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# AW: st: Interaction of dummy variable with log-transformed variable

 From P K To statalist@hsphsun2.harvard.edu Subject AW: st: Interaction of dummy variable with log-transformed variable Date Fri, 27 Aug 2010 08:01:30 +0000 (GMT)

```Dear Clive,
Thank you very much for your response and the clarifications. I forgot to
mention that I included the dummy in my model, i.e. I have tested the model

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

Y is not log-transformed.

Comparing the model without the interaction (i.e. Y = a + b_IV + c_D  + e) to
the model with interaction (Y = a + b_IV + c_D + d_IV*D + e) yields the
following results for the coefficients:

b changes from 5 to -6 (not significant in both models)
c changes from 12 (significant) to -12 (not significant)
interaction coefficient for model with interaction is 42 and significant.

I am not sure on the following issues:
(1) Does the significant and positive interaction term imply that the effect of
the logged IV on Y is positive and significant when the dummy is 1? This
somewhat

the effect of your logged IV on Y turns negative when the dummy shifts to 1."

(2) If I want to test whether the logged IV moderates the relationship between
the dummy and Y, is the following interpretation right?
- dummy c has positive and significant relation with Y
- logged IV positively moderates the relationship between dummy and Y
(interaction term positive and significant)?
(3) What are possible explanations for the dummy turning negative and
insignificant when the interaction with logged IV is entered? May it be that the
interaction

between dummy and logged IV has relationship with Y, rather than dummy
only?
(4) Is there any way to give an idea how large the moderation effect of dummy
and logged IV are on Y? (i.e. total effect = c+d  or  c+b+d?)

I appreciate your help on this.

Thanks,
Susan

----- Ursprüngliche Mail ----
An: statalist@hsphsun2.harvard.edu
Gesendet: Freitag, den 27. August 2010, 0:25:00 Uhr
Betreff: Re: st: Interaction of dummy variable with log-transformed variable

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

"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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