Re: st: Interaction effect or running seperate models

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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.


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Richard Williams, Notre Dame Dept of Sociology
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