First flag: This is a controversial area. Experts disagree.
There is a brief but penetrating discussion of this issue within
McCullagh, P. and Nelder, J.A. 1989. Generalised linear models. Chapman
and Hall.
Search also for Nelder's writings on what is called the heredity
principle.
Nick
[email protected]
John Antonakis
Yes. What's important is the coefficient of the AB term. The test A B AB
is simply the F-test that the coefficients are simultaneously different
from zero. If you care about interaction, AB is what is important,
regardless of the significance of B or A or A B or A B AB..
Here is an interesting paper about this question: Bedeian, A. G., and
Mossholder, K. W. Simple Question, Not so Simple Answer: Interpreting
Interaction Terms in Moderated Multiple Regression. Journal of
Management, 1994, 20, 159-165 (get it here:
http://www.bus.lsu.edu/management/faculty/abedeian/articles/SimpleQues-J
OM1994.pdf
).
Michael I. Lichter wrote:
> 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?
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