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Re: FE: st: Interaction effects

From   Maarten buis <>
Subject   Re: FE: st: Interaction effects
Date   Tue, 15 Jun 2010 07:48:49 +0000 (GMT)

--- On Mon, 14/6/10, wrote:
> No.  The variable used to represent SIZE in the
> cross-product needs to be the same as that used
> for the lower order terms.  The cross-product is
> not an interaction until the constituent
> variables are partialled out.  So the lower
> order SIZE should be the same as that used to
> compute the cross-product. 

I agree that you (almost always) need to add some
form of main effects when including cross-product
effects. I disagree with you that they need to have
the same functional form. To me it is perfectly OK
to have a main effect in a quadratic form or spline
form and have the interaction in a linear form. So,
the fact that Lorenzo added the main effect in linear
form and the interaction in dummy form is no problem.

> Greene addresses the suggestion by Ai & Norton and, in
> contrast to Ai & Norton, would suggest yes.  

The problem with this debate is that it is often 
formulated in terms of a contrast, either one or the
other is "the best way". Truth is that non-linear
models allow you to test a variety of subtly different
hypotheses. So both are partially correct, in the sense
that if you want to test their null hypothesis their
method is the best. However, to make a statement that
one type of null-hypothesis is generically the best 
is obviously wrong, as the null-hypothesis obviously
depends on the question that one wants to answer. 

I don't think that the authors believe that one type 
of null-hypothesis is generically the best, they just
argue that in their experience one type of null-hypothsis
is most common. However, the most common type of 
null-hypothesis is likely to differ substantially across
disciplines and even sub-disciplines. Moreover, the fact
that one type of hypothesis is most common in your sub-
discipline doesn't mean that it is necessarily the best
for your problem.

So I think the way forwards in this debate is to specify
which method tests which null-hypothesis and to clarify
what the difference is between these hypotheses, rather
than to invent ever more "best way to test for 

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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