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Re: st: Basic regression interaction term question


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Basic regression interaction term question
Date   Sat, 11 Oct 2008 11:06:35 +0200

Hi Clive:

Right. Although I did not allude to the fact that one must include the first order terms in the regression, it is imperative that they be included so that the interaction term is correctly scaled--i.e., one must first partial out the main and lower level interaction effects from the multiplicative term in the regression equation. This is another debate, and one with which I agree with you. As concerning the case of Michael, I think that what is important is the significance of the interaction term and not the overall F-test, as discussed in my previous post.

As an aside, in the management literature there have been many cases of researchers testing Y=b0 +b1a.b.c (without having included the main effects of a, b, and c, as well as their two-way interactions)--case in point the "motivating potential score" of the job characteristics model. In a paper we recently published, we stated that not include lower-order terms would result in rubbish--Evans (1991: 7) went as far as to state that anything short of this procedure [not including lower-order terms] would yield results that would be "profoundly and fatally flawed," and that the extant literature was "cluttered with suspect results that continue to be cited approvingly by subsequent authors and by studies that continue to use the suspect methods because 'they have always been done that way'. . .pleas to conduct multiplicative tests correctly have been ignored by the reviewers and editors of the very journals that published the original critiques of the inappropriate techniques." (Evans, 1991: 13).

Best,
J.

Evans, M. G. 1991. The problem of analyzing multiplicative composites. */American Psychologist/*, 46: 6-15.

____________________________________________________

Prof. John Antonakis
Associate Dean Faculty of Business and Economics
University of Lausanne
Internef #618
CH-1015 Lausanne-Dorigny
Switzerland

Tel ++41 (0)21 692-3438
Fax ++41 (0)21 692-3305

http://www.hec.unil.ch/people/jantonakis&cl=en
____________________________________________________



Clive Nicholas wrote:
Michael I. Lichter wrote:

This is a pretty basic question, but I haven't been able to find any
examples in the lit with this particular configuration ...

Suppose you regress Y on A and B, and you expect an interaction between A
and B.

In the regression Y = A + B, the coefficient for B is not significant, but
you have reason to think that it will be significant once you introduce the
interaction term.

However, in the regression Y = A + B + AB, the coefficient for B remains
non-significant even though the coefficient for AB is significant. Yet,
"test A B AB" is significant.

Is it reasonable to treat this as a significant interaction?

What if AB is not significant either but "test A B AB" is still significant?

Woe betide anyone who dismisses any of Nick's flags on this list (!),
but I'm firmly with John on this one. As far as 'experts' working in
the fields of political science and political methodology are
concerned, this debate is all over bar the shouting. Including
first-order terms in an interaction model is no longer a nice-looking
optional extra.

What's important to remember here is that you only include the
first-order terms because:

(1) their exclusion would assume that they equal 0: which is almost
never the case;

and

(2) it allows you to get as precise a parameter estimate as possible
on the interaction term.

Braumoller (2004) - a member of this list - and Brambor et al (2006)
make these points and explain in detail what they consider to be good
practice in this area, at least from a social science perspective.

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