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st: RE: transforming predictions from loglinear models

From   "Nick Cox" <>
To   <>
Subject   st: RE: transforming predictions from loglinear models
Date   Fri, 26 Aug 2005 12:14:58 +0100

An excellent solution to this has been 
available for 33 years, namely generalised
linear models with log link. So, switch to -glm-. 

glm y ln_x1 ln_x2, link(log) 

That way, you can also think about other error 
families that might be better for your problem. 

Alternatively, Duan's technique of smearing 
often works well. Rich Goldstein published 
a program some while back, and I have 
a more modern variant somewhere. 

W. Manning, who I think is a Stata user but 
possibly not a member of Statalist, has 
published lots in this territory, especially 
I think in (health) economics. 

> I want to estimate a simple log-linear OLS regression in 
> Stata and then
> use the model to generate predictions. Say the model looks like this:
> regress ln_y ln_x1 ln_x2
> where all the variables are in logs. After running the model, I'd like
> to predict values of y over different values of x1, holding 
> x2 fixed at
> the mean. The problem is that my predicted y is in log form, which I
> want to transform to y. One solution is to simply take 
> exp(prediction of
> ln_y), but this has been shown to result in a biased predictor. The
> following article discusses various techniques for dealing with this,
> focusing specifically on a Laplace conversion:
> van Garderen, Kees Jan, 2001.
> "Optimal prediction in loglinear models," Journal of Econometrics,
> Elsevier, vol. 104(1), pages 119-140
> Does anyone know if any such techniques have been implemented 
> in Stata?
> Would predictnl do the trick, as in:
> predictnl yhat = exp(_b[cons] + _b[ln_x1]*ln_x1 + _b[ln_x2]*ln_x2],
> se(yhat_se) 

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