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Re: st: Basic regression interaction term question


From   "Michael I. Lichter" <mlichter@buffalo.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Basic regression interaction term question
Date   Fri, 10 Oct 2008 15:03:23 -0400

Thanks Nick & John! I'll check out those references.

Michael

Nick Cox wrote:
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
n.j.cox@durham.ac.uk
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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--
Michael I. Lichter, Ph.D.
Research Assistant Professor & NRSA Fellow
UB Department of Family Medicine / Primary Care Research Institute
UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
Office: CC 125 / Phone: 716-898-4751 / E-Mail: mlichter@buffalo.edu
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