Re: st: Interpretation of Interaction terms in log-lin

[Maarten Buis <maartenlbuis@gmail.com>]

On Tue, May 22, 2012 at 12:24 PM, Lukas Borkowski wrote:
> Dear all,
>
> my simplified model can be written as y = b0 + b1x1 + b2x2 + b3x1_x2 with the last expression being an interaction term.
>
> However, the dependent variable is in logs and the explanatory variables are not. I now wonder whether I have to add b2 and b3 before putting them into the e-function or to exponantiate each coeffecient seperately and then do the addition?

I assume you first took the logarithm of your dependent variable and
than used that in a linear regression model (-regress-). In most cases
you would not do that. When you apply the exponential transformation
to coefficients of a linear regression with a log transformed
dependent variable you get effects in terms ratios of geometric means
rather than ratios of arithmetic ("normal") means, see: (Newson 2003).
In most cases you would want the latter and not the former.

To get effects in terms of ratios of "normal" means you need to use
the dependent variable in the original metric and use the log link
function, that is, either use -glm- with the -link(log)- vce(robust)-
options or use -poisson- with the -vce(robust)- option. See:
<http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/>

Consider the example below:

*------------------ begin example ---------------------
sysuse nlsw88, clear
gen black = race==2 if race <= 2
gen c_grade = grade - 12
glm wage i.black##c.c_grade c.ttl_exp##c.ttl_exp , ///
    link(log) vce(robust) eform
*------------------- end example ----------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

We can interpret that as follows:
A white individual with 12 years of education (= high school) and 0
experience (= just entering the labor market) can expect a wage of 3.5
dollars an hour (the exponentiated constant).

A black individual with 12 years of education can expect (1-.84)*100%=
-16% less wage than white individuals with 12 years of education.

A white individual can expect a 7% increase in wage for every year
extra education.

This effect of education is 4% larger for black individuals. So the
effect of education for black individuals is 1.04*1.07=1.11, i.e. a
year increase in education leads to an 11% increase in wage for black
people. You can also compute this by adding the raw coefficients and
exponentiating that sum, which you can do by typing:

lincom c_grade + 1.black#c.c_grade, eform

Hope this helps,
Maarten

Roger Newson (2003) Stata tip 1: The eform() option of regress. The
Stata Journal, 3(4):445.
<http://www.stata-journal.com/article.html?article=st0054>

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


http://www.maartenbuis.nl
--------------------------
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