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


From   Richard Goldstein <richgold@ix.netcom.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Correction for bias in regression estimates after log transformation
Date   Wed, 17 Dec 2008 08:59:10 -0500

I thank Nick for mentioning my old program; note however, that the program offers a choice between smearing and what I call the naive estimator (treating the result as lognormal) -- see the article for more on this

my preference these days is generally to use glm with the appropriate link (which might, or might not, be the log link)

Rich

Nick Cox wrote:
The issue as I understand it for response y arises because the mean of
log(y) differs from the log of mean(y). What you do to the predictors is
immaterial. The problem is generic to any nonlinear transformation.
I see there being two main relatively simple ways of tackling this
problem. (There are other more complicated methods; my experience, such
as it is, indicates that they don't give very different results except
when results are highly dubious anyway.) 1. Avoid it altogether by using -glm- with appropriate link. 2. Use smearing.
Richard Goldstein implemented -predlog- in 1996, which includes
smearing.
STB-29  sg48  .  Predictions in the original metric for log-transformed
models
        (help predlog if installed) . . . . . . . . . . . . . . . R.
Goldstein
        1/96    pp.27--29; STB Reprints Vol 5, pp.145--147
        calculates three different retransformations, which allow
        obtaining predictions in the original metric

Both the software and the original article are accessible to all.
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