Hi everyone!
I think you have pretty much addressed the issue already, but here is
another tip:
See this article for a discussion on significance testing using
interaction terms.
Braumoeller, Bear F. 2004. Hypothesis Testing and Multiplicative
Interaction Terms. International Organization 58 (Fall):807-820.
What I find really interesting is that when testing an interaction,
the relationship may only be significant over a certain range of one
of the variables involved. Thus, just as the impact of one variable
varies across the values of the other variable involved in the
interaction, sometimes this impact may not be different from zero!
Johanna
..............................................................
Johanna Söderström, PhD candidate
Department of Government
Uppsala University
Box 514
751 20 Uppsala
SWEDEN
Office: Teatrum Economicum, Gamla Torget 2 (A410)
+46-(0)18-471 34 50 (work)
+46-(0)73-05 05 545 (cell)
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Date sent: Mon, 28 Jul 2008 22:35:00 -0400
Send reply to: Political Methodology Society
<[log in to unmask]>
From: William Clark <[log in to unmask]>
Subject: Re: [POLMETH] interactions and analyses for subsets
of the sample
To: [log in to unmask]
> Carlos,
>
> I think it depends on what you mean by "the interaction was not
> significant."
>
> if I understand you correctly you ran something like:
>
> y = b0 +b1 Trade + b2 LateInd + b3 Trade * LateInde + a bunch of
> other stuff.
>
> if by "the interaction was not significant" you mean you can't
> reject
> b3 = 0 then there is very little tension between that statement
> and
> the statement "it turns out trade IS significant in the set of
> late
> industrializers"
>
> Given the dichotomous modifying variable, the coefficient on the
> interaction term is a test of the the hypothesis that the effect of
> trade on whatever y is different for lateindustrializers than for
> early industrializers. That's an interesting question, but it is
> quite different than a test of the hypothesis that trade has a non
> zero effect on whatever y is in late industrializing countries
> (which
> is what your split sample test is telling you).
>
> There a number of logically possible patterns of coefficients in the
> interactive model consistent with
>
> a) "trade has non zero effect in late industrializers"
> b) "trade's effect in late industrializers is not significantly
> different that its effect in early industrializers.
>
> (I don't know what y is, but lets assume you're finding a positive
> and
> significant coefficient on trade in the late industrializers sub
> sample.
>
> You might find b1> 0 and significant and b3 =0. this might
> suggest
> that trade has a positive effect in both early and late
> industrializers, but to be sure about the later, you need to
> calculate
> b1+b3 and compare it with its standard error.
>
> you can get appropriate standard error from matt golder's homepage
> on
> interaction effects (http://homepages.nyu.edu/~mrg217/
> interaction.html) or, you can type
>
> "lincom trade+trade*Lateinde" into stata after estimating your model
> (where "trade*Lateinde" is whatever you called your interaction
> term)
> and it will produce the coefficient for b1, its standard error, t
> test, confidence interval.
>
> Another possibility is that you find b1>0 and not significant, b3> 0
> and not significant. Are these null results? again, depends on
> what your hypothesis is.
>
> If your hypothesis is that trade has an effect on y in late
> industrializers, but not in early industrializers, then your finding
> that trade is significant in the late industrializer sub sample
> suggests you may be right. There is, not, however, any way to
> tell
> if there is any tension between such a result and the interactive
> model until you calculate b1+b3 and compare it to its standard error
> (see above). My guess is that you'll find, through the use of
> lincom, that b1+b3 >0 and is significant.
>
> these results would suggest that the effect of trade on y is
> positive
> and significant for late industrializers, is positive and
> insignificant for early industrializers, but is not sufficiently
> different in late and early industrializers to be statistically
> distinguishable. (for example, you might have a coefficient of 1.5
> for early; and 2.25 for late with the later significantly different
> from zero, but not significantly different from 1.5)
>
> If b1+b3=0 then the puzzle behind your question is worth scratching
> your head about and you should see Rob Franzese's answer. (I'm also
> not sure what you mean by the difference in N's ... that should
> effect standard errors but not coefficients if you have say N1
> observations in the early ind, N2 observations in lateinds and
> N3=N2+N1 in the pooled interactive model ...but check to make sure
> that's true, its possible that the way you handle missing data when
> calculating the interaction term or something means that N3=N2+N1 -
> in
> other words the "sub sample" you're thinking about the pooled test,
> isn't the same sub-sample that your looking at in the split sample
> test).
>
> The bottom line, however, is that when you have a dichotomous
> modifying variable, the statistical significant of the coefficient
> on
> the interaction term is telling you something about the difference
> between the slopes between in the two groups. That's distinct from
> to
> the question of whether either of those slopes is different from
> zero.
> (which is what the split sample tests or an examination of b1 or
> b1+b3
> in the above model will tell you)
>
> Hope this helps,
>
> Bill Clark
>
> On Jul 28, 2008, at 6:03 PM, Carlos Rodriguez wrote:
>
> > Dear POLMETH list,
> >
> > I am working with TSCS data and would appreciate some advice on
> this
> > issue.
> > I have run some regressions with an interaction between trade and
> a
> > dummy for late industrializers. The interaction was not
> significant.
> > However, I reran the analysis dividing my dataset into two
> groups:
> > early industrializers and late industrialzers. It turns out
> that
> > trade iIS significant in the set of late industrializers. Why
> would
> > the interaction between trade and late industrializers in the
> whole
> > sample fail to achieve significance whereas trade comes up as
> highly
> > significant when the regression is run separtely on the group of
> > countries that are late indutrialers? Can the difference be put
> down
> > to the dissimialr Ns? Moreover, which result shall I "believe"?
> >
> > thanks for your advice.
> > Carlos Rodriguez
> >
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