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# RE: st: Duan smearing for retransformation

 From "Bontempo, Daniel E" To Subject RE: st: Duan smearing for retransformation Date Tue, 18 May 2010 11:57:21 -0500

```Thanks for the followup.

So if I understand, the smearing is needed when ln(E(y|x)) because
simply taking exp(x*b) is insufficient. BUT in the GLM I can simply take
exp(x*B).

I agree the random coefficients are less clear, but I could live with
that.

Without log transform or link (i.e., modeling the skewed distribution)
xtmixed and gllamm are giving somewhat different results for the fixed
effects, and markedly different results for the random effects. This is
why I decided to compare gllamm with link(log) to xtmixed using
log-transformed DV with smearing correction.

I think I will gather my thoughts and see if I have a questions about
why xtmixed and gllamm results differ so much with skewed data.

Thanks again,
-Daniel

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Partha Deb
Sent: Tuesday, May 18, 2010 10:41 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Duan smearing for retransformation

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
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/

Emancipate yourselves from mental slavery
None but ourselves can free our minds.
- Bob Marley

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```