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Re: st: boostrapping from a log regression

From   Maarten buis <>
Subject   Re: st: boostrapping from a log regression
Date   Thu, 2 Sep 2010 11:09:24 +0000 (GMT)

--- On Thu, 2/9/10, wrote:
> Its the actual Beta Coefficient im having difficulty
> trying to obtain in natural units not the predicted
> values of the dependent variables (y).

That is exactly the same issue, so you should use 
> I had understood from a colleague that it is possible
> to obtain this by bootstrap. 

There are a variety of ways to "fix" the problems you
get when you log transform your dependent variable, but
why try to fix something when you can prevent it?

> I have actually tried a number of models including GLM
> models, but the AIC on the log transformed model is so
> much lower that i`d prefer to use it if it is at all
> possible.

That difference is artificial, and just due to the 
difference in scaling of your dependent variable (which
happens to be the very problem you try to solve...).  
*IC measures can help in comparing some non-nested models,
but that does not mean you can use them to compare all
models with one another. 

> Failing that, does anyone know if i would need to perform
> any similar transofrmations on beta coeficients from a GLM
> -Gamma- link(identity)-, or -Gamma- -link(log).

You should not use the -link(identity)- option here, than
you just get a variation on linear regression (key difference
is that the residual variance changes as the mean changes).
The key option for your application is the -link(log)- option.

Consider the example below:
*--------- begin example ----------
sysuse auto, clear

sum mpg, meanonly
gen c_mpg = mpg - r(mean)
gen byte baseline = 1

glm price c_mpg foreign baseline, ///
    link(log) family(gamma)       ///
	eform nocons
*---------- end example -----------
(For more on examples I sent to the Statalist see: )

The coefficient of baseline is the constant, i.e.
the price (in dollars) when both foreign and c_mpg
are zero. c_mpg is 0 when mpg is average, and foreign
has the value 0 when the car is domestic. So a domestic
car with average mpg costs about $5529,-. This price
changes by a factor 1.30 (i.e. 30%) when the car is
foreign, and changes by a factor 0.96 (i.e. -4%) for
every extra mile per gallon.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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