Re: st: Basic regression interaction term question

[John Antonakis <John.Antonakis@unil.ch>]

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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