Re: FE: st: Interaction effects

[Maarten buis <maartenbuis@yahoo.co.uk>]

--- On Mon, 14/6/10, frone@ria.buffalo.edu 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 
interaction".

Hope this helps,
Maarten

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

http://www.maartenbuis.nl
--------------------------


      

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