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Re: st: Duan smearing for retransformation

From   Partha Deb <>
Subject   Re: st: Duan smearing for retransformation
Date   Tue, 18 May 2010 11:41:12 -0400

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

-----Original Message-----
[] On Behalf Of Partha Deb
Sent: Monday, May 17, 2010 8:22 PM
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



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
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

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?


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Partha Deb
Professor of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398

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