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Descriptively, there is no difference between MR-QAP and plain vanilla OLS
regression. That is, you can interpret the interaction term as you would
in any ordinary MR problem. You can standardize the matrices, but this is
not really necessary unless the multicollinearity creates computational
problems. Indeed, it did cause problems once for me, and I was forced to
mean-center the interaction term in order to get rid of the problem for a
MR-QAP analysis. See Krackhardt and Kilduff (1999) "Whether Close or Far",
Journal of Personality and Social Psychology.
However, there is a caveat on the inference tests. David Dekker has
uncovered a problem with MRQAP under simultaneous conditions of
multicollinearity and autocorrelation, and clearly an interaction term will
create a reasonable degree of multicollinearity (a couple of us are working
with David on this problem, but David was the one who discovered it and
should get most of the credit for its resolution). It turns out that
whether MRQAP is calculated based on simply permuting Y, or based on a
partialling method (which is what I had recommended back in 1988), or based
on a semipartialling method (a close cousin to the partialling method,
suggested by David Dekker) makes a difference in such cases. The Y
permutation method, it turns out, is most susceptible to these
multicollinearity problems; both the other methods appear in our
simulations to be reasonably robust against this problem. Dekker's idea of
a semipartialling approach I think will ultimately win, as he has shown
that theoretically the semipartialling approach is invulnerable to this
problem. But, you should know that (I think, anyway) UCINET still uses the
Y permutation method in its MRQAP routines. At least it did the last time
I spoke with Steve about this issue a couple of months ago. Steve did
commit to changing this within UCINET, but you should probably pay
attention to whether the change has taken place before proceeding with the
UCINET version of MRQAP.
-David (Krackhardt, not Dekker)
PS - Please say hi to Giuseppe Soda and the OB crowd at Bocconi for me.
--On mercredi 16 avril 2003 10:42 +0100 Alessandro Usai
<[log in to unmask]> wrote:
> ***** To join INSNA, visit http://www.sfu.ca/~insna/ *****
> Dear all,
> I have a question concerning the use of interaction terms in Multiple
> Regression among matrices (in particular using the UCINET QAP procedure).
> Is it correct to proceed as in normal statistics (i.e. standardizing the
> matrices and then multiplying the main effects)? Is there any empirical
> piece that adopted this procedure? What are the potential issues linked to
> the use of interaction terms?
> I thank in advance anyone who may have ideas or experience with that
> Alessandro Usai Phd.
> Department of Organization and Information Systems
> Bocconi University
> Viale Isonzo, 23
> 20125 Milano
> tel: (direct) +39-2-184.108.40.206
> tel: (sec.) +39-2-220.127.116.11
> // // 33
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> e-mail: [log in to unmask]
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David Krackhardt, Professor of Organizations, editor of JoSS
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