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Re: st: transformation of continuos variable

From   Maarten buis <>
Subject   Re: st: transformation of continuos variable
Date   Wed, 14 Apr 2010 07:54:03 +0000 (GMT)

--- On Tue, 13/4/10, riyadh shamsan wrote:
> I am using STATA 10. I did a linear regression on log transformed
> variable. To present the result i anti-logged the results but now the
> confidence interval is a bit confusing as it doesn't cross 0

By anti-logging your predictions you did not create predictions on
the original unit but conditional geometric means, which is probably
not what you want. The reason is that you moddeled how the 
log-transformed dependent variable changes when your independent
variables change, while you probably wanted to model how the dependent
variable changes (in a possible non-linear way) when the independent 
variables change. There are ways of correcting the predictions, but 
the better way is to avoid the problem by estimating the right model
from the start by using -glm- in combination with the -link(log)- 
option. See for example:

Nicholas J. Cox, Jeff Warburton, Alona Armstrong, Victoria J. Holliday 
(2007) "Fitting concentration and load rating curves with generalized
linear models" Earth Surface Processes and Landforms, 33(1):25--39.

So to give a concrete example. In the example below you can see that
someone who is white, with no education, no experience, and without
union membership can expect an hourly wage of 1.66 dollars (the 
baseline). Union membership lead to an increase of wage by a factor 
of 1.10 (that is, 10%), a year extra education leads to an increase 
in wage by a factor of 1.08 (i.e. 8%) and begin black leads to a 
change in wage by a factor of .91 (i.e. -9%).

In order to create predictions in Stata 10 while keeping some of the
covariates constant, it is convenient to use the -adjust- command. So 
in the example below the graph shows how the expected wage for white 
union members with average work experience, change over education.

*-------------- begin example ---------------
sysuse nlsw88, clear
gen byte baseline = 1
gen byte black = race == 2 if race != .
glm wage grade union ttl_exp black baseline, ///
    link(log) eform nocons

adjust union=1 black=0 ttl_exp,      ///
       by(grade) ci exp replace

twoway rarea lb ub grade ||          ///
       line exp grade, legend(off)   ///
       ytitle(predicted hourly wage)

*------------- end example -------------------
(For more on examples I sent to the Statalist see: )

Hope this helps,

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


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