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Re: st: Interaction of dummy variable with log-transformed variable


From   Clive Nicholas <clivelists@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interaction of dummy variable with log-transformed variable
Date   Fri, 27 Aug 2010 08:25:00 +0100

Susan 'P K' wrote:

> I have trouble interpreting the following results and would appreciate your
> help:
>
> I ran an OLS regression with an interaction between a dummy variable and a
> log-transformed variable on a continuous dependent variable.
>
> i.e.,
>
> DV = a + b*log-transformed IV + c*log-transformed variable*dummy variable
>
> The coefficient of the interaction term on the dependent variable (DV) is 42.00,
> the coefficient for the log-transformed variable is -6.00.
>
> What is the the combined weighting factor on the DV?
> - Interpretation of the log-transformed variable´s coefficient: One percent
> increase in log-transformed variable increases DV by (-6/100) units.
> - How can I interpret the coefficient of the interaction term of the
> log-transformed variable and the dummy?

Several points:

(1) You need to add the dummy variable in your model in order to
obtain a finer estimate of your interaction term, so that you have

Y = a + b_IV + c_D + d_IV*D + e

(2) Once done, the easiest interpretation of _d_ is that the effect of
your logged IV on Y turns negative when the dummy shifts to 1. If _d_
attains significance, it means that the effect of your logged IV on Y
varies by the values of your dummy variable;

(3) You don't mention if Y is also logged. If it is, you might be
better served fitting this model using -glm-.

-- 
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]

"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson.

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