can perform antilog transformation after regression with correction
> for bias in regression estimates? 

Bias means nothing else than that your estimates don't mean what you
think they mean. So there are two ways of addressing bias: Either you
change interpretation of the results so that the interpretation
corresponds to the estimate, or you change your estimate so that it
measures what you think it does. Another consequence of this is that
there is no such thing as a biased estimate perse: you always need to
specify what the estimate is a biased estimate of. Trivially all
estimates are biased estimates of most concepts (e.g. the annual tea
consumption of Burundi is a biased estimate of the number of ants per
square inch in Amsterdam), and at the same time all estimates are
unbiased estimates of the thing that they measure (but the thing they
measure may not be of interest).

The distinction between changing the interpretation and changing the
estimate is nicely illustrated by looking at a log transformed
dependent variable. If you fist transform the dependent variable and
than perform a regular regression you can interpret the exponentiated
coefficients as ratios of geometric means, but not as ratios of
arithmatic means. You can get estimates in terms of ratios of
arithmatic means when you use -glm- on the untransformed dependent
variable with -link(log)- option. So if you are interested in the
effect on the geometric mean, then -glm- will provide you with biased
estimates. You can solve this either by changing your interpretation of
the results to the effect in terms of the arithmatic mean or by
estimating your model with -regress-. 

I have discussed a detailed example of this issue here:
http://www.stata.com/statalist/archive/2008-11/msg00137.html

Also see:
Roger Newson (2003) Stata tip 1: The eform() option of regress. The
Stata Journal 3(4): 445.
http://stata-journal.com/article.html?article=st0054

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


      
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