Re: st: Duan smearing for retransformation

[Partha Deb <partha.deb@hunter.cuny.edu>]

In a GLM if you are using the log link, E(y|X) = exp(X*b) where b 
denotes the vector of coefficients.  If, instead, you modeled E(ln(y)) = 
X*b, E(y|X ) would not be equal to exp(X*b), i.e., some smearing would 
be needed.

As best as I can tell -xtmixed- fits a linear model, i.e., it does not 
admit link-type transformations.  If you use -gllamm- , you are fitting 
a generalized linear model, and the equation above applies (except for 
the treatment of the random effects).  I don't know what -predict- after 
-gllamm- gets you in terms of how the random effects are treated.

Bontempo, Daniel E wrote:
> I am not sure exactly what is meant by "not needing" - does this just
> apply to predictions? The coefficients do not seem to be in the
> non-logged metric.
>
> If I use gllamm to run the same model I used in xtmixed, except specify
> a log link function, it is not clear to me what scale the estimated
> model parameters are on, or if I can transform them back to original
> metric.
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Partha Deb
> Sent: Monday, May 17, 2010 8:22 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Duan smearing for retransformation
>
> One of the advantages of using GLM with a log link vis-a-vis taking logs
>
> of y is that you do not need a retransformation.  Retransformation with 
> Duan (or any other) smearing works only under stated assumptions which 
> may or may not be met.  Duan smearing with heteroskedastic errors, as is
>
> implied by multilevel models, is far from straightforward although I 
> imagine it could be done.  You are much better off with a generalized
> model.
>
> HTH
>
> Partha
>
>
> Bontempo, Daniel E wrote:
>   
> > Hi -
> >
> > I am looking at LEVPREDICT and thinking about using the mean of
> > log-residuals (Duan smearning) to eliminate bias in
> >     
> back-transformation
>   
> > of predictions after regression with log-transformed DV.
> >
> > My 1st question is whether this correction would be needed to properly
> > back-transform coefficients after a generalized model with link
> >     
> function
>   
> > log?
> >
> > My 2nd question is would this be possible to apply after random
> > intercept model in xtmixed. If it is possible, would the smearing use
> > the level-1 residual variance, the level-2 variance, or both? I am
> > assuming ln_sd of the random components would need to be obtained.
> >
> > So does this correction seem possible after two-level ri model?
> >
> > Thanks
> >
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> >     
>
>   

--
Partha Deb
Professor of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398
http://urban.hunter.cuny.edu/~deb/

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	- Bob Marley

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