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Re: st: Interaction effect or running seperate models

From   Richard Williams <[email protected]>
To   [email protected], [email protected]
Subject   Re: st: Interaction effect or running seperate models
Date   Fri, 28 Sep 2007 01:27:02 -0500

At 12:07 AM 9/28/2007, Quang Nguyen wrote:
Dear Clive et al,

Thanks! Yes, I certainly understand that. However, it is not my
question. I am actually interested in the situation in which the
effect is significant when we run seperate estimations, whereas the
interaction term in the signle equation is not significant. Perhaps,
an example will clarify this.

Suppose: Y= a0+ a1*x + u
Let Z is  binary variable. Now, we can run two sperate OLS for Z=1 and
Z=0.Suppose that a1 is significant for the OLS for Z=1

Alternatively, we have a single equation with interaction term:

Y= m0 + m1*x + m2*z*x + v
You also need the main effect of z in the equation:

Y = m0 + m1*x + m2*z + m3*z*x + v

m0 will be the intercept for group 0, m2 + m0 = intercept for group 1.

My question is how we can explain the case in which m2 is
insignificant? Can we still say x has signficant effect on Y only
given Z=1 as implied by the seperate OLS? If yes then is it better to
run seperate OLS  than single OLS w/interaction term given that the
former can identify which sample of population impose a significant
effect of x on y?
You have to be careful about comparing significance of coefficients across groups. A coefficient might be significant in one group but not the other mostly because one has a larger sample size than the other. You shouldn't just say that the effect is significant in one group but not the other; a formal test of the difference across groups should be done.

Richard Williams, Notre Dame Dept of Sociology
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